Quantum Physics Paper Analysis

The overhead exponent -- characterizing the scaling of the number of noisy magic states with respect to the target distillation error -- has been a central quantity to benchmark magic state distillation protocols. On the other hand, a related but less investigated quantity motivated by an information-theoretic viewpoint is the asymptotic distillation rate, the largest ratio of output to input magic states such that error vanishes asymptotically. These two quantities are tightly related in the specific case -- the overhead exponent is zero if and only if the asymptotic distillation rate is linear. However, their relationship in other regimes has been unclear. Here, we show that their quantitative relation is generally not robust, by presenting a family of magic state distillation protocols with an overhead exponent not close to zero -- in fact, larger than one -- that still achieves the asymptotic rate arbitrarily close to the linear rate. This implies that the distillation rate is not constrained by the overhead exponent within the sublinear rate regime. Notably, our protocol is based on error checking by measurements of logical Clifford operators, which underlies the recent magic state cultivation protocol, suggesting the potential of this mechanism for asymptotic magic state distillation.

Strongly simulating a quantum circuit, that is, computing an output amplitude, amounts to summing the circuit's Feynman paths, a weighted count over assignments to the Boolean ``path'' variables. The circuit's gates induce correlations among these variables, forming a graph whose structure determines the hardness of the simulation task. This sum-of-powers viewpoint underlies recent simulators built on knowledge-representation tools from artificial intelligence, namely binary decision diagrams and weighted model counting. We show that the structural quantity most accurately governing the difficulty is the rank-width of the path-variable graph, and we give an algorithm that evaluates the amplitude in time that is exponential only in this rank-width and polynomial in the circuit size. Rank-width can be far smaller than the widths that control competing methods: as corollaries, our algorithm reproduces a recent decision-diagram simulation breakthrough as a special case and matches the Markov--Shi tensor-network contraction bound. To complement this, we exhibit circuit families on which our algorithm provably beats both competing methods. The new method applies to every circuit built from Hadamard and diagonal gates, in particular to circuits over Clifford+T. In practical terms, general-purpose decision-diagram and model-counting tools can serve as the workhorse, with our specialized algorithm dispatched to exploit a small rank-width of the associated graph when it is present.

QEM is widely regarded as a plausible bridge from NISQ devices to FTQC. Yet the empirical studies used to assess the effectiveness of QEM techniques on concrete problems have received comparatively little scrutiny with respect to the validity of their conclusions. We systematically review 81 recent QEM papers using an eight-criterion framework covering statistical rigour, reproducibility, and reporting quality. Among the applicable papers, only 15 (25%) use inferential methods, while 25 (42%) report uncertainty only descriptively, without testing whether the claimed effects are statistically supported. To demonstrate the consequences of these omissions, we use ZNE as a representative and widely used case study and identify two compounding sources of artefacts in current QEM benchmarks. First, we observe parameter sensitivity: in a 132-configuration sweep, implicitly assumed choices such as scale factors, extrapolation method, and hardware calibration are not merely incidental but active, with variations changing conclusions from statistically significant improvement to statistically significant degradation. Second, we identify a drift-induced effectiveness illusion: in a 72-hour longitudinal study on real hardware, temporal drift alone can make the same ZNE configuration exhibit an effect size more than three times as large, depending solely on when it is executed, and also drastically reduces the effective number of independent observations. These findings do not imply that QEM methods are intrinsically unsound; rather, they show that current evaluation practice can make mitigation performance appear more robust than the evidence warrants. We therefore propose minimum reporting standards for QEM evaluations, including explicit parameter documentation, robustness checks, longitudinal drift assessment, and inferential statistical testing with effect-size reporting.

We study a class of quantum error-correcting codes through the geometry of complex abelian varieties. These codes, introduced by Gottesman--Kitaev--Preskill, are built from symplectically integral lattices and therefore naturally define polarized complex abelian varieties. We give a precise mathematical formulation of this relationship and extend it to a dictionary between the main structures of GKP code theory and classical objects in the theory of abelian varieties. For instance, under this dictionary, the finite-dimensional code space becomes the space of theta functions $H^0(X, L)$, logical Pauli gates arise from the theta group, passive logical Clifford gates correspond to automorphisms of the polarized abelian variety, and concatenation with stabilizer codes corresponds to isogeny. We also prove several key results that give precise mathematical formulations of statements about these codes that often appear in heuristic form in the physics literature. In particular, we prove that the encoding is asymptotically isometric, that every logical Clifford gate is realized by a Gaussian unitary, and that, for noise of small variance, the failure probability is governed to first order by the shortest nontrivial displacement in the kernel of the polarization isogeny, a systolic invariant of the underlying polarization. This leads naturally to optimization problems on the moduli space of polarized abelian varieties.

Distinct Clifford orbits of magic states can exhibit different stabilizer ranks at small tensor powers. We establish this for qutrits, where the single-qutrit Clifford group has four inequivalent orbits of magic states: Strange, Norrell, Hadamard-eigenstate, and the qutrit T-state, but a nontrivial upper bound on the asymptotic exponent had been pinned down for only the qutrit T-state. For the other three orbits we give explicit stabilizer decompositions, yielding upper bounds on the per-copy asymptotic stabilizer-rank exponent: $γ_S \le \log_3(2)/2 \approx 0.316$ for the Strange state, and $γ_{H_3}, γ_N \le \log_3(4)/3 \approx 0.421$ for the Hadamard-eigenstate and Norrell orbits, all strictly below the prior $γ_{T_3} \le 1/2$ baseline. We also prove the first nontrivial $Ω(m / \log m)$ asymptotic lower bounds for the Hadamard-eigenstate and Norrell orbits, and exhibit two-qutrit Clifford circuits that convert two copies of these states into an injectable phase state with constant success probability, enabling constant-overhead injection of one non-Clifford diagonal gate per orbit. In the case of qubits, we give a closed-form decomposition of the qubit T-type orbit at four copies matching the existing $γ_T \le \log_2(3)/4 \approx 0.396$ exponent via a direct algebraic identity rather than an entangled cat-state construction. An open-source library stabrank accompanies the paper, with Lean 4 proof formalizations of all the decompositions.

We construct a detailed microscopic noise model for multi-qubit (MQ) gate operations in the context of trapped ion architecture with all-to-all connectivity. We find that phonon heating and motional dephasing are well captured by effective single- and two-qubit error channels that can, in principle, act between arbitrary pairs of qubits. Nevertheless, the median magnitude of two-qubit errors between uncoupled qubits is substantially smaller than that of errors between gate-coupled qubits. Errors associated with photon scattering are shown to solely propagate to qubits participating in gate operations. Lastly, we combine all noise sources, assigned with experimentally relevant parameters, and explore the scalability of a quantum error correction (QEC) scheme based on the rotated surface code, as a function of error rates and code size. Our analysis bridges device-level physics and QEC performance for MQ gates in trapped-ion architectures.

We introduce a low-overhead technique for quantum error mitigation based on post-selection using auxiliary qubit measurements. The method exploits the structural property that, in an error-free computation, auxiliary qubits are often expected to return to the zero state after use. By selectively measuring these qubits at carefully chosen points in the circuit, erroneous shots can be identified and discarded, improving result fidelity with minimal hardware overhead. To account for circuit noise, including measurement errors, we analyze the likelihood that a measurement outcome indicates a corrupted shot. This analysis is informed by the measurement's backward light cone, namely the set of circuit operations that could affect the outcome. Shots whose auxiliary measurement outcomes imply a corruption likelihood above a tunable threshold are rejected. Simulations show that the method reduces the false-negative rate by approximately 10% while discarding only approximately 1% of valid shots. The threshold controls the bias-variance tradeoff inherent to post-selection, allowing the method to be adapted to the fidelity and sampling requirements of different applications.

Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for non-additive codes that lack a stabilizer description. We present a general learning-based framework that, given only an encoding circuit, constructs physical implementations of logical operations while enforcing structural properties such as transversality or shallow depth. Our approach is validated by rediscovering known logical operations of standard stabilizer codes. We then extend it to a co-design procedure, dubbed variational early fault-tolerant quantum computing (VarEFTQC), which tailors non-additive encodings to a given noise model and enforces desired logical gate sets, such as transversal IQP-type families or low-depth universal sets. A software library implements the complete learning pipeline, including loss-function variants, ansatz families, and optimization routines. Together, these results position VarEFTQC as a practical tool for discovering hardware-adapted logical gadgets for early fault-tolerant quantum computing.

The development of scalable quantum networks requires coherent interfaces capable of converting microwave photons used in superconducting quantum processors into optical photons suitable for long-distance fiber transmission. This review surveys recent progress in microwave-to-optical quantum transduction across optomechanical, electro-optic, and magneto-optic platforms, with emphasis on conversion efficiency, bandwidth, added noise, and operating temperature. In addition to standard metrics, we propose the internal efficiency eta_in and the magnon decay rate kappa_m/2pi as normalized parameters that enable fairer comparison across heterogeneous implementations. Optomechanical systems achieve internal phonon-to-photon efficiencies of 93% with sub-quantum added noise of 0.25 quanta at millikelvin temperatures. Electro-optic devices based on LiNbO3 and AlN have advanced from room-temperature efficiencies below 1% to millikelvin systems with internal efficiencies approaching 99.5%, added noise as low as 0.16 quanta at 60 mK, and bandwidths extending to several tens of megahertz. Magneto-optic (optomagnonic) platforms exhibit the lowest efficiencies (typically $10^{-10}$ to $10^{-8})$, but offer intrinsic non-reciprocity and broadband magnonic operation, with emerging approaches based on topological heterostructures and magnon squeezing predicting enhancements up to $10^{-4}$. Optomechanical systems appear promising for high-fidelity quantum state transfer, electro-optic transducers for high-bandwidth coherent links, and magneto-optic devices for non-reciprocal network components. We discuss the fundamental trade-off between efficiency and added noise across all three platforms, and argue that heterogeneous microwave-optical transduction is emerging as a key enabling technology for distributed quantum computing and large-scale quantum networks.

Near-term and early fault-tolerant quantum computing architectures are expected to exhibit highly non-uniform error rates. In particular, local operations within a chip can be substantially more reliable than operations connecting different chips or dilution refrigerators. Such inter-module operations can therefore become a dominant bottleneck, even when quantum error correction is applied. Entanglement distillation provides a natural way to trade additional operations and qubits for higher-fidelity entanglement. Standard distillation protocols, however, are usually formulated in an LOCC resource model, in which several noisy Bell pairs are generated initially and all subsequent processing consists only of local operations and classical communication. Here, we consider a generalized model tailored to modular quantum computing hardware, in which the two modules have access to high-fidelity local operations and to repeated uses of the same noisy inter-module entangling operation during the protocol. We develop practical small-scale entanglement distillation protocols designed to minimize both space and time overhead. Remarkably, our main protocol requires only two qubits per module, yet achieves quadratic error suppression of inter-module errors, assuming local operations are much cleaner. Compared with existing small-scale protocols, our space-optimal protocol provides more space- and time-efficient quadratic error suppression and achieves the best performance in our simulations and experiments on noisy links of current superconducting quantum processors. These results suggest that inter-module-gate-assisted entanglement distillation can be a practical primitive for overcoming noisy links in modular quantum computing architectures.

Crosstalk noise derives from phenomena in quantum devices which inhibit individual addressability or cause unintended interactions among qubits. It is widely considered one of the major problems to be solved for a quantum computing platform to operate at scales beyond one or two qubits. Despite this, detailed discussion of crosstalk is often neglected when quantum device performance is described both in the context of device benchmarking and individual algorithm execution. Additionally, while the potential for crosstalk exists in all quantum platforms, the mechanisms and severity of crosstalk between platforms varies significantly, increasing the barrier of entry associated with understanding and performing research on unfamiliar quantum platforms. While previous work focused on theoretical formalism or platform specific details, in this review article, we provide a comprehensive overview of crosstalk from quantum computing literature across a range of physical systems focusing on physical origins, methods of mitigation and known consequential security vulnerabilities. We describe multiple crosstalk mechanisms for all major quantum computing platforms, which are usually implicitly addressed through device design, tuning, and mitigation techniques. We also observe accelerating research regarding security implications, however with multiple avenues for further exploration, especially for non-superconducting systems. Together, this review provides a comprehensive entry point for researchers and industry engineers interested in understanding and addressing the challenges arising from crosstalk phenomena in modern quantum computing systems.

Logical T state preparation is a major overhead source in fault tolerant architectures built from stabilizer operations. Existing protocols, however, are reported under different code families, noise models, postselection rules, and cost conventions, making direct comparison difficult. We compare three representative preparation routes: magic state distillation, magic state cultivation, and code switching, using currently available results. Rather than reducing heterogeneous data to a single cost metric, we retain source native cost units and record output error, single attempt cost, expected cost per accepted output, footprint, latency, and reporting completeness for each configuration. Within the current dataset, distillation reaches the lowest output error regime; code switching achieves the lowest reported single attempt cost and the smallest explicit footprint among the compatible rows; and recent RP2 cultivation results add low cost cultivation points with output errors between 1e-6 and 1e-9. As a simple algorithm level case study, we also examine the reported preparation routes under an error budget motivated by Shor factoring algorithm, in order to relate single state preparation costs to full workload requirements. The resulting comparison clarifies the trade offs currently supported across the literature, while remaining bounded by the conventions and coverage of the underlying papers.

Quantum control is essential for quantum information science and technology, yet designing high-fidelity control protocols remains challenging due to complex optimization landscapes, hardware noise, and long pulse sequences. Existing numerical solvers often require problem-specific engineering and produce opaque control amplitudes, while naive large language models (LLMs) lack the physical consistency and long-horizon precision for reliable quantum control synthesis. Here we introduce VF-QCTRL, a physics-informed large language model framework for general quantum control that combines symbolic reasoning with optimization to propose analytic control ansätze and coherently refine their parameters through feedback. To systematically evaluate LLM-driven quantum control, we develop QCTRL-BENCH, a benchmark spanning sixteen tasks across single- and multi-qubit systems, closed and open quantum dynamics, noiseless and noisy settings, and both analytic and numerical protocols. Across the benchmark, VF-QCTRL demonstrates strong universality, accuracy, efficiency, and interpretability: it applies to generic quantum control systems without task-specific training, achieves performance competitive with or exceeding state-of-the-art conventional solvers in both noiseless and noisy regimes with query efficiency, exhibits favorable inference-time scaling and pulse resolution scaling, and derives physically interpretable analytical protocols directly from prompts. Our results establish physics-informed LLM-based quantum control as a promising paradigm for accurate, efficient, interpretable, and training-free quantum control protocol design across a broad range of quantum systems.

Control architectures that reduce hardware overhead while maintaining high-fidelity operations are essential for the continued scaling of superconducting quantum processors. Here we experimentally realize a unified control architecture for fluxonium qubits, in which both transverse ($XY$) and longitudinal ($Z$) operations are implemented through a single flux-control channel driven by a single arbitrary waveform generator channel. This architecture imposes competing requirements on the shared control channel, which must simultaneously support low-frequency flux transmission for reset operations while strongly attenuating broadband noise near the qubit transition frequency. We address this challenge through frequency-selective cryogenic filtering together with compensated waveform synthesis that corrects the pulse distortion introduced by the filtered control line. Experimentally, this approach preserves coherence times above 100 $μ$s while enabling active reset with approximately 98% fidelity and 20-ns single-qubit gates with fidelities exceeding 99.99%. We further demonstrate FPGA-native instruction-level waveform synthesis based on reusable pulse primitives for unified flux control. These results establish unified flux control as a scalable architecture for fluxonium qubits that reduces control hardware overhead while preserving high-fidelity operation.

Power side-channel attacks on AES exploit data-dependent physical leakage to recover secret keys, but turning noisy leakage observations into a verified AES-128 key remains a hard combinational search problem. SAT-assisted power side-channel cryptanalysis addresses this challenge by encoding AES semantics, key constraints, plaintext/ciphertext consistency, and leakage predicates as CNF, so that candidate keys must satisfy the exact cryptographic specification. These cryptanalytic SAT formulas are large and highly structured; our largest controlled AES-oriented power-SCA instances contain up to 39,389 variables and 137,712 clauses, making a full-formula Grover search well beyond the scale studied here and beyond currently practical near-term implementations. We propose QGCL, a Quantum-Guided Conflict-Driven Clause Learning (CDCL) framework in which Grover search is invoked only on small subformulas extracted dynamically around CDCL conflict cores. The quantum subsolver returns candidate assignments and violation scores that bias branching heuristics, while final SAT/UNSAT decisions and key verification remain classical. We evaluate QGCL on AES-oriented cryptanalytic SAT instances derived from power side-channel CNFs with leakage-derived hint configurations, measuring conflicts, restarts, decisions, and propagations. The experiments show consistent reductions in these solver-internal statistics on harder instances, with up to an 86% reduction in conflicts compared with the classical conflict-learning baseline. Parameter sweeps over the number of Grover oracle calls and the subproblem size identify a regime in which a modest quantum resource allocation captures most of the observed improvement.

Formal verification of power side-channel leakage and its countermeasures in cryptographic algorithms is challenging, as SAT-based methods fail to scale on XOR-heavy, time-unrolled cryptographic circuits with realistic leakage models. We construct compact Conjunctive Normal Form (CNF) cases modeling one-bit leakage under two-trace conditions, linking key dependence and state evolution. Classical solvers quickly reach complexity limits, so we propose Q-LEAK, a quantum-based verification approach using Grover's algorithm, compiling each CNF into an oracle and applying amplitude amplification to search in O(sqrt(N)) oracle calls, with oracles that encode the two-trace leakage predicate and the CNF constraints. Benchmarking against classical SAT shows both potential gains and practical resource limits. In noiseless tests on 5-7 variable benchmarks, Q-LEAK consistently recovered a satisfying assignment within 1-4 tries, with marked bitstrings amplified clearly above the background distribution, exceeding 20 percent probability. The evaluation of Q-LEAK on real quantum hardware revealed at least one classically verified SAT assignment, despite the presence of noise. These results point to a potential path toward quantum-assisted verification of side-channel protections.

Homomorphic quantum error correction aims to protect quantum data against both unauthorized access and environmental noise during server-based processing. We investigate the algebraic compatibility between quantum homomorphic encryption and quantum error correction, determining precise conditions under which encrypted encoded states remain inside the relevant code space during storage and computation. Our work establishes a necessary and sufficient criterion for an $[[n,1,d]]$ stabilizer code to remain compatible with the restricted transversal block-Pauli masking $U_{\rm enc}(a,b)=(X^aZ^b)^{\otimes n}$, stated explicitly for $[[n,1,d]]$ codes and extending directly to code-space preservation for $[[n,k,d]]$ codes. We verify this condition for standard examples (bit-flip and Shor codes, with the phase-flip repetition code following analogously), derive a practical criterion for Calderbank-Shor-Steane codes, and extend the analysis to three-dimensional color codes. A critical challenge emerges for non-Clifford gate implementation: the Shor code lacks a naive transversal $T$-gate implementation of the desired logical operation on encrypted encoded data. We present two routes around this obstruction. First, suitable triorthogonal codes admit transversal $T$-type logical implementations, up to Clifford corrections. Second, logical-gate masking gives code-space compatibility for arbitrary stabilizer codes, provided that suitable unitary representatives of the required logical gates are available. These results separate code-space compatibility from a full cryptographic security proof and provide explicit criteria for combining error correction with homomorphic processing in cloud quantum computing.

We propose the use of certain low-density generator-matrix (LDGM) codes as syndrome measurement (SM) codes for quantum low-density parity check (QLDPC) codes. We use an efficient progressive-edge-growth-like algorithm to create LDGM SM codes with column and row weights that result in measured stabilizers that have constant weight, thus preserving the desirable properties of the underlying QLDPC code. This process allows for control over stabilizer weights and SM code distance, resulting in significantly better performance than repeated syndrome extraction and allowing for both higher distances and fewer syndrome measurements. We implement these SM codes on a distance-5 rotated surface code, and show that this procedure results in a lower probability of logical error. As syndrome measurements performed are a reasonable metric for the time a circuit takes to implement, we conclude that these LDGM codes allow for improved implementation of QLDPC codes without sacrificing the low weights of the syndrome measurements performed.

We develop a theoretical and numerical framework to analyze the effect of transport on the motional states of ions in a trapped-ion quantum processor. We decompose the shuttling protocol into primitive operations and characterize these in terms of their heating performance. Instead of having to simulate the whole transport protocol for each complete ion trajectory, the method allows us to determine the heating properties of each primitive operation separately and obtain the global result through an algebraic expression. We demonstrate our method by applying it to an 8-qubit quantum processor design based on linear transport and swap operations for all-to-all connectivity. We show how to incorporate the price of motional operations at the level of the compiler as a cost function.

We develop a straightforward analytical framework for the propagation of spatial light modes through a turbulent atmosphere. Built upon the split-step approach with the mode-based optical field representation, it directly assesses how turbulence-induced phase fluctuations deplete the optical power in the original mode and re-distribute it into neighboring spatial modes. Importantly, this power transfer scales linearly with the propagation distance in a uniform channel, yielding a simple solution for arbitrary distances in the form of a matrix exponential. The transfer rate is determined by the spatial spectral overlap between the turbulence spectrum and the acceptance spectrum for a pair of interacting spatial modes. The model predicts the average power in each spatial mode and is exact when a single mode strongly dominates all others. Our predictions show reasonably good agreement with simulations up to medium-to-strong turbulence levels. The model also confirms the scalings with mode order previously known as empirical observations.

It is well known from classical physics that weakly coupled self-sustained oscillators may spontaneously lock their phases. Just like classical synchronization is known to break down due to noise induced phase slips, we show here how the synchronization of continuous variable quantum systems breaks down by proliferation of quantum phase slips. Within a Keldysh path integral formulation of limit cycles, we analyze the phase dynamics and show how, in spite of strong phase correlations, quantum phase slips degrade the actual phase locking. This approach also allows us to address non-Markovian effects on the synchronization of limit cycles, which we illustrate explicitly for superconducting resonators coupled via a voltage biased double quantum dot.

We establish improved sample-complexity bounds for sample-based Lindbladian simulation based on the Wave Matrix Lindbladization (WML) algorithm. For a jump operator $L$ with dimension $d$, we derive an explicit non-asymptotic sample complexity bound $n_d^*(t,\varepsilon) \le \left( \frac{2d+3}{8} \right) \|L\|_\infty^2 \left( \frac{t^2}{\varepsilon} \right)$, holding for simulation time $t$ and error $\varepsilon$. This refines the dimension dependence of the best previously known bound, $O(d^2 t^2/\varepsilon)$, from [Go et al., Quantum Sci. Tech. 10, 045058 (2025)]. Remarkably, we show that this dimensional overhead can be entirely avoided when $\| L\|_\infty^2 = O(1/d)$, a condition satisfied with high probability for random Lindblad operators, yielding a typical-case sample complexity of $O(t^2/\varepsilon)$. On the other hand, in the worst case, we show that WML necessarily requires $Ω(dt^2/\varepsilon)$ samples by constructing an explicit example with a rank-one Lindblad operator. Our results reveal a sharp dichotomy between typical and adversarial sample complexities in Lindbladian simulation, thereby strengthening the theoretical foundations of sample-based quantum algorithms.

Synchronization, a ubiquitous phenomenon in classical systems, has recently been extended to the quantum domain. Here, we show quantum synchronization of a bosonic mode exhibiting a Fock state-like limit cycle, manifesting as a steady state with a negative Wigner function. We demonstrate that this non-classical state can be phase-locked to an external drive, achieving synchronization within an Arnold tongue regime. We argue that synchronization is a dynamical property and fundamentally tied to the suppression of phase slips, which we show to occur with exponentially decreasing probability. We introduce a novel method to extract the phase slip rate from the Lindblad time evolution of the system. This work opens new avenues for understanding and manipulating non-classical synchronization dynamics.

In this work, we compare three qubit-mapping strategies to study the structure of the nuclear ground state within the shell model description employing the Variational Quantum Eigensolver (VQE) approach. Although the initial point for different mappings is a Hamiltonian matrix in many-body particle basis or Slater determinant (SD) basis, the structure of the trial wavefunction and resource counts are different for each mapping. These three mappings are tested for a mid $p$-shell nucleus $^{10}$B and compared the quantum resources required to find the ground state for each mapping. Further, we extend the qubit-efficient mapping to study the ground state of one more mid $p$-shell nucleus $^{12}$C. We run circuits up to 26-qubits representing their ground states on a noisy simulator (IBM's FakeFez backend) and quantum hardware ($ibm\_fez$). The best post-error mitigated results from the hardware for $^{10}$B ground state is obtained following SD to qubit mapping with a percent error of 0.21 \%. The percent errors for the same state following cSD and pnSD mapping are 3.37 and 8.88 \%, respectively. On the other hand, following the cSD mapping, the post-error mitigated ground state energy of $^{12}$C is 6.82 \% away from the exact result. We further evaluate the fidelity of the VQE wavefunctions obtained from hardware with respect to the shell model wavefunctions for the cSD mapping. This cSD mapping can be useful for scaling the VQE algorithm for complex nuclei across different mass regions in terms of qubit efficiency.

The increasing complexity of industrial scheduling and transport routing problems motivates the study of alternative optimization formulations and computational paradigms. In this work, we study how higher-order unconstrained binary optimization (HUBO) formulations of such problems map onto quantum optimization workflows in both noisy and fault-tolerant regimes. We consider three representative logistics and manufacturing use cases and formulate each as a HUBO problem. This captures process intricacies, such as highly correlated assembly-line scheduling rules, which are difficult to express faithfully with the standard quadratic (QUBO) form, while at the same time reducing the number of binary variables required in the quantum mapping, thus lowering qubit demand. We compare the HUBO formulations with corresponding QUBO encodings, highlighting a key trade-off: while HUBO reduces qubit requirements through compact binary encoding, it introduces higher-order interaction terms that increase circuit depth, limiting feasibility on current quantum hardware. The proposed formulations are validated using classical solvers across several problem instances and benchmark small routing problem instances using bias-field digitized counterdiabatic quantum optimization in classical simulation. We complement these results with a resource and scalability analysis, focusing on the capacitated vehicle routing problem as a representative large-scale industrial use case. Our analysis indicates that while HUBO formulations offer advantages in qubit scaling compared to QUBO encodings, their practical implementation is constrained by gate fidelity, coherence, and circuit depth, making hybrid quantum-classical workflows and early fault-tolerant quantum hardware the most plausible settings for their practical use.

Can causal relations be subject to quantum indefiniteness, similar to other physical properties? The process-matrix framework formalises this possibility: valid processes are defined by what local laboratories can implement, without assuming a global causal order. Standardly, the local labs are assumed to implement arbitrary quantum instruments. We ask what happens when symmetries restrict these local operations. Symmetry constraints, such as those arising from missing reference frames, superselection constraints, or the antiunitary symmetry defining real quantum theory, enlarge the admissible process cone. Do these extra processes generate genuinely new correlations? We prove a sharp dichotomy: no for any finite unitary symmetry, yes for real quantum theory. Recent work has shown that, under fixed and definite causal order, complex quantum theory is strictly richer than real quantum theory. Our work shows that this hierarchy is reversed under indefinite causal order: real quantum theory realizes strictly more process correlations than complex quantum theory.

The realization of universal control in hybrid oscillator-qubit quantum processors enables the systematic design and implementation of quantum algorithms. However, the algorithmic development for such platforms remains at an early stage. While the Quantum Approximate Optimization Algorithm (QAOA) has been extensively studied in both continuous-variable (CV) and discrete-variable (DV) quantum systems, its development in the hybrid CV-DV setting remains limited. In this paper, we propose a hardware-native non-Abelian mixer for QAOA on hybrid CV-DV quantum processors and develop a corresponding hybrid ansatz for the Max-Cut problem. We evaluate the proposed ansatz on unweighted Erdős-Rényi graphs and benchmark it against the standard transverse-field mixer using the approximation ratio and optimal-solution probability. Across all graph sizes and Fock cutoffs in our simulations, the proposed non-Abelian mixer consistently improves both expected solution quality and the probability of sampling an optimal solution relative to the transverse-field mixer. These results indicate that the proposed non-Abelian mixer is a promising building block for QAOA on hybrid oscillator-qubit platforms.

We show that bright squeezed vacuum light, combined with a single-shot quadrature measurement of the post-interaction light, enables the ultrafast generation of macroscopic quantum states in matter. Although in the weak-coupling regime multiphoton quantum light leaves the unconditional matter state as a classical mixture due to light--matter entanglement, quadrature-based heralding prepares the matter in a Gaussian-weighted quantum superposition. For an ensemble of resonantly electric-dipole-coupled two-level systems, this heralding dynamics acts as a Gaussian filter with respect to the electric polarization, with brighter squeezed-vacuum light accelerating the preparation of the zero-eigenvalue Dicke state. Counter-rotating terms further drive a stroboscopic transition from this Dicke state to a cat-like state. Our results open a route to ultrafast engineering of macroscopic quantum matter with strong-field quantum light.

Noise is typically treated as the adversary of quantum information processing. For open quantum dynamics, however, dissipation is part of the target physics, creating a tension with fault-tolerant architectures designed to suppress decoherence. Here we show that logical noise can instead be turned into a calibrated resource. We treat the error-correction cycle as a programmable primitive: one fault-tolerant round induces a logical completely positive trace-preserving map, and decoder/recovery randomization generates a controllable family of logical channels whose convex mixtures realize Kraus-channel mixing. This enables direct compilation of target dissipators into effective logical dynamics without explicit ancilla qubits for encoding the bath degree of freedoms. We derive an accuracy criterion for multi-step simulation in which the code distance is chosen so that uncontrolled logical errors remain a small fraction of the intended dissipation per step, rather than being driven below an arbitrarily small closed-system tolerance. Partial quantum error correction thus repurposes fault-tolerant structure to sculpt dissipation, offering a resource-efficient route to quantum simulation of open quantum systems.

The kinetic isotope effect (KIE) is the conventional probe for quantum tunneling, yet its composite nature conflates tunneling with zero-point energy and classical kinetics. Here, we introduce the tunneling phase diagram, a machine-learning framework that decouples true tunneling strength by decoding the nonlinear relationship between KIE and the tunneling factor (\k{appa}). With exceptional fidelity (R^2 > 0.98, RMSE = 0.21), this framework reveals an anomalous high KIE-low \k{appa} spanning 300-600 K, thereby defining a paradigm for the quantitative assessment of quantum tunneling.

We construct a quantum-circuit framework for finite-temperature molecular dynamics in the canonical ensemble (NVT) with a Langevin thermostat, connecting canonical state preparation to subsequent physical-property readouts. The classical nuclear phase-space distribution is encoded as a Koopman--von Neumann (KvN) wave function, and canonical state preparation is formulated as Langevin-type Fokker--Planck relaxation. The Hamiltonian Liouville flow, momentum friction, and momentum diffusion are decomposed into separate circuit blocks. The friction block is represented by a symmetrized momentum-space dilation, whereas the diffusion block is implemented as a cosine filter realized by probabilistic imaginary-time evolution (PITE). We analytically quantify the leading-order temperature bias caused by replacing the Gaussian diffusion kernel with this PITE-realized cosine filter. This analysis yields an internal-temperature correction that targets the desired physical equilibrium distribution. As a proof-of-concept demonstration connecting quantum chemistry to KvN nuclear dynamics, we study the H$_2$ molecule. Numerical simulations show relaxation from a nonequilibrium phase-space distribution to a canonical KvN state. From this canonical state, we demonstrate two complementary readouts: a dynamical quantum-phase-estimation readout of the vibrational density of states associated with the H--H stretch coordinate and a static canonical evaluation of the transition-state-theory (TST) rate constant. This work demonstrates, in a minimal molecular system, a circuit-level protocol that connects Langevin canonical state preparation to physical-property calculations, providing a concrete step toward quantum--classical hybrid molecular dynamics on quantum computers.

We formulate the Green--Kubo transport coefficients of classical molecular dynamics as a readout problem for quantum algorithms using the Koopman--von Neumann (KvN) representation. Both NVE and Nosé--Hoover-type NVT dynamics are derived as unitary evolutions on Hilbert spaces associated with the corresponding classical phase spaces. Numerical benchmarks on finite grids show that the discretization error in the correlation function decreases as a power law in the number of grid points $N_z$. Equivalently, with $N_z=2^{n_z}$, the error decreases exponentially in the register size $n_z$, so a target accuracy $ε$ requires $n_z=\mathcal{O}(\log(1/ε))$ qubits. To read out a transport coefficient, we input a flux-excited state to quantum phase estimation (QPE). The probability $P_0$ of measuring the QPE ancilla register in the all-zero state corresponds to a Bartlett-windowed Green--Kubo integral. With maximum-likelihood amplitude estimation, the statistical estimation of $P_0$ defined by this QPE oracle improves from the $N_{\rm queries}^{-1/2}$ scaling of direct shot sampling to scaling close to $N_{\rm queries}^{-1}$. Our circuit-resource analysis shows that one step of the NVE propagator can be built with $\mathcal{O}(n^2)$ CX gates, where $n=n_x+n_p$ is the total number of position and momentum qubits. For the NVT propagator, the centered-difference Pauli-decomposition implementation of the Nosé--Hoover friction term scales as $\mathcal{O}(n_ξn_p\,2^{n_p})$, where $n_p$ and $n_ξ$ are the numbers of momentum and thermostat qubits, respectively. The proposed framework is a concrete step toward translating the principles of quantum algorithms into the transport-coefficient calculations required in practical molecular simulation.

Ground-state preparation is a fundamental task in quantum simulation, because the overlap of the prepared state with the true ground state significantly affects the overall cost of subsequent quantum algorithms. We propose a three-stage framework in which a matrix product state (MPS) of an $N$-site system obtained by the density-matrix renormalization group (DMRG) is loaded onto an $N$-qubit quantum register through an optimization-free matrix product disentangler (MPD) encoding circuit, and the residual error is then reduced by probabilistic imaginary-time evolution (PITE). We demonstrate that the central-bond Schmidt rank of intermediate states during MPS encoding grows logistically with the number of layers. Its inflection point $L^{*}$ marks the boundary of the efficient encoding regime. Beyond this point, the gain in fidelity slows rapidly, and the number of additional MPD layers required to reach a target infidelity $\varepsilon$ empirically scales as $\mathcal{O}(N^5\log(N/\varepsilon))$. To avoid this encoding-only tail, we stop the encoder at $L^{*}$ and suppress the remaining excited-state components by PITE, with the linear PITE schedule fixed deterministically from the ground-state energy, the effective gap, and the reference overlap estimated by DMRG. Numerical experiments on the spin-$1/2$ staggered-field Heisenberg chain show that the framework avoids very deep encoding circuits and substantially suppresses the post-selection overhead intrinsic to PITE. Combining classical preprocessing by DMRG, optimization-free MPS encoding, and deterministically scheduled PITE, the present framework offers a practical hybrid route to ground-state preparation in quantum simulation.

The deterministic many-interacting-worlds method proposed in 2014 showed potential among the numerous interpretation of quantum mechanics. The successful application of this method in harmonic oscillator has been promoted for a long time. In this article we continue the idea about using this method to solve some bounded systems different from harmonic oscillator potential and extend to 2 dimension cases. We focus on the potential with singularity like coulomb potential and finite trap potential by some asymptotic smooth method. The numerical simulation mainly based on the dynamical algorithm proposed in many-interacting-worlds method will be used to approach the stationary states of given systems. Our results shows the consistency to the matrix Numerov method in standard quantum mechanics in solving bounded systems and provides the possibility to solve more complex systems.

In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the adiabatic theorem. We propose several alternative processes that achieve the same goal, but can easily be implemented on a gate-based quantum computer without the overhead of simulating time-dependent Hamiltonian evolution. We give a general framework for deriving `adiabatic' theorems for these processes. As an application, we give various algorithms for solving the Quantum Linear Systems Problem (QLSP) with optimal scaling in the condition number. One of these algorithms was previously developed in [Cunningham, Roland 2024] and another can be seen as a randomised version of the discrete adiabatic algorithm of [Costa et al. 2022]. We also describe versions of Trotterisation in our framework, which allows several results from [An et al. 2025] to be reproduced in a randomised setting. In particular, bounds on the Trotter error in terms of the fidelity are obtained that are asymptotically better than the standard bounds.

This book examines a number of problems of quantum mechanics, most of which are not usually discussed. What is the origin of probabilities in the mechanics of the microworld? What is the nature of Planck's constant h? What is the nature of probability amplitudes? What is the wave function? A system of axioms for quantum theory is formulated. A model is studied according to which a classical oscillator in a thermostat can be interpreted as a quantum one. The measurement problem is discussed in detail. For advanced undergraduate students, graduate students, and specialists interested in the foundations of quantum theory.

We identify chiral inversion points in slow-light, glide-plane-symmetric, photonic-crystal waveguides, defined as fixed locations where the local optical chirality changes sign over a narrow wavelength range. We experimentally access this behaviour using a waveguide-embedded InAs/InGaAs quantum dot. The slow-light spectral region is determined from time-integrated and time-resolved photoluminescence, and the dot exciton is electrically tuned across the slow-light bandwidth via the quantum-confined Stark effect. As the emission wavelength is swept through the slow-light region, the directional emission contrast shows a strong wavelength dependence and a sign reversal, consistent with the identified chiral inversion point. Numerical simulations attribute the switching primarily to the pronounced spectral variation of the local optical chirality for emitters displaced from the waveguide center. These results demonstrate on-demand electrical switching of chiral light-matter coupling in nanophotonic waveguides and enable tunable chiral interfaces for integrated quantum photonic devices.

Driven-dissipative qubit-resonator dynamics, which are the basis of most dispersive superconducting qubit measurement schemes, are often modeled with Lindblad master equations built from subsystem local jump operators, even when the qubit and resonator are appreciably hybridized. In this work we revisit this setting using a microscopic Bloch-Redfield approach, where dissipation is constructed in the eigenbasis of the coupled qubit-resonator Hamiltonian with a complete, frequency dependent, open system description of the transmission line environment. Here, we show that the Lindblad and Bloch-Redfield decay rates can be quantitatively different in the absence of driving, while in the driven case we demonstrate that the time-independent Redfield dissipator and its time-dependent generalization can show qualitatively different behaviors as a function of driving strength. Finally, we investigate the effects of driving in structured spectral densities, recovering the suppression of measurement-induced relaxation in the presence of a so called Purcell filter.

Noise is usually regarded as the main obstacle to achieving a scalable quantum advantage, but recent evidence in quantum reservoir computing [L. Domingo, F. Borondo, and G. G. Carlo. Taking advantage of noise in quantum reservoir computing, Scientific Reports, 13:8790, 2023] suggests that certain channels can, in appropriate regimes, improve performance by enriching the reservoir's effective dynamics. Motivated by this idea we propose a geometric mechanism to explain how non-unital noise applied together with a universal gate set leads to a faster approach to Haar-like distributions of the final states. We find that noise of this kind induces an effective volume expansion on the manifold of pure states. In order to intuitively understand this we use a minimal 1 qubit model where we take the amplitude damping channel and combine it with a renormalization rule that associates to each resulting mixed state a representative pure state. This composition defines a globally expanding nonlinear map on the space of pure states. We analytically derive the local area expansion factor and identify the global expansion threshold. Finally, we combine amplitude damping with the G3 = {H, T, CNOT} universal gate set to show how the approach to Haar-like behavior is faster in an appropriate parameter region. This leads us to propose noise as a possible resource in future quantum algorithms.

Electric flow sampling (elfs) is a new tool in the quantum walk toolbox and a useful primitive for solving search, sampling and optimization problems on graphs. We refine this tool by showing that there exists a zero-error transducer for implementing elfs. More broadly, we establish a zero-error transducer for reflecting about the intersection of two subspaces, yielding an errorfree transducer version of the effective gap lemma. Building on this result, we obtain improved quantum walk algorithms for estimating effective resistances and span program witness sizes with an optimal error scaling, and for sampling from the random walk arrival distribution, via the composition of many elfs. Using this last algorithm, we obtain an up-to-quadratic quantum speedup for semi-supervised learning on expander graphs.

We introduce a one dimensional spin $\frac{1}{2}$ Hamiltonian with multi-site interactions, but still local. The algebra of its Hamiltonian densities resembles that of the transverse field Ising model. Using this fact we show that its spectrum is free-fermionic but with a huge degeneracy for each level. The source of the degeneracy is a set of local conserved quantities that act like a classical background field for the quantum system. The thermodynamics of this system is contrasted with the standard Ising model. At the gapless points in the energy spectrum, we show that this system can be derived from the quantum inverse scattering method adapted to a multi-site generalization of the Yang-Baxter equation as introduced by E. Rowell and Z. Wang. The $R$-matrix is constructed using generators of extraspecial 2-groups. This helps us extract all the conserved charges and lay the framework for a general mechanism to generate such multi-site interaction spin systems that are transverse field Ising models under the hood. A remark on how to obtain P. Fendley's free-fermion in disguise models in this formalism is also included.

Large-scale quantum networks will enable entirely new applications of quantum information science in fields such as quantum communication, distributed quantum computing, sensing, and metrology. To build nodes of such networks, diamond color defects are one of the promising candidates. Their excellent optical properties, fast spin-qubit control, and long spin coherence times make them well-suited for quantum information processing and quantum memory applications. Additionally, recent advances in the heterogeneous integration of diamond nanophotonic structures with photonic integrated circuits have made these systems more efficient and well-suited for scalable quantum processor architectures. In this comprehensive review, we discuss the optical and spin properties of these systems, recent progress in the building blocks of quantum networks, and demonstrations of metropolitan-scale quantum networks, as well as the challenges associated with these systems at both the fundamental and experimental levels, along with potential solutions.

Compiling arbitrary-connectivity NISQ circuits onto monolithic single-zone neutral-atom devices is constrained by a finite interaction range and a minimum separation between simultaneously addressable sites. Under the minimum-separation constraint, the SWAP-only configuration of our pipeline does not return a schedule within a practical time budget on a range of circuits, including circuits as small as nine qubits. We address this with hub traps, a small number of dynamically placed empty traps that serve as transit waypoints, together with a per-gate rule that chooses between SWAP-based routing and hub-mediated shuttling. We evaluate the compiler on seventeen benchmarks using analytic estimates of execution time and a per-layer fidelity proxy, comparing against a placement-matched baseline and against ablations of our own pipeline. Hub traps make these otherwise-unsolved circuits compile in seconds to minutes and remove SWAP gates entirely on every completed circuit, so their role is to enable routing rather than only to optimize fidelity. The benefit is concentrated on routing-dominated circuits and is absent on routing-free ones, which we separate by the structure of the interaction graph. On the most routing-dominated circuit the fidelity proxy improves by up to three orders of magnitude over the placement-matched baseline. The gain comes primarily from eliminating SWAP overhead, as the absolute fidelities there remain low.

The $k$-local Hamiltonian problem is a central model for quantum many-body systems and Hamiltonian complexity. Semidefinite programming and noncommutative sum-of-squares hierarchies provide systematic certificates for ground-state energies, but existing finite-convergence results give no quantitative guarantee on the accuracy of the low hierarchy levels accessible in computation. We prove explicit finite-level convergence rates for these hierarchies in the Pauli setting. For $k$-local Hamiltonians whose Pauli expansion contains only even-weight terms, we show that both the NPA-type lower-bound hierarchy and the upper-bound hierarchy on the spectral minimum have error at most $C(k)ξ^{n,4}_{d+1}/n$, where $ξ^{n,4}_{d+1}$ is the smallest root of a Krawtchouk polynomial and $C(k)$ is independent of the number of qubits $n$ and the hierarchy level $d$. General $k$-local Hamiltonians reduce to this even-weight case by adding one ancilla qubit while preserving the spectrum. The proof constructs almost-reproducing kernels for the Pauli algebra and relates their spectra to Krawtchouk polynomials, giving a noncommutative analogue of recent kernel-based convergence analyses for commutative polynomial optimization. These results provide the first quantitative finite-level accuracy guarantees for noncommutative semidefinite relaxations of Pauli Hamiltonians.

We propose and demonstrate a dynamical mirror compensation scheme to restore velocity immunity in a large-area dual-atom-interferometer gyroscope. In an ideal Mach-Zehnder configuration, the phase shift is inherently immune to atomic velocity, but this property is broken by the Earth's rotation via the Coriolis effect. We overcome this by actively rotating the Raman mirrors during the pulse sequence to cancel the time-dependent angular offset. The implementation relies on a decouplable calibration-compensation chain to remove rotation-induced time-dependent terms. The scheme is validated on a dual-atom-interferometer gyroscope with an interference area of 21.1 cm^2. After compensation, the phase's dependence on atomic velocity is reduced 40-fold, and the velocity contribution to scale-factor stability is evaluated to be 0.13 ppm. The sensor achieves a rotation sensitivity of 1.3\times10^{-8} rad/s/Hz^{1/2} and a stability of 1.9\times10^{-10} rad/s at 4500 s integration, together with a common-mode noise rejection ratio of up to 459, demonstrated in a seismic event. This work removes a key obstacle to scale-factor stabilization in atom-interferometer gyroscopes and paves the way for their applications in inertial navigation and geophysics.

We evaluate FALQON parameter transfer for Max-Cut, transferring sequences from small donors ($n \in \{8,10,12\}$) to 14-node recipients. Using 3-regular and Erdős-Rényi families, we show that transfer success is dictated by the recipient graph, not the donor. Transfer excels for dense recipients -- achieving high approximation ratios regardless of the donor -- but remains challenging in sparse cross-family cases. Crucially, performance is highly resilient to donor size, with 8-node donors matching larger instances. Thus, cheap small graphs can provide robust parameters for larger targets, significantly reducing the measurement overhead of the feedback loop.

We consider a non-spherical neutral particle spinning in free space and interacting with the electromagnetic quantum vacuum. When the rotation axis is orthogonal to the particle symmetry axis, the scattered field develops frequency sidebands that induce the parametric emission of dynamical Casimir photon pairs. Under the structural constraint of a maximum tip velocity, the emission rate is maximized for a nearly spherical geometry and is further enhanced near a polaritonic resonance. For realistic material parameters, even these optimized upper bounds remain exceedingly small, setting stringent quantitative limits on free-space rotational dynamical Casimir emission with a single nanoparticle.

As with classical neural networks, quantum machine learning (QML) models are vulnerable to small input perturbations that can significantly alter output predictions. Certifying the robustness of QML models, particularly on NISQ hardware, is therefore a fundamental step toward trustworthy quantum AI. This chapter reviews our recently developed comprehensive formal framework for verifying adversarial robustness in QML. The core of this framework is a fidelity-based robustness lower bound computable directly from the measurement outcome distribution, which enables both formal verification and empirical estimation on real quantum devices. Additionally, the optimal bound can be computed via semidefinite programming (SDP) with full knowledge of the quantum machine learning models. We incorporate these results into: (1) an efficient formal verification framework; (2) VeriQR, the first dedicated QML robustness verification tool; and (3) the first experimental benchmark of quantum adversarial robustness on a 20-qubit superconducting processor. Together, these systematic advances enable scalable, physically grounded robustness evaluation of QML models.

The universal statistics of density fluctuations of localized quantum states may offer unprecedented opportunities to probe and understand quantum transport in connection with dimensionality, coherence, symmetry and disorder. To date, the possible role of topological phase transitions in the fluctuation statistics is not studied yet. Using a Su-Schrieffer-Heeger chain subject to off-diagonal disorder (so that chiral symmetry is preserved), this work investigates how a disorder driven topological phase transition impacts on the spatial fluctuations of the logarithmic wave-packet density $\ln P(r)$ at distance $r$ from the initial excitation. Away from the transition, in both topological and trivial localized phases, the standard deviation follows the conventional one-dimensional scaling $σ[\ln P(r)]\sim r^θ$ with $θ\simeq 1/2$. Near the transition, however, the fluctuation growth is enhanced: the fitted exponent $θ$ increases above $1/2$ in a nonmonotonic manner before returning close to $1/2$ at criticality. We interpret this behavior from the energy-resolved density of states and localization length. Near the transition, several energy sectors carry appreciable spectral weight and exhibit competitive decay rates, preventing a single localization scale from dominating the accessible wave-packet tail and thereby enhancing the fluctuations of $\ln P(r)$. Our results establish wave-packet fluctuation statistics as a dynamical diagnostic of disordered chiral topological transitions and motivate broader studies of fluctuation phenomena in disordered topological quantum systems.

We study two-way covert communication schemes, where information is transmitted by passively modulating a reflected signal back to the source. We consider optical systems, described by quantum bosonic channels. While broadband classical and quantum light sources offer high covert throughput in theory, the associated mode-matching and phase-synchronization requirements make them impractical. Therefore, we employ a narrowband laser source to experimentally demonstrate a proof-of-concept two-way covert communication system, where the adversary is assumed to be quantum-capable. Furthermore, we propose a correlator-based receiver that attains the broadband gain offered by a quantum light source without the need for precise mode matching.

We propose gate-parameter Lee-Yang zeros of Loschmidt amplitudes as probes of dynamical phases in finite quantum circuits. We illustrate this approach using a brickwork model, where the time evolution is generated by repeated application of a Floquet operator. The Loschmidt amplitude can be expressed as a rational function of the gate parameters. At fixed system size and large circuit depth, its zeros in one complexified gate parameter, with the other parameter held fixed, condense onto limiting curves. We show that these curves comprise a universal component governed by equimodular Floquet eigenvalues, as described by the Beraha-Kahane-Weiss theorem, together with state-dependent contributions controlled by the overlap of eigenstate of the Floquet operator with the initial state. As one of the parameters is varied, the set of zeros reorganizes abruptly, providing a finite-qubit diagnostic of a dynamical phase transition. This mechanism does not rely on integrability: while integrability enables an exact calculation of the Loschmidt amplitude, the condensation of zeros follows from spectral competition and local unitarity alone.

We investigate the indistinguishability of Raman photons generated from two trapped $^{40}$Ca$^+$ ions using few-nanosecond excitation pulses. We elucidate how spontaneous scattering back to the initial state affects Hong-Ou-Mandel interference. We identify the mean number of back-decays as a measurable single-emitter quantity that correlates with achievable interference visibility of photons from two identical emitters.

Certifying the fidelity of a prepared state to a target stabilizer state is a fundamental task in quantum information processing. Ref. [Phys. Rev. A 99, 042337 (2019)] gave the optimal worst-case lower bound from one fixed stabilizer generator gauge, but gauge dependence can leave a large fidelity ambiguity. We develop an adaptive extension that reports the full certified fidelity interval. First, for a single gauge, we derive the complementary optimal worst-case upper bound. We then formulate gauge selection as an adaptive design problem in which each round solves exact endpoint linear programs and chooses a new gauge by a witness elimination policy. We prove monotonic tightening, exact recovery once all nontrivial stabilizers are covered, and the worst-case necessity of full coverage. Finally, we identify structured syndrome distributions for which adaptivity beats this exponential benchmark, and we numerically confirm faster concentration.

Security proofs in quantum cryptography rely on conditional entropies. In a many-round protocol, their estimation is a challenging task; one must account for the most general attacks by an eavesdropper, including those that are not independently and identically distributed (i.i.d.) across all rounds. Chain rules address this problem by relating the conditional entropy of a structured, but non-i.i.d. process to a sum of entropy contributions from each round. They are a key ingredient in entropy accumulation theorems (EATs), which provide a versatile security proof framework for many protocols in quantum cryptography. Recently, chain rules in the setting of trusted devices have lead to tight i.i.d. reductions at a finite number of rounds, and whether analogous results can be recovered in the device-independent (DI) setting has not been addressed. Surprisingly, we show that a natural tightening of the chain rule of Dupuis et al. [Commun. Math. Phys. 379, 867-913, (2020)] that would answer this question affirmatively cannot hold, highlighting a limitation of the current DI security proof approach. Nonetheless, we show that an intermediate improvement is possible by proving a new chain rule in this setting. Following the framework of Arqand et al. [Phys. Rev. X 15, 041013 (2025)], we use our chain rule to provide a slightly tighter version of the Rényi EAT in certain contexts. In addition, we provide a self-contained framework that unifies existing chain rules and compares their applications, framing our results in a broader context.

Quantum tomography can reconstruct fine phase-space structures that are not necessarily resolved by measurement itself. We show that the effective resolution of tomography is determined by a sampling operator linked to the Gram matrix of the measurement, which defines the experimentally accessible degrees of freedom and reconstruction bandwidth of the quantum state. Acting analogously to a transfer function in imaging, this operator provides an operational criterion for distinguishing genuinely resolved quantum features from artefacts induced by incomplete sampling or reconstruction assumptions. Reconstruction in the Gram eigenbasis emerges as an efficient measurement-adapted compression of the tomographic problem. Within finite frame theory, the same structure appears naturally as the frame operator. Our results establish a resolution-based framework for quantum tomography relevant for contemporary experiments probing highly structured nonclassical states.

A set of orthogonal product states is said to exhibit "quantum nonlocality without entanglement" if it is locally indistinguishable, i.e. no sequence of local operations and classical communication (LOCC) can perfectly discriminate the states. Building on this foundational idea, recent studies have highlighted the phenomenon of "genuine activation of hidden nonlocality", where a set of initially distinguishable orthogonal states becomes locally indistinguishable through orthogonality-preserving LOCC transformations. In this letter, we establish that any complete orthogonal product basis that is initially locally distinguishable remains so under all orthogonality-preserving local projective measurements, thereby ruling out activation via orthogonality-preserving local projective measurements and classical communication. We further introduce and formalise the notions of "strongly local sets", namely locally distinguishable sets that remain non-activable under all bipartitions. Interestingly, the study of "local activability" of distinguishable sets is useful to characterise the boundary between LOCC distinguishability and its irreversible loss in multipartite systems. Our results provide a rigorous structural understanding of local-to-nonlocal transitions in quantum state discrimination.

While quantum computers have shown significant promise for electronic structure calculations, their potential to accelerate density functional theory (DFT) calculations remains unclear. In this work, we present a qubit-efficient encoding scheme for wavefunctions in Kohn--Sham (KS) DFT, together with a quantum algorithm that computes all occupied orbitals simultaneously. We further show that our algorithm is particularly well suited to the Harris functional, enabling the total energy to be evaluated with a potential exponential speedup over classical approaches by entirely avoiding the costly readout of the electronic density. In addition, we propose a second method for achieving self-consistent DFT calculations using multiple copies of the wavefunction, which likewise circumvents density readout. The applicability of our algorithms is demonstrated through several numerical examples, and their efficiency is compared with that of existing approaches.

Starting from the exact Projected Central Limit Theorem on hyperspheres, we rederive the Beta distribution for subsystem occupation probabilities and Lubkin's purity formula from elementary hyperspherical moments, quantifying the finite-size ``platykurtic'' suppression of tails relative to the Gaussian approximation used in standard eigenstate-thermalization and typicality treatments. Our main new result concerns the bipartite quantum mutual information $\langle I(A{:}B)\rangle$ for Haar-random pure states. We show that its full asymptotic expansion in $1/N$ admits a Bernoulli-factorized form in which every order $k \ge 1$ carries the symmetric factor $(d_A^{2k}-1)(d_B^{2k}-1)$ and all higher odd-order corrections vanish identically. Through an exact algebraic reorganization of Page's formula (conjectured in Ref.~\cite{Page1993} and subsequently proven~\cite{Foong1994, SanchezRuiz1995, Sen1996}), we establish that the leading finite-size correction separates into a dominant $\mathfrak{su}(d_A) \otimes \mathfrak{su}(d_B)$ bipartite quantum coherence contribution $(d_A^2 - 1)(d_B^2 - 1)/(2N)$ and a subtracted classical-probability (Cartan $\otimes$ Cartan) contribution $(d_A - 1)(d_B - 1)/(2N)$, and we trace this separation to the difference between diagonal and eigenvalue entropies via Schur's majorisation theorem, with the dimensional counts $(d-1)$ and $(d^2-1)$ acquiring meaning through the Cartan structure of the generalised Bloch decomposition. These results admit a single non-perturbative closed form: the exact typical mutual information factors as $\langle I(A{:}B)\rangle = (d_A^2-1)(d_B^2-1)\,\mathcal{G}(d_A,d_B,d_E)$, with $\mathcal{G}$ given by an explicit Bose--Einstein integral whose asymptotic expansion in $1/N$ reproduces the Bernoulli series.

The average bipartite quantum mutual information $\langle I(A{:}B)\rangle$ of Haar-random pure states can be expressed exactly through Page's formula in terms of digamma functions. We show that this quantity admits a single non-perturbative closed form: $\langle I(A{:}B)\rangle = (d_A^2-1)(d_B^2-1)\,\mathcal{G}(d_A,d_B,d_E)$, where $\mathcal{G}$ is given by an explicit convergent integral over a Bose--Einstein kernel. The overall factor $(d_A^2-1)(d_B^2-1)=\dim[\mathfrak{su}(d_A)]\cdot\dim[\mathfrak{su}(d_B)]$ is exact, not merely asymptotic. The asymptotic expansion of $\mathcal{G}$ in $1/N$ yields a Bernoulli-factorised series whose coefficients involve $ζ(1{-}2k)$; this series diverges, and our integral is its exact Borel sum. The integral representation also makes $\langle I\rangle < (d_A^2{-}1)(d_B^2{-}1)/(2N)$ manifest via a scale-inversion symmetry of the kernel. Our derivation traces the mutual information's structure to an exact decomposition of Page's entropy into a diagonal (Dirichlet) contribution and a Schur-majorisation eigenvalue correction, whose assembly into the mutual information cleanly separates classical from quantum correlations.

We study local phase estimation for a single quantum emitter coupled to a bosonic Su-Schrieffer-Heeger (SSH) bath within a microscopic lattice model. Dimerization opens a central gap supporting an in-gap emitter-bath bound state, which suppresses complete relaxation of the emitter coherence. A Dyson-equation analysis yields the local bath Green's function, the in-gap bound-state condition, and the emitter residue controlling the retained phase information. The phase quantum Fisher information links gap formation, detuning, and emitter-bath coupling to the post-transient metrological response. At resonance, stronger coupling enhances transient hybridization but reduces the retained signal by lowering the emitter weight in the bound state. Away from resonance, late-time averages, retention times, and useful interrogation windows track how phase-information protection weakens as the emitter is tuned toward and beyond the band edge. A uniform-chain control shows that the retained signal disappears when the gap closes. In the bulk local-coupling geometry considered here, the response is insensitive to the sign of the dimerization, so the protocol probes spectral-gap physics and bound-state support rather than the SSH winding sector.

On superconducting quantum devices with sparse qubit connectivity, transpilation of long-range two-qubit interactions inserts additional SWAP gates, increasing hardware cost and execution error. Gate cutting via quasi-probability decomposition (QPD) can remove a selected two-qubit gate and thereby reduce routing overhead, but its sampling cost makes cut placement critical. We propose TW2S, a graph-only two-stage gate-cut selection method that operates on the circuit interaction graph without backend-specific transpilation at selection time. Stage 1 analyzes a min-fill elimination trace and scores edges by their contribution to a treewidth upper bound. Stage 2 ranks the resulting candidates by edge betweenness centrality with a degree penalty to identify routing bottlenecks. Across grid, Watts-Strogatz, barbell, and stochastic block model benchmarks transpiled to IBM's FakeSherbrooke backend, TW2S consistently outperforms random cut selection when the interaction graph contains identifiable sparse cuts. The advantage is governed not by absolute graph density but by moderate community structure and accessible inter-community edges. We further derive a mean-squared-error breakeven condition showing that, under a shared total shot budget, QPD is beneficial only when the ECR reduction is large enough and the signal strength is sufficient. Under an expanded per-subcircuit budget the signal-strength requirement is substantially relaxed. In noisy simulations of the J1-J2 transverse-field Ising model, TW2S achieves $Δ$ECR = 47 for n = 8, compared with approximately 9 for random selection, and yields lower estimation error than the uncut baseline in the tested strong-signal regime, with larger gains at increased shot budgets. These results position graph-structural cut selection as a practical compiler-side tool for turning circuit cutting into a targeted routing-reduction strategy.

The central aim of the thesis is to examine how non-classical resources in finite-dimensional quantum systems can be identified, characterized, and protected for practical use in the presence of realistic noise. Using the discrete Wigner functions (DWFs) framework, we introduce negative quantum states and examine how their Wigner negativity, mana, coherence, and teleportation fidelity evolve under unital and non-unital channels, with particular attention to non-Markovian random-telegraph and amplitude-damping dynamics. We also analyze protection strategies based on weak measurement and quantum measurement reversal, showing that these methods can enhance quantum correlations, reduce fidelity deviation, and improve teleportation performance for two-qubit negative states in memory-bearing environments. Moreover, we demonstrate that certain negative states, derived from phase-space point operators, exhibit greater resilience than Bell states in measures of entanglement under non-Markovian noise. Further, this thesis focuses on developing and implementing quantum circuits for generating these states on superconducting hardware and realizing them for the first time on IBM's ibm-Brisbane device. Their preparation is verified using quantum state tomography, demonstrating high fidelity under realistic noise conditions. We propose a teleportation scheme that leverages one of the two-qubit negative quantum states as a resource. Moreover, these two-qubit negative quantum states are also found to perform better than the Bell states for maximal CHSH violation and Fisher information in noisy conditions. We believe that these negative quantum states have the potential to be used in place of the traditional Bell states in scenarios where non-Markovian errors are prevalent. (continued in the PDF)

Quantum key distribution (QKD) via geostationary Earth orbit (GEO) satellites offers a compelling route to continuous, continental-scale secure communications. However, operation in this regime entails extreme channel loss and significant background noise, particularly if daylight operation is desired. We present a comprehensive end-to-end feasibility study of a decoy-state BB84 protocol in a GEO downlink configuration, incorporating variable-length finite-key security and tight statistical bounds to expand the achievable positive-key regime. Our analysis encompasses the principal receiver architectures relevant to downlink QKD and employs a physically realistic channel model that captures the dominant loss and noise mechanisms. We evaluate performance across rural, urban, and coastal environments at multiple wavelengths, including visible Fraunhofer absorption minima and the telecom band. Using historical cloud data across Europe, we forecast the annual secret-key yield across the continent. Through a systematic exploration of the high-dimensional parameter space, we identify key trade-offs and performance bottlenecks that determine feasibility. These results establish practical operating thresholds and provide actionable design guidelines for future GEO-QKD missions.

Efficient generation of multiquanta emission is crucial for quantum information processing but remains challenging due to its typical reliance on higher-order quantum processes. Here, we theoretically demonstrate strongly correlated photon-phonon emission enabled by direct tripartite interaction. This interaction facilitates the formation of high-order multiquanta states without more intermediate state transitions, thereby avoiding the suppressed transition rates associated with multiple sequential processes and substantially improving resonant transitions. As a result, high-efficiency strongly correlated even-quanta emission (e.g., two photons and two phonons) can be achieved in the presences of dissipation. Beyond that, we show that introducing two-photon dissipation enables strongly correlated odd-quanta emission (e.g., two photons and one phonon) in the tripartite interaction system by parity-protected suppression of single-photon loss and reconstruction of higher-order multiquanta processes. Our work extends multiquanta emission into the tripartite coupling regime and holds promising potential for applications in hybrid quantum networks.

For treating correlated electronic systems on quantum computers, we propose a quantum-classical hybrid scheme for dynamical mean-field theory (DMFT). In the quantum part of the scheme, we use modified quantum phase estimation (QPE) circuits suitable for the one-particle Green's function (GF) at a finite temperature so that we can extract spectral amplitudes and the excitation energies without knowing the excitation channel invoked at each measurement. In the classical part of the scheme, we adopt an approach that estimates reasonably the GF based on the data collected from the QPE sampling. We dub the approach the QPE averaged over variable grids (QAVG), that may help one to reconstruct the GF via optimization of trial parameters and modeling the probability distributions for various settings of the QPE circuits. We apply the QAVG-DMFT scheme to SrVO$_3$ to demonstrate its validity via numerical simulations.

Quantum phase estimation (QPE) is an underlying technology for extracting the excitation spectra of many-electron systems, yet its practical use on current hardware is hindered by low grid resolution and environmental noises. Here we propose QPE averaged over variable grids (QAVG), a vernier-type approach that combines low-resolution QPE with multiple origin shifts and physically motivated continuous parametrization to reconstruct the spectra accurately. We introduce this approach into an end-to-end workflow for the {\it ab initio}-based model system for a CO molecule adsorbed onto the $χ$-Fe$_5$C$_2$ surface. We perform experiments on Quantinuum H2-2 using both physical QPE circuits and logical QPE circuits encoded in the Steane code with offline bit-flip correction. We demonstrate that QAVG accurately reconstructs the spectra with deviations much smaller than the nominal QPE resolution, even when the noisy histograms are used. The cost landscapes averaged over the shifted grids substantially suppress the local minima arising from the spectral leakage, thereby stabilizing the optimization of trial parameters. These results indicate that QAVG provides a robust route to quantum simulations of correlated spectra toward the era of early-fault-tolerant quantum computers.

Two-dimensional van der Waals materials exhibit a variety of correlated electron phases, and optical driving offers a promising route toward manipulating them. For example, cavity-enhanced, continuous-wave (CW) Raman excitation has been suggested as a way to coherently and superradiantly populate phonons or charge density waves via material excitons. A steady-state phonon population may be sustained with sufficiently strong electron-phonon coupling to drive novel collective response. We describe an apparatus built to meet the requirements of such an experimental program: Namely, an ultrahigh-vacuum system housing a length-tunable confocal Fabry-Pérot cavity with an intracavity sample, both cryogenically cooled and stabilized against vibrations. A four-axis nanopositioner aligns the sample and supports electrical leads for sample carrier density modulation and transport measurements. Transmission through the multimode cavity enables in situ sample imaging for alignment; the sample is a transition metal dichalcogenide in this work. Operating near the confocal geometry concentrates the optical field into a localized supermode that substantially enhances light-matter coupling. This enhancement is preserved despite the millimeter-scale cavity length, which provides room for sample alignment and exchange.

Microwave devices capable of near-quantum-limited signal processing are essential components in the toolbox of solid-state quantum technologies. The manipulation and readout of single-photon microwave signals through amplifiers, mixers, isolators, etc. must fulfill strict requirements in terms of signal integrity to ensure reliable operation. These active microwave quantum devices operate in complex cryo-electronic setups. This poses challenges to their characterization, since all relevant figures of merit must be expressed at the reference planes of their ports. Even though cryogenic S-parameter calibration is non-trivial, metrological approaches are converging toward rigorous methods. Furthermore, preserving signal integrity must be quantified via absolute noise levels at the ports of the Device Under Test (DUT), requiring an absolute power reference. In this work, we present an in situ noise metrology protocol based on substituting a controllable noise source for the DUT. We motivate this choice by showing that placing the noise source at the DUT input impacts the separability of the calibration from the DUT characteristics. Our proposed architecture combines Planck spectroscopy using a Variable Temperature Stage with Short-Open-Load-Reciprocal scattering-parameter calibration, so that noise and scattering quantities are referred to the same cryogenic reference planes. In this configuration, the readout-chain calibration is separated from the internal dynamics of the DUT. As a demanding use case, we apply the protocol to a Josephson Traveling Wave Parametric Amplifier and extract its gain and input-referred added noise under pump conditions activating multimode nonlinear behavior. This illustrates how our device-agnostic protocol supports portable noise characterization of nonlinear cryogenic microwave devices.

Sharing entanglement among multiple users remains a central challenge for scalable quantum networks. Recent work proposed an on-demand entanglement packet architecture in which a controller uses a Time Division Multiple Access (TDMA) approach to allocate network resources. Quantum nodes are assigned a periodic schedule that probabilistically fulfills application requests for end-to-end entanglements. The schedule is recomputed periodically using well-known algorithms, such as Earliest Deadline First (EDF). However, a static schedule offers limited flexibility when outcomes are stochastic and arrivals are asynchronous. To overcome this limitation, we propose an online scheduler that dynamically schedules, defers, retries, or drops entanglement distribution reservations. In our simulations, the dynamic scheduler achieves lower completion time, higher completion ratio, and higher throughput than the static baseline. Furthermore, when the network is overloaded, the dynamic scheduler continues to construct deadline-feasible schedules and degrades gracefully.

We propose a definition of a non-invertible symmetry enriched topological order (NI-SETO), and we implement our definition for string net models. We do so in two ways, using full inclusions of unitary fusion categories (UFCs), as well as anyon condensation. In both cases, the NI-SETO is a relative center of UFCs. All NI-SETOs can be realized in either model, where we can use enriched UFCs to get chiral examples on the boundary of a 3D Walker-Wang model representing the anomaly. We describe several examples of NI-SETOs and compute the qualitative symmetry action on anyons and symmetry defects using tube algebra techniques.

Stokes' theorem turns Abelian Berry phases into curvature fluxes, whereas path ordering precludes such a simple formula for non-Abelian holonomies. We show that a quantitative form of this intuition survives: arbitrary Wilczek--Zee holonomies obey a universal quantum geometric limit~(QGL), in which the holonomy magnitude is bounded by a surface integral of the non-Abelian curvature norm. Recasting holonomic evolution as an effective Stokes--Schrödinger dynamics driven by transported curvature, we identify the QGL as the geometric counterpart of conventional quantum speed limits, with a time-integrated generator norm replaced by a surface-integrated curvature cost. The induced contour--surface variational problem is governed by a non-Abelian Lorentz force, which we address with a brachistochrone ansatz of curvature-weighted geodesics. Applied to an SU(2) tripod dark subspace, near-optimal protocols spontaneously align the transported curvature along a single Lie-algebra direction, effectively taming non-Abelianity.

Variational Quantum Algorithms (VQAs) combine quantum circuits with classical optimization to tackle problems that may benefit from the capabilities of near-term quantum hardware. In knowledge graph embedding, recent proposals based on this approach follow a similar overall architecture but differ in the way they compute the score function and in the number of qubits they require. One design uses $n+1$ qubits and obtains the score through a switch test on an ancillary qubit, while another employs $2n+1$ qubits and applies a swap test between two registers. In both cases, entities and relations are represented in a Hilbert space of dimension $d = 2^n$, with comparable computational cost and the same mean squared error loss. This work introduces a unified framework that captures the two schemes and makes it possible to explore new variants. Within this setting, we propose an alternative that keeps the intuitive meaning of the score function while dispensing with ancillary qubits and entangled measurements. The result is a model better suited to current NISQ devices, reducing hardware demands without sacrificing interpretability.

A set of quantum data can look classical in every local test and still fail to admit a single classical explanation of the whole composite system. We formulate this failure as global contextuality. Here global means global in the physical sense of the whole multipartite system, not the local/global terminology of sheaf theory. Each party's local statistics are noncontextual and each measured multipartite context admits a generalized local hidden-variable description, but the GLHV block descriptions cannot be promoted to a single noncontextual hidden-variable model for the whole system. Three bipartite constructions exhibit this separation. A polarization-path construction gives a direct global obstruction. A qubit-qutrit KCBS construction gives an algebraic scenario-level example, with explicit formulas for the unconditional KCBS operator, the correlation-polytope constraints, and the postselected violation. A flagged qutrit Werner-local state gives a state-level example: the state is entangled and local for all projective measurements, its local qutrit marginals do not violate KCBS, yet postselection rules out a single GNCHV model. We also spell out the classical composition lemma: classical conditional hidden variables can be absorbed into a larger hidden variable, whereas quantum contextual data need not allow such a factorization. Within the general Bell-type framework considered here, with arbitrary parties and arbitrary local compatible contexts, but no cross-party joint measurements, the absence of local contextuality and GLHV-type generalized Bell nonlocality does not imply the existence of a global noncontextual hidden-variable model. Global contextuality is thus a compositional obstruction to classical explanation.

Nonlinear optical light sources enable the generation of photons with quantum states that are intrinsically linked to underlying material dynamics, rather than imposed through external modulation. Here we investigate fundamental quantum communication metrics of four-wave-mixing signal fields generated by the two-dimensional perovskite (PEA)2PbI4. Using polarization-resolved interferometric measurements together with a microscopic nonlinear response model for the Bloch vector, we reconstruct effective single-photon polarization density matrices inferred from the experimental signal fields and evaluate the corresponding Holevo bound and effective secret-bit rates as a function of the coherence time, population time, and detection wavelength. We find that incorporating the coherence-time degree of freedom systematically lowers the Holevo bound by approximately 2.6-5.8% across the various excitonic resonances, indicating reduced distinguishability of the polarization states when the full multidimensional parameter space is sampled. To connect the polarization-state indistinguishability with experimentally achievable throughput, we further introduce an effective secret-bits-per-pulse metric that enables rapid evaluation of secure information throughput for candidate materials without requiring photon-number-resolved detection. For the present system, control of the population time via spin-dependent evolution yields substantially higher secret-bit rates than manipulation of the coherence time, while spectral regions associated with single-exciton and biexciton resonances define complementary operating regimes for secure communication. More broadly, this work positions nonlinear spectroscopy as a framework for exploring how emergent optical materials can generate and structure quantum states in ways that are advantageous for established quantum communication schemes.

Many applications in quantum simulation, quantum chemistry, and quantum machine learning require not a single quantum state but an ensemble of states characterizing the heterogeneity of a target system. Preparing such ensembles state-by-state is prohibitive in both variational and fault-tolerant settings, motivating a generative-modeling approach. We introduce latent-conditioned parameterized quantum circuits (LPQCs), a hybrid quantum-classical framework in which classical neural networks map a latent variable sampled from a prior distribution to the parameters of a parameterized quantum circuit. We prove that LPQCs are universal approximators for probability measures over density operators in the $1$-Wasserstein distance, extending classical universal approximation theorems to the quantum-distribution setting. We additionally introduce a multimodal latent prior and a mixture-of-experts circuit architecture, and show that it empirically alleviates the barren plateau problem during optimization. Numerical experiments validate the framework on a synthetic multi-cluster ensemble of mixed quantum states and on a QM9-derived ensemble of 3-D molecular structures. In these tasks, LPQC outperforms recent quantum generative baselines while remaining competitive with typical classical baselines at substantially reduced output dimensionality. By leveraging classical expressivity in the latent space, LPQCs offer a tractable route to quantum generative modeling.

This paper establishes that Krylov complexity contains the entire information about the dynamics of a quantum operator, extending the list of equivalent quantities that can serve this purpose, such as the Lanczos coefficients, the return amplitude, and the spectral density. To demonstrate this equivalence, an explicit recursive algorithm is constructed to calculate Lanczos coefficients from the Taylor expansion of the Krylov complexity around $t=0$. Furthermore, the paper discusses the distinction between Krylov and spread complexity, clarifying why a similar recursive algorithm cannot exist for the latter without additional dynamical input. These results provide a ``proof of principle'' for using Krylov complexity as a complete characterization of operator evolution in quantum systems.

We run a numerical linked-cluster expansion with a quantum algorithm (NLCE+QA), computing ground-state energies and one quasi-particle dispersions in the thermodynamic limit using a 20-qubit trapped-ion quantum processing unit (QPU). The NLCE+QA framework extracts thermodynamic-limit properties from small-cluster calculations, making it naturally suited for near-term quantum devices. Projector-based block-diagonalization schemes such as projective cluster-additive transformation (PCAT) are essential to NLCE+QA, and they involve matrix inversion and square root operations that amplify measurement noise. A central question is therefore whether current hardware can provide expectation values that are accurate enough to withstand non-linear classical post-processing. We explore this challenge for the transverse-field Ising model (TFIM) in one dimension, on a ladder geometry, as well as in a longitudinal field in one dimension. For the quantum algorithm, we consider adiabatic state preparation (ASP), as well as a variational quantum eigensolver (VQE) trained on a classical device. The final expectation values are obtained from the QPU, using a novel alternative to the Hadamard test that we name the CX-test. We explore the regimes currently attainable on quantum devices and comment on the improvements needed for quantum computers to achieve results beyond classical reach.

In this note, we formulate the notions of the direct and inverse problems and contact points for the Feynman diagrams. For the electron-photon interaction case, the solutions of these direct and inverse problems are presented. The interrelations between Feynman diagrams and the classical colored graphs are discussed.

We present a theoretical investigation of coherent control over the orientation of an individual molecule strongly coupled with a cavity using chirped-pulse driving. Specifically, we explore the dynamics of carbonyl sulfide (OCS) molecules under the influence of two chirped pulses with different spectral phases. We compare two pulse configurations: one with equal chirp rates ($β_{+} = β_{-}$) and another with unequal chirp rates ($β_{+} \neq β_{-}$). Numerical simulations reveal that chirped pulses enable precise control of the molecular orientation, achieving a maximum orientation degree of 0.5773. By analyzing the distribution of molecular polariton states, we show that chirped pulses can activate multiphoton processes, leading to deviations from the predictions of first-order Magnus expansion methods. Additionally, we demonstrate the robustness of the maximum orientation with respect to chirp amplitude and detuning, providing insights into the role of pulse parameters in optimizing control. This work introduces a new strategy for controlling molecular orientation in cavity-based systems and offers valuable perspectives for future experimental applications.

Matrix product states (MPS) serve as a key tool for studying quantum systems from chemistry and condensed-matter physics, making their preparation on quantum computers an important task in interfacing classical and quantum simulation. Many systems of interest have $U(1)$-symmetries induced by particle number and spin projection conservation, allowing to restrict the MPS tensors to be of block-sparse form, a property widely used in the implementation of classical algorithms such as the density matrix renormalization group. We reduce the cost of fault-tolerantly preparing block-sparse MPS within the standard ancilla-assisted linear-depth approach by implementing row and column permutations that transform the block-sparse matrices into block-diagonal form. These block-diagonal unitaries are then implemented via unitary synthesis, with the cost being determined by the size of the largest block. In this context, we modify the unitary synthesis approach of Berry et al. in order to reduce the Toffoli cost for real-valued unitaries by a factor of $\sqrt{2}$. In numerical benchmarks, we achieve Toffoli cost improvement factors of $10 - 30$ compared to the state-of-the-art for MPS of various molecular systems.

Due to their exceptional isolation from the environment, magnetically levitated particles are explored as extremely sensitive mechanical sensors. For future gravity experiments on quantum superpositions, such systems need to be cooled close to their ground state. To demonstrate the combination of state of the art vibration isolation, milligram levitated high Q mechanical resonators and position detection with low noise, we present linear feedback cooling of a magnetically levitated gravity sensor to below 2 picometer amplitude and below 10 millikelvin mode temperature for two translational modes (the x- and y-mode) simultaneously. The sensor is a levitating permanent magnet in a type I superconducting trap, where its six resonance frequencies are measured with a superconducting coil coupled to a DC SQUID. This signal is measured with a lock-in amplifier and a feedback signal is sent to a piezoelectric actuator, allowing the cooling of resonant modes at 50.6 and 68.0 Hz simultaneously. These two translational modes have Q factors of $3.8 \cdot 10^6$ and $5.5 \cdot 10^6$ respectively. The experiment is mounted inside a dry dilution refrigerator where it is vibrationally attenuated with 110-130 dB at these frequencies. In this work, we discuss future improvements on the setup which may enable quantum ground state cooling on a magnetically levitated particle, that has previously been shown to be a gravitational sensor.

Dynamic circuits use real-time outcomes of mid-circuit measurements, processed by a classical controller, to adapt subsequent operations during circuit execution. This additional flexibility over static circuits comes at a price. Mid-circuit measurements are typically slower and noisier than unitary gates. Furthermore, classical feedforward requires exchanging information between the quantum processor (QPU) and the classical controller, introducing latency that erodes the practical performance of dynamic circuits. We propose a compile-time optimization framework that reduces the use of classical controls in dynamic circuits while preserving their semantics. At its core, the framework uses a static analysis that symbolically executes the circuit by propagating classical information alongside the quantum state. By combining this classical-quantum information with the Probabilistic Circuit Model extended with probabilistic controls that emulate classical feedforward, we obtain an intermediate probabilistic representation of the dynamic circuit. In this representation, mid-circuit measurements and classically controlled operations can be removed or rewritten as purely unitary operations and probabilistic components. Compared to existing compile-time optimizations that target only mid-circuit measurements, our method applies to a broader class of dynamic circuits expressible in modern quantum programming languages. We evaluated our framework on randomly generated dynamic circuits, achieving about 50% classical feedforward reduction and even higher reductions in favorable settings.

Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an alternative approach that avoids an explicit treatment of the continuum by formulating the problem in terms of discrete quantum states. Our discussion is based on the stabilization method, in which the system is confined to a finite region such that the continuum is replaced by a discrete energy spectrum. Resonances then appear as characteristic features in the energy levels under variation of the confining box size, providing an intuitive interpretation in terms of a two-level system while remaining closely connected to standard quantum mechanics curriculum. We review the method, derive selected results, and discuss practical strategies for extracting resonance parameters from stabilization diagrams. In addition to established fitting procedures, we introduce a novel approach based on the analysis of spatial localization of resonant states, which enables a robust identification of resonance properties. The approach is illustrated using both attractive and repulsive delta-shell potentials, which serve as simple and instructive model systems amenable to analytical treatment.

Genuine multipartite entanglement and full inseparability are two inequivalent quantum resources. Even though all genuinely multipartite entangled states are also fully inseparable, not all fully inseparable states are genuinely multipartite entangled. There exist fully inseparable states that can be prepared as convex mixtures of states separable with respect to different bipartite splits. Here, we are interested in examples of Gaussian states that possess this type of entanglement, so-called fully inseparable biseparable states. We show for several archetypical families of multimode Gaussian states that fully inseparable biseparable candidate states are actually genuinely multipartite entangled. Using projections to finite-dimensional subspaces and fully decomposable witnesses, we observe a shrinking of the regions of potentially fully inseparable biseparable Gaussian states with growing dimension of the projection subspaces. We therefore conjecture that all fully inseparable Gaussian states are genuinely multipartite entangled.

Molecular rectifiers, as prototypical components of molecular electronics, present unique opportunities for pushing device miniaturization to its ultimate limits. Nevertheless, challenges including limited rectification ratios (RR), insufficient robustness, and poor reproducibility impede their practical deployment. To make molecular rectifiers competitive with silicon-based devices, it is important to fully understand the design principles and fabrication methods from both mechanistic and experimental perspectives. By holistically considering the transport mechanisms, modulation strategies, fabrication, characterization techniques, and theoretical simulations, this review provides a comprehensive overview of molecular rectifiers. Representative examples of conceptually significant and high-performance molecular rectifier systems are highlighted to illustrate the relationships between rectification mechanisms, molecular design strategies, and device realization. Building on these discussions, we present an outlook for current bottlenecks and future directions to guide the development of molecular rectifiers. This review aims to serve as both a conceptual framework and a technical reference for researchers working at the intersection of molecular electronics and nanoscale device engineering in the post-CMOS era.

In recent years, light detection and ranging (LIDAR) has seen a steep rise in the sensitivity of measuring the distances of remote objects. Here, we propose to enhance the sensitivity of LIDAR even further by exploiting Dicke's concept of superradiance, i.e., the collective light emission of statistically independent light sources. By using $N$ thermal light sources (TLS) and measuring intensity correlations of order $m \geq 2$ instead of $m=1$, i.e., the intensity, we show that the Cramér-Rao bound on the measurement of the distance of a remote object undercuts that of traditional LIDAR by a factor of $N$, and can be reduced further with increasing correlation order $m$. Our numerical calculations are supported by analytical expressions for the special cases of two and three TLS and a general approximate expression for any number of TLS.

Quantum Cramér--Rao theory is intrinsically local: it bounds precision near a specified parameter value, and its saturating measurement generally depends on that value. Barankin-type bounds use finite parameter displacements, but remain anchored to a chosen reference value. This leaves open a basic global-estimation problem: when the parameter is known only within a broad domain, what precision can be guaranteed by a single estimator and a single measurement strategy fixed before the true value is localized? We answer this question by introducing global score functions tied to a weighted variance over the whole parameter domain. Their correlations generate a hierarchy of precision bounds: global Cramér--Rao and Barankin-type bounds arise as restricted levels, whereas unrestricted score correlations yield a fully global bound for the prescribed weighted variance. The hierarchy recovers local Cramér--Rao theory in the many-repetition limit and reveals genuinely global precision limits for finite data over broad domains. In the quantum setting, the construction identifies when this fully global bound can be realized by a single parameter-independent measurement. The same framework extends to Bayesian estimation, recovering the Van Trees bound in the local limit while yielding stronger finite-width lower bounds on the Bayesian mean-square error beyond this limit.

Parametric Hamiltonians often exhibit point-like spectral degeneracies (diabolic points, or conical intersections), which can lead to singularities in the Provost-Vallee metric of eigenstate manifolds. We regularise the metric by a coordinate transformation and develop a formalism in which diabolic points act as bridges between adjacent eigenstate manifolds, glueing them into a single connected state manifold. We characterise the topology of this structure and refine the rules for nodal lines governing the Berry phase. The connected state manifold restores the numerical stability near diabolic points, enlarges the class of geodesics allowing for new geodesic shortcuts, and provides a new mechanism for Berry phase computation, even along paths traversing diabolic points.

We propose a practical computational framework for detecting structural changes in parameter-dependent topological data. In many applications, such as time-series data analysis, anomaly detection, and monitoring of systems under changing control parameters, persistence diagrams describe the birth and death of topological features at each parameter value, but they do not fully capture how these features are reorganized over time. To address this limitation, we represent homological features by zero modes of the ordinary combinatorial Hodge Laplacian and track the corresponding feature spaces in a common ambient chain space. This allows us to compute curvature and holonomy as descriptors of local reorganization and accumulated memory in evolving topological structures. Curvature highlights parameter regions where homological features mix or change rapidly, while holonomy summarizes the net effect of such changes after a closed cycle. We also establish stability estimates showing that these descriptors are robust under perturbations of the Hodge Laplacian on regular regions. Numerical experiments on controlled time-dependent point-cloud data show that the proposed method detects tracking instability, distinguishes systems with nearly identical persistence diagrams, and captures cycle-level memory invisible to pointwise feature matching. These results suggest that zero-mode transport geometry can serve as a useful computational tool for analyzing dynamic topological data.

Quantum light sources such as squeezed light are essential for quantum information science and technologies, but the scalable production of multiple beams of them remains a challenge. Here,we experimentally demonstrate a novel approach to the generation of a large spatial array of polarization-squeezed light beams via atomic-coherence-enhanced nonlinear optical processes using a single atomic vapor cell. Unlike schemes based on independent squeezing generators, the squeezing dynamics of each channel here are governed by a common collective ground-state atomic coherence, produced by all input beams, homogenized by the thermal motion of the atoms, and protected against wall collisions by a paraffin coating. Consequently, the optical states of all channelsare coupled and regulated by each other via the moving atoms, leading to synchronization behavior.We realized a 30-beam array of polarization squeezed state with 2.03 dB of squeezing, experimentally verified the synchronization, and observed improved purity of the squeezed state as well as the system response to perturbations when the size of the array increases. This work provides a pathway towards scalable high-performance quantum light sources for applications in precision measurement, quantum imaging and quantum information processing.

Levitated mechanical systems are promising candidates for quantum gravimetry, as gravity couples directly to their center-of-mass motion, enabling the large mass of a mesoscopic particle to serve as a sensing resource. In this paper, we propose a mechanical squeezed-Fock qubit gravimeter using a Duffing oscillator that is driven by a detuned two-phonon pump. In the squeezed-Fock basis, the gravitational force couples to the anti-squeezed quadrature, which enhances the gravity-induced transition rate while preserving the direct mass scaling of the mechanical force coupling. We show that sensitivity improves with reduced effective qubit splitting that is controlled by the squeezing parameter and the Duffing nonlinearity. We further analyze mechanical damping and show that squeezing converts ordinary dissipation into anisotropic qubit noise, setting a practical trade-off between signal amplification and decoherence rate. These results identify the mechanical squeezed-Fock qubit as a new platform for quantum-enhanced gravimetry.

Optical control of electron-generation sites has broadly enabled ultrafast nanoscale imaging, spectroscopy, and functional control. Existing approaches achieve nanoscale site selectivity by shaping localised optical fields around nanostructures, thereby limiting independent site selectivity within the same local-field hotspot. Here, using a single-molecule electron emitter, we show that site selectivity can instead be encoded in the electronic excitation pathway, enabling subnanometric control of electron birth sites within the same local-field hotspot. By tuning the photon energy, we selectively access molecular states of different spatial symmetry and reversibly switch the electron birth site between distinct locations in the same emitter, with the change read out directly in the far-field emission pattern. The switching depends on photon energy alone and is absent under variations in intensity or polarisation. Our results establish optical birth-site selectivity that is not dictated by the local-field distribution, opening a route to electron birth-site control through the electronic excitation pathway.

Heat conduction in low-dimensional systems exhibits strong deviations from Fourier behavior due to anharmonicity and long-lived vibrational correlations, challenging conventional computational approaches. The $β$-Fermi--Pasta--Ulam--Tsingou ($β$-FPUT) chain provides a minimal nonlinear lattice model for studying anomalous transport, yet its quantum real-time dynamics remain difficult to access with classical methods. We develop a first-quantized digital quantum-simulation framework for the quantum $β$-FPUT lattice, targeting fault-tolerant quantum computers. By working directly with discretized lattice displacements rather than truncated phonon occupation spaces, the approach captures anharmonic interactions while avoiding bosonic encoding overheads. We construct Trotterized circuit blocks for real-time evolution and introduce a Hermitian quadrature decomposition of Fourier-mode displacement operators that enables shallow quantum circuits for mode-resolved displacement correlators. We analyze the quantum resources required for the full simulation and measurement workflow, providing qubit counts, gate complexity, circuit-depth and resource estimates as functions of system size and resolution within a fault-tolerant workflow. These results establish a concrete algorithmic blueprint for simulating quantum transport dynamics in nonlinear low-dimensional lattice models on fault-tolerant quantum hardware.

In traditional quantum computing, it has been established that real quantum computation augmented with non-Clifford gates is as powerful as universal quantum computation. Here we investigate this phenomenon in the non-Hermitian setting. We show that a non-Hermitian quantum computer equipped with the real gate set ${H, \text{CCNOT}, G}$, where $G = \operatorname{diag}(g^{-1}, g)$ with $g > 0$ and $g \neq 1$, can solve problems in $\text{P}^{\sharp\text{P}}$ in polynomial time, matching the capability of its universal non-Hermitian counterpart ${H, T, \text{CNOT}, G}$. This demonstrates that non-unitarity, rather than universality, is the essential resource, and that complex numbers are unnecessary.

Fluid simulations, especially at high Reynolds numbers, are computationally expensive on classical computers, making them promising application targets for quantum computing. Recent studies have combined the lattice Boltzmann method (LBM) with Carleman linearization to design quantum algorithms for computational fluid dynamics (CFD). However, practical quantum-circuit implementations of these algorithms that incorporate non-periodic boundary conditions have not been fully explored. In this work, we implement a quantum algorithm for two-dimensional linearized fluid flow around an obstacle, using block-encoding of the linear-system matrix and quantum singular value transformation (QSVT) to solve it. Inflow, outflow, and no-slip boundary conditions are formulated as sparse matrix operations and efficiently embedded into quantum circuits using index-value encoding. We demonstrate logarithmic scaling of the required numbers of qubits and gates with respect to the number of lattice points, suggesting the potential feasibility of quantum-computational fluid dynamics simulations.

Critical exceptional points (CEPs) are nonequilibrium critical points in open many-body systems at which multiple collective excitation modes coalesce. CEPs are known to amplify classical fluctuations, but their effect on genuinely \textit{quantum} fluctuations remains unclear. Here, we show that dissipative collective-spin systems hosting CEPs exhibit parametrically enhanced steady-state \textit{quantum} spin squeezing. Close to the CEP, the optimally squeezed variance scales as $|Z|$, whereas the anti-squeezed variance diverges as $|Z|^{-1}$, with $Z$ the dimensionless order parameter. Importantly, the anti-squeezed fluctuation direction asymptotically aligns with the coalescing eigenvector of the stability matrix, reflecting the defective nature of the CEP dynamics. These scalings are robust against dephasing channels generated by spin components orthogonal to the coalesced critical collective mode. Our results identify CEPs as a route to engineering steady-state anisotropic quantum fluctuations and correlations in driven-dissipative platforms.

Decoherence is mostly detrimental in quantum information and quantum optics applications. However, the interplay between environment-induced incoherent dynamics and unitary evolution can give rise to novel quantum many-body phenomena that can be harnessed as a useful resource. As is well known, in dense subwavelength atomic arrays only a single collective eigenmode in the single-excitation manifold couples strongly to free-space radiation, exhibiting superradiant spontaneous emission. Most of the remaining eigenstates form a manifold of weakly radiative modes, giving rise to long-lived subradiant excitations. Here we demonstrate that populating these subradiant modes via additional decoherence mechanisms, such as dephasing or coupling to phonons, can significantly enhance single-photon absorption in a nanoring of quantum emitters. Such nanoring geometry is particularly appealing due to its unique optical properties and its resemblance to natural light-harvesting complexes, which serve as efficient antennas in photosynthesis. Our findings may shed light on fundamental aspects of energy absorption in nature; despite the much greater complexity of biological systems, they may nonetheless operate according to similar underlying optical principles.

We study correlations between two Unruh-DeWitt detectors coupled to a scalar field in a cylindrical cavity. Boundary conditions strongly modify the detector-correlation dynamics relative to free space. The entanglement negativity is suppressed in the cavity and vanishes for smaller separation as compared to the free space. Increasing the cavity radius does not recover the free-space behavior of the negativity. In contrast, mutual information and quantum discord remain nonzero over much larger separations. While the mutual information decays monotonically with separation, the quantum discord is enhanced near the cavity boundary. Our results demonstrate that geometric confinement can selectively suppress distillable entanglement while preserving and even enhancing more general non-classical correlations, providing a controlled setting to probe the hierarchy of correlations in quantum field theory.

Designing compact and accurate circuits for the variational quantum eigensolver (VQE) is a central challenge in near-term quantum chemistry. Existing adaptive methods such as ADAPT-VQE design circuits by iteratively selecting operators from a predefined pool guided by gradient information and greedy heuristics. In this work, we adopt differentiable quantum architecture search (DQAS) as a circuit design framework based on the UCCSD operator pool, and introduce two complementary strategies: a global mode that simultaneously optimizes all operator selections, and a layerwise mode that constructs circuits incrementally while preserving previously learned structure. By relaxing discrete operator selection into a continuous differentiable optimization, DQAS enables gradient-based exploration over the combinatorial space of UCC circuit architectures. Benchmarks on BeH2, H4, LiH, H6, and H2O (8-14 qubits) show that both strategies achieve higher accuracy and fewer CNOT gates than ADAPT-VQE in the compact circuit regime, with up to 2.7-fold accuracy improvement for H2O and CNOT reductions of 13-17% at equivalent circuit depths. Benchmarks on the qubit-excitation-based (QEB) operator pool confirm that both advantages generalize beyond UCCSD. These results demonstrate that differentiable architecture search provides an effective and generalizable framework for designing accurate and compact VQE circuits in near-term quantum chemistry.

Subspace diagonalization techniques based on quantum sampling, such as quantum selected configuration interaction (QSCI) and sample-based quantum diagonalization (SQD), have recently emerged as promising quantum-centric approaches for approximating ground-state energies of many-body systems. However, their performance is fundamentally limited by an intrinsic trade-off between sampling efficiency and the sparsity of the ground-state wavefunction, which becomes particularly severe in strongly correlated systems. Here, we introduce a filter-assisted SQD protocol that engineers wavefunction sparsity via a quantum filter, i.e., a unitary transformation of the Hamiltonian designed to concentrate the ground-state weight onto a small number of computational basis states. Using the Gini coefficient as a robust sparsity measure, we establish a quantitative relationship between wavefunction sparsity and the resource requirements of SQD, providing theoretical bounds on the required subspace dimension and sampling cost. To realize the quantum filter, we employ a tensor-network-based circuit-encoding algorithm that maps target states to quantum circuits with controllable fidelity. We benchmark our approach on the quantum Ising model with transverse and longitudinal fields using both numerical simulations and quantum hardware experiments. Our results demonstrate that, compared with standard SQD, the proposed protocol significantly enhances wavefunction sparsity, reduces ground-state energy estimation errors by orders of magnitude, and substantially lowers sampling overhead. These findings establish filter-assisted subspace diagonalization as a powerful and scalable framework for quantum many-body calculations in the strongly correlated regime.

The Einstein-Bohr recoiling-slit gedankenexperiment, a cornerstone of quantum complementarity, has long been constrained by the zero-point fluctuations of the atomic slit -- the spatial Standard Quantum Limit (SQL). Here we transcend this fundamental boundary through active quantum state engineering of a single-atom slit. By implementing a non-adiabatic quench-evolve-quench protocol, we prepare the atomic motion in a squeezed state, dynamically redistributing phase-space uncertainty to suppress which-path information and restore high-visibility interference beyond the static vacuum limit. We report an intrinsic visibility of $0.938_{-0.008}^{+0.004}$, violating the SQL ($0.819$) by over 10 standard deviations, corresponding to $7.6(2)$ dB of effective squeezing. Our work reveals Kerr-induced non-Gaussian dynamics and reinterprets the traditional interferometer as a powerful tool for continuous-variable Wigner tomography, bridging the gap between quantum foundations and advanced metrology.

Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and quantum-data settings, sensitive to small eigengaps, and unnecessary when downstream tasks only require principal-subspace scores. Such score-based objectives are important in applications such as anomaly detection, spectral-energy profiling, and other postselection tasks. To address these needs, we introduce a measurement-based soft PCA framework replacing the hard top-$k$ projector with an entropy-regularized Fermi--Dirac filter. This filter is the unique optimizer of an entropy-regularized variational formulation of PCA and converges to the classical PCA projector in the zero-temperature limit. This filter has a direct interpretation as a quantum measurement, which naturally suggests a quantum approach. For centered covariance operators represented by quantum feature states, a single fixed circuit, together with threshold calibration, accesses all optimal filters for different rank budgets or retained-variance levels without rank-dependent circuit updates or eigenvector recovery. For new inputs, the same calibrated quantum circuit yields soft principal subspace scores, spectral energy profiles, and postselected filtered states. The required centering of both training and test data is performed coherently inside the quantum protocol, which is particularly important for quantum data where no classical feature vectors or centered Gram matrix are directly available. By reframing PCA as a calibrated measurement task, this framework bypasses the need for iterative eigenvector extraction and achieves a dimension-independent sample complexity $O(η^{-2})$ for normalized fractional-rank or retained variance scoring at additive accuracy $η$.

The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new paradigm. This paper presents a comprehensive benchmarking study of classical and quantum machine learning models for image recognition on the MNIST handwritten digit dataset, evaluating both traditional models, a Classical Support Vector Machine (CSVM) and a Quantum Support Vector Machine (QSVM), and deep neural network models, a Classical Convolutional Neural Network (CCNN) and a Quantum Convolutional Neural Network (QCNN), across four performance dimensions: classification accuracy, computational runtime, parameter count, and memory requirements. Experiments are conducted as functions of both feature dimensionality and sample size, and across CPU and GPU execution environments, providing a controlled, multidimensional comparison to address gaps in prior work. For the SVM-based models, QSVM consistently outperforms CSVM in accuracy, reaching $\sim$ 0.90 versus $\sim$ 0.85 at 1,000 samples, with a higher computational cost. A feature count of 10 qubits and a sample size in the range of 200 -- 500 emerge as practical operating points that balance accuracy and runtime. For the neural network models, CCNN and QCNN achieve comparable classification accuracy, both exceeding 0.96 at 64 features and 60,000 samples, yet QCNN offers substantially superior parameter and memory efficiency, requiring $\sim$ 94\% fewer parameters and $\sim$ 75\% less memory than CCNN at higher feature counts, while incurring higher runtime. Across both model families, quantum models consistently outperform classical models by greater margins in accuracy as feature dimensionality or sample size increases.

Quantum computing is a promising technology for accelerating partial differential equation solvers applied to large-scale real-world problems. However, reconstructing a classical representation of the solution from the quantum state remains a significant bottleneck. We propose a problem-specific method, called proper orthogonal decomposition-based readout (PODR), to improve readout efficiency by precomputing characteristic features of the solution. The present method consists of an offline stage and an online stage. In the offline stage, a set of basis functions representing the dominant features of the target problem is constructed from representative solution data using classical computations. In the online stage, the quantum state is projected onto this reduced basis, and only the minimal set of weight coefficients is extracted to reconstruct the solution. Since the offline stage is carried out only once, the proposed PODR method is especially advantageous for simulations with varying parameters, which are common in computational fluid dynamics (CFD). Futhermore, we apply the proposed method to benchmark problems in fluid dynamics and demonstrate that PODR significantly reduces both the number of measurements and the computational resources in the online stage compared with conventional readout methods.

We elucidate the Bures metric in quantum state space near a rank-changing point of the density matrix and show contrasting behavior for two-level ($N=2$) systems versus higher-level systems. Due to the smooth pure-state boundary for $N=2$, we prove the apparent metric divergences to be merely coordinate artifacts and present three Lindblad processes exhibiting qualitatively different evolution near rank-changing points, showing geodesic approach, power-law scaling, and pure-state escape law. For higher-dimensional ($N\ge 3$) systems, the geometry near a rank-changing point differs fundamentally. Under suitable restrictions of the density matrix and its approach towards a pure state, the Bures metric reduces to a conical metric with the pure state at the cone tip. Such a conic geometry leads to genuine curvature singularities: A two-dimensional cone exhibits a Dirac delta-function curvature near the tip while a higher-dimensional cone shows a power-law divergence of the curvature towards the cone tip. A construction of Lindblad evolution for $N=3$ systems with conic singularities is presented, along with possible implications for future experimental and theoretical research.

We introduce noise-adaptive quantum key distribution (QKD) protocols, in which the honest parties optimize the encoding (state preparation) and decoding (measurement basis) operations according to the noise models affecting the honest subsystems induced by an eavesdropper. This extends conventional QKD schemes that employ fixed encoding and decoding strategies independent of the noise characteristics of the communication channel. We investigate three representative protocols: entanglement-based secure dense coding (SDC), the entanglement-free Lucamarini and Mancini (LM05), and a two-way prepare-and-measure Bennett Brassard (BB84) protocols. Using entropic uncertainty relations, we derive the corresponding secret key rates for both adaptive and conventional non-adaptive scenarios under collective attacks. For independent but identical noise acting on the forward and backward transmission channels, as well as for correlated and non-Markovian environments, we identify classes of channels for which adaptive schemes yield enhanced secret key rates for the considered protocols. In contrast, we also determine Pauli channels, including depolarizing and bit flip channels, for which adaptive strategies provide no benefit. We further show that these optimal sets are generally non-unique and can differ substantially from the unitaries that maximize dense-coding capacity in the absence of security constraints. Our results establish noise-adaptive encoding and decoding as a powerful framework for improving secure communication over realistic noisy quantum channels.

A lead-vacancy (PbV) center in diamond exhibits coherent emission above the liquid helium temperature, making it highly attractive for quantum network applications. Here, we report the magneto-optical and spin properties of PbV centers in diamond. We record a spin lifetime of 12 ms at 7.5 K under large off-axis magnetic field. Furthermore, we observe formation of the coherent dark state by coherent population trapping and estimate a spin dephasing time of 354 ns at 6.5 K. This work demonstrates the outstanding thermal robustness of the PbV spin compared to other group-IV centers above 4 K.

The Variational Quantum Eigensolver (VQE) is a fundamental algorithm in quantum computing, yet a coherent geometric characterization of VQE remains missing due to fragmented analyses across fixed-ansatz and adaptive-circuit formulations. In this paper, we establish a geometric analysis of VQE in terms of optimization landscape, initialization guarantee, and noise robustness. First, we study the optimization landscape via an ansatz-free product-unitary formulation over the unitary group, unifying both paradigms. For the single-unitary case, we establish linear convergence of Riemannian gradient descent (RGD) and prove the strict saddle property. For the product-unitary case, we show the convergence rate deteriorates polynomially with circuit depth, providing a geometric explanation of the barren plateau phenomenon. Second, we prove that small-angle random Pauli-rotation circuits satisfy the required initialization conditions with high probability. Third, we show that RGD retains linear convergence under finite-shot measurements, and that coefficient-adaptive allocation achieves strictly lower statistical error than uniform sampling under a fixed measurement budget.

Precision interferometry with atomic wavepackets confined in a one-dimensional optical lattice is an emergent paradigm in quantum sensing of forces and fields, with applications in gravimetry, accelerometry, geophysics, and fundamental physics tests. We report on the realization of a lattice-trapped interferometer where the two arms are sourced from a weakly-interacting ytterbium Bose-Einstein condensate, coherently split and trapped by pulsed optical standing waves before recombination. We directly observe atomic interactions through contrast changes and phase shifts of the interferometer. By changing either the atom number or the sample volume to vary the density, we demonstrate control over interactions and optimize interferometer performance. Our observations are effectively captured by a mean-field theoretical model of the system. This work experimentally probes the boundary where improved performance from source brightening through higher phase space density transitions into a regime beyond single-atom physics in lattice-trapped atom interferometry, and opens a door to incorporating many-body effects for metrological advances in such platforms.

Atomic parity violation (APV) provides a low-energy probe of the weak interaction between electrons and nuclei, complementary to collider tests of the Standard Model. Isotope-chain measurements are especially attractive because they test weak-charge scaling while reducing dependence on absolute atomic-structure theory. We review the APV mechanism, the state of the art in Cs and Yb, and recent trapped-ion, optical-lattice, and molecular proposals. Motivated by progress in coherent control of atoms, ions, and molecules, we ask a metrological question: given N probes distributed over an isotope chain, what quantum strategy optimally measures a deviation from Standard Model weak-charge scaling? The optimum is a particular form of a cross-isotope cat state protocol. We compare this protocol with the standard quantum limit, squeezed-array, same-isotope cat, and discuss extension to recently suggested decoherence-free subspace protocols. We show that entanglement can strongly accelerate statistical averaging, but the ultimate precision is set by APV-specific systematic floors which require careful studies.

We train an instantaneous quantum polynomial-time (IQP) Born machine on real high-energy-physics calorimeter shower images at $64$ qubits and compile the trained model into a single sampling-hard IQP circuit for quantum deployment. The pipeline has three components: a Mixture-of-IQP (\moiqp{}) architecture, whose Walsh-diagonal MMD$^{2}$ loss is classically trainable by Van den Nest Fourier Monte Carlo; the Pearson-Stabilized Correlation Kernel (\psck{}), a positive-definite MMD kernel that biases descent toward correlation-sensitive directions through a data-evaluated Jacobian of the empirical Pearson matrix; and an exact deferred-measurement compilation of \moiqp{} into a single IQP circuit on $\nfeat + \lceil \log_2 \Lcomp \rceil$ qubits (\ciqp{}). Across five seeds at $\Lcomp = 8$, $1500$ epochs, the model reaches $\maerho = 0.069 \pm 0.008$ against a $0.052$ encoding-fidelity floor on the training split and $0.071 \pm 0.008$ on a held-out test split, versus a Liu--Wang baseline at $\maerho = 0.100$. The compiled \ciqp{} reproduces the \moiqp{} marginal to $0.591 \pm 0.012$ times the Monte Carlo noise floor.

We introduce a new class of quantum channels, the Generalized Multilevel Amplitude Damping (GMAD) channels, to model noise and decoherence effects in a qudit coupled to a thermal environment. The degradation of energetic resources under GMADs is investigated by evaluating work functionals and ergotropic capacitances, with particular attention to the coherent and incoherent contributions to ergotropy, for which we introduce new quantifiers. Our analysis sheds light on how to optimally prepare a qudit in a thermal environment in order to preserve its value from the perspective of work extraction, and reveals several counterintuitive phenomena: the ergotropic capacitance of a GMAD channel is not monotonic in the temperature of the environment; moreover, iterating the map can lead to crossings between ergotropic functionals at different temperatures, indicating the presence of a Markovian Mpemba effect.

We study spin and entanglement dynamics in spin-1/2 XXZ chains under periodic monitoring and show that this system exhibits two measurement-induced phase transitions: a steady-state entanglement phase transition similar to those in monitored quantum circuits and a ballistic-to-diffusive transition in transient dynamics. Specifically, we discover that at low monitoring rate, an initial configuration containing a domain wall $|\uparrow\uparrow\uparrow\ldots \downarrow\downarrow\downarrow\ldots\rangle$ spreads ballistically while, at large monitoring rates, the domain melting is diffusive. Extensive numerical simulations, supported by theoretical arguments, indicate that the ballistic-diffusive transition is intimately interlinked with the entanglement phase transition. In contrast to the entanglement phase transitions, which require exponentially complex postselection, the ballistic-diffusive transition can be observed without postselection and constitutes an experimentally accessible manifestation of the many-body Zeno effect.

Transport-induced self-sustained oscillations in electromechanical systems convert a static electrochemical bias into robust, autonomous oscillatory motion in the absence of any external periodic drive. However, an exact description of such self-oscillations remains challenging in nanoscale electromechanical devices featuring a simultaneously large bosonic Hilbert space, strong interactions, and structured fermionic leads. We formulate a tensor-network framework that combines a binary representation of the vibrational mode with mesoscopic reservoir embeddings that enable controlled access to the self-oscillatory steady states and relevant transport observables without explicit real-time propagation. We demonstrate the emergence of mechanical self-oscillations across a broad set of operating conditions, in which strong electromechanical backaction, nonadiabatic oscillator dynamics, and energy-dependent electronic tunneling processes compete. Furthermore, we observe that for both slow and fast vibrating mechanical modes, suppressed vibrational occupation fluctuations in the self-oscillation window along the electromechanical coupling strength sweep is preceded by a peak in the occupation fluctuations. Collectively, we explore how both intrinsic system properties and environmental parameters govern such autonomous oscillations over a broad range of operating conditions. The generality of our framework will enable the method to be employed straightforwardly to more complicated or experimentally relevant scenarios.

We report a comparative analysis of three dynamic neural network (NN) architectures -- NAR, NARX, and NIO -- to evaluate their efficiency in estimating the critical-measurement-strength parameter ($c_{crit}$) characterizing topological phase transitions in geometric phases induced by weak measurements. Our results demonstrate that the NARX architecture achieves superior predictive fidelity, reaching a Mean Squared Error (MSE) of $10^{-27}$ -- the limit of numerical precision -- at an optimal delay of $d=1$. This exceptional performance implies the identification of a perfect functional identity, suggesting that the relationship between winding numbers $W$ and $c_{crit}$ is mathematically deterministic. We observe a "complexity paradox" where the NARX model's accuracy collapses at higher delays ($d=4$), a phase-sensitivity that confirms the model captures a high-precision dynamic mapping rather than a trivial pattern. While the NAR model remains robust for local-trend capture, the NIO architecture fails to accurately resolve the phase transition despite increased neuronal capacity. These findings underscore that both autoregressive feedback and immediate exogenous context are essential for the exact characterization of topological phases, establishing NARX as a robust framework for deriving governing laws in complex quantum systems, where analytical solutions remain elusive.

Classical simulation of many-body quantum systems remains economical only when wavefunction amplitudes stay localized in the working basis. Fixed-basis sparse-state simulators scale memory as $\mathcal{O}(k)$ by keeping the largest computational-basis amplitudes; however, fidelity drops once entanglement or basis rotations spread weight across the Hilbert space. In this work, we introduce an algorithm called Basis-Adaptive Sparse-State Simulation (BASS), which updates each qubit's local representation basis during execution rather than locking the computational basis for the entire circuit. Before truncation, each qubit is rotated into the eigenbasis of its single-qubit reduced density matrix, following the natural-orbital idea from quantum chemistry, so the retained amplitudes stay clustered. We prove that top-$k$ selection is uniquely optimal for one-step truncation in any fixed basis and that the one-body reduced-density-matrix eigenbasis is a stationary product basis for the inverse participation ratio (PR), with a residual bounded by local entanglement coherence. We perform a systematic benchmarking over a variety of quantum circuits and demonstrate that the ratio \(k/\text{PR}_Z\) (sparse budget over computational participation ratio) serves as an indicator for regimes in which adaptive measurement bases provide a performance advantage. On structured brickwork circuits, BASS achieves substantially higher fidelity than the fixed-basis approach, while incurring only a moderate increase in wall-clock time in the memory-limited regime. Moreover, for disordered Ising circuits, BASS systematically provides an improvement of approximately one order of magnitude in state overlap at a fixed computational budget.

We optimize the trade-off between privacy and utility in the high-privacy regime. We adopt local differential privacy (LDP) and its quantum extension, quantum local differential privacy (QLDP), for privacy protection, and investigate utility functions including the Holevo information (which reduces to the mutual information in the classical case) and the error exponents in symmetric and asymmetric hypothesis testing. These utility functions have classical and quantum optimal values, which are denoted by $C$ and $Q$, respectively, in this abstract for simplicity. In this paper, we provide optimal LDP and QLDP mechanisms achieving the classical and quantum optimal values in the high-privacy regime, and prove that the asymptotic ratio $Q/C$ in this regime takes the same value regardless of the utility function. Our results reveal quantum advantages (more precisely, $Q/C\ge3/2$) for the above utility functions when the protected private data are $n$-ary with $n\ge3$.

In quantum purity amplification, one is given $n$ copies of a noisy quantum state $ρ\in \mathbb{C}^{d \times d}$ and asked to prepare $k$ copies of its principal eigenstate $|v_d\rangle$. Several prior works have derived information-theoretically optimal algorithms for this problem, but the bounds they prove are only shown in the asymptotic regime as the number of samples $n$ tends to infinity. In this paper, we establish the following nonasymptotic guarantee: if $ρ$'s eigenvalues are sorted $p_1 \leq \cdots \leq p_d$ and $p_{d-1} < p_d$, then \begin{equation*} n = O\Big(k + \frac{k}δ \cdot \frac{1-p_d}{(p_d-p_{d-1})^2}\Big) \end{equation*} copies suffice to output a state with fidelity at least $1-δ$ with $|v_d^{\otimes k}\rangle$. Our bound holds for arbitrary spectra, and is independent of the dimension $d$. In the case of depolarizing noise, our finite-sample guarantee matches the optimal asymptotic scaling. Our proof is based on the combinatorics of random Young diagrams.

We establish that semidefinite programs (SDPs) over the unbounded positive semidefinite cone are mathematically equivalent to thermodynamic systems of independent bosonic modes: the eigenvalues of the optimization variable play the role of expected occupation numbers, the linear objective plays the role of total expected energy, and the linear equality constraints play the role of conserved non-commuting charges. Building on this perspective, we recast general SDPs as bosonic free-energy minimization problems at strictly positive temperature, regularized by the Bose-Einstein entropy; the original SDP is recovered in the zero-temperature limit. The optimal primal variable takes the form of a Bose-Einstein thermal operator parametrized by the dual variables. We prove an approximation-error bound that depends on the ground-space degeneracy and the spectral gap of the dual slack operator, improving on the linear-in-dimension worst-case duality gap of interior-point methods. We also introduce the Bose-Einstein quantum relative entropy as a Bregman divergence on the unbounded positive semidefinite cone, generated by the negative Bose-Einstein entropy. We propose it as a natural divergence for unnormalized positive operators, for which the standard Umegaki relative entropy can become negative, and we show that it satisfies a restricted monotonicity property under affine maps modeling bosonic Gaussian channels. Finally, we develop hybrid quantum-classical algorithms for the regularized SDP using only Hamiltonian simulation, Hadamard tests, and classical sampling, and bound their runtime in closed form. Unlike existing quantum SDP solvers, whose runtimes scale polynomially with an a priori upper bound on the primal trace, our framework operates directly on the unbounded cone, replacing this bound with a dependence on the spectral structure of the dual slack operator.

Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external driving or environment. While related phenomena have long been studied in classical nonlinear systems, their realization in entangled quantum matter represents a distinct frontier. The theoretical understanding of discrete time crystals has substantially advanced, yet recent experiments using modern quantum devices and quantum processors reveal regimes beyond established paradigms. These developments call for an extended classification of time-crystalline phases according to both their stabilization mechanisms and their physical character, including discrete and continuous, closed and open, critical, topological, quasiperiodic, and controlled realizations. We review recent implementations of time crystals on quantum platforms and propose such a classification framework, identifying promising directions for the discovery of novel time-crystalline phases of matter.

We adapt Microsoft's QuantumKatas -- a well-established quantum computing curriculum -- from Q# to Qiskit, the most widely-adopted quantum computing framework, and package it with an evaluation framework for systematic LLM assessment. The resulting benchmark comprises 350 tasks across 26 categories, spanning fundamental gates through advanced algorithms (Grover's, Simon's, Deutsch-Jozsa), error correction, key distribution, and quantum games. Each task includes a natural language prompt, canonical solution, and deterministic test verification via classical circuit simulation. By building on the QuantumKatas' proven pedagogical design rather than creating tasks from scratch, we inherit a principled difficulty progression and comprehensive concept coverage while contributing the framework adaptation, evaluation infrastructure, and empirical analysis. We evaluate 16 LLMs across 7 prompting configurations -- a total of 39,200 model runs -- to demonstrate the benchmark's utility. Three key findings emerge: (1) the benchmark effectively differentiates model capabilities, with best-configuration pass rates ranging from 32.3% to 83.1% and a 26.1 pp average gap between frontier and open-source models; (2) models perform well at implementing known algorithms (SimonsAlgorithm 82.1%, BasicGates 81.6%) but struggle with problem encoding (SolveSATWithGrover 34.4%, DistinguishUnitaries 40.0%); and (3) chain-of-thought prompting shows a modestly bimodal effect -- it is the best strategy for three models (two of them explicitly reasoning-tuned per vendor documentation) but degrades performance for the rest, leaving it mid-pack in aggregate (56.3% mean) behind few-shot-5 (57.8%). We release the benchmark, evaluation framework, and baseline results to support research on LLM capabilities in quantum computing.

We investigate beyond-mean-field dynamics in a fully connected $\mathrm{SU}(3)$ spin-exchange model, focusing on the interplay between chaotic dynamics and quantum fluctuations. Using the two-particle irreducible (2PI) effective action formalism, we derive equations of motion that systematically account for higher-order correlations generated by interactions, and demonstrate how quantum fluctuations can regularize chaotic dynamics displayed by macroscopic observables. Our results show that an accurate treatment of fluctuations is essential for describing macroscopic dynamics in quantum many-body systems and promote 2PI as a robust framework for connecting microscopic correlations to macroscopic nonequilibrium phenomena.

Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes full tomography of general quantum states statistically and computationally prohibitive. This challenge has motivated extensive research on structured quantum state tomography, where prior structure, such as low-rankness, tensor-network representations, shallow quantum circuits, and neural quantum states, can substantially reduce the effective degrees of freedom and enable scalable recovery. In this review, we provide a unified perspective on QST for structured quantum states through three closely related themes: compact state representations, measurement design, and computational algorithms. After reviewing common models for structured quantum states, we survey existing work on geometric preservation properties of measurement frameworks, ranging from informationally complete POVMs to randomized measurements, and their implications for sample complexity. On the algorithmic side, we review optimization methods for reconstructing structured quantum states from empirical measurements. By connecting QST with broader principles from compressive sensing, matrix sensing, and structured inverse problems, this survey highlights common theoretical foundations underlying sample complexity, measurement efficiency, and scalable recovery.

We report on the impact of the stoichiometry of superconducting MoSi thin films on the performance of superconducting nanowire single-photon detectors (SNSPDs). Specifically, we investigate the relation between the film parameters critical temperature Tc , sheet resistance Rs and superconductor thickness d and observe a universal scaling behavior. To benchmark the performance of SNSPDs fabricated from films having different stoichiometry, we measure the bias dependent count rate curves, while the detector is illuminated with wavelengths between 780 nm and 1550 nm. The detector performance as a function photon energy for different nanowire widths reveals a linear relation between the detection current and the photon energy. Furthermore, we determine the interfacial thermal boundary conductance $β$ between the superconducting thin film and the substrate, by measuring the return current of the SNSPD and find an increase of $β$ with increasing Mo concentration. The highest sensitivity amongst all compared devices is achieved for Mo$_{0.53}$Si$_{0.47}$, with low Tc (4.1 K) and high Rs (397$Ω$/sq) at a film thickness of 5.4 nm.

We investigate the zero-temperature phase diagram of a one-dimensional constrained quantum spin chain realized in coherently driven Rydberg-atom arrays with competing local Rabi driving and dipole-dipole exchange interactions. Projecting onto the blockade-constrained Hilbert space yields an effective model in which local and nonlocal quantum fluctuations compete on equal footing. Combining exact diagonalization, the density-matrix renormalization group, and variational uniform matrix-product-state calculations, we establish a complete phase diagram comprising a Luttinger liquid, an antiferromagnetic ordered phase, and a polarized paramagnet. We identify two distinct mechanisms for the destruction of antiferromagnetic order: a conventional Ising transition at strong driving and a continuous quantum melting into the Luttinger liquid at weak driving, characterized using entanglement-based diagnostics and finite-entanglement scaling. In addition, we uncover an exact ground-state factorization line embedded within the ordered phase, providing an analytically tractable zero-entanglement reference point for experiments with programmable Rydberg quantum simulators.

The fundamental correspondence between quantum chaotic single-particle systems and random matrix theory is well-understood via periodic orbit theory. In contrast, we show that many-body systems with explicit subsystem structure possess characteristics different from the single-particle theory. We present a periodic orbit theory for many-body systems with well defined semiclassical limit. For this we identify periodic orbit families arising exclusively in the many-body setting and implement a central limit theorem characterizing their correlations. Based on this we demonstrate that spectral correlations in chaotic quantum circuits are characterized by the breaking of individual time translation invariance of periodic orbits in the subsystems into residual synchronous time translations only. This provides a systematic approach to confirming random matrix universality in deterministic many-body systems.

We consider the problem of testing whether an unknown unitary is close to a specified level of the Clifford hierarchy. Bu, Gu, and Jaffe proposed a candidate tester for this task based on a connection with noncommutative analogues of the Gowers uniformity norms. The complexity of this tester -- whose analysis depends on a robust characterization of the near-extremizers of these norms -- was left open. We establish such a characterization for the fourth noncommutative uniformity norm and, as a consequence, obtain an efficient tester for the third level of the Clifford hierarchy. We further discuss possible routes toward resolving the problem of testing for all higher levels, highlighting the main barriers that remain.

Entanglement is a key resource for fundamental tests of physics and emerging quantum technologies. In quantum optics, two perspectives on entanglement coexist. In the continuous-variable framework, entanglement is understood as holding between optical modes. In contrast, discrete-variable quantum optics focuses on quantum correlations in degrees of freedom such as polarization that label fixed numbers of photons. In this paper, we show that entanglement can transcend this separation. Spontaneous parametric down-conversion inherently generates correlations in optical phase space, photon number, and labelling degrees of freedom simultaneously. In polarization, this structure is traditionally described by macroscopic Bell states. Existing witnesses, however, fail to detect the genuine hybrid entanglement of these states, which goes beyond the continuous-discrete-variable categorization. Here, we lay the groundwork for a general framework unifying continuous- and discrete-variable notions of entanglement. In particular, we derive an operational witness providing a sufficient criterion for genuine hybrid number-polarization entanglement and outline its experimental implementation. Finally, we discuss exemplary states which, together with our results on macroscopic Bell states, motivate a broader classification of genuine hybrid quantum correlations.

We review and numerically study a protocol for Liouvillian learning based on randomized Pauli states and measurements. In particular, in the two-body, long-range interactions, and single-body noise setting, we describe the complete workflow to obtain the coefficients of the Liouvillian in an efficient and pairwise manner, meaning that the required classical memory is independent of the system size. We also provide guidelines for choosing the parameters for data acquisition and postprocessing that minimize the total reconstruction error.

Imaginary-time evolution by a local Hamiltonian cannot induce a phase transition in one dimension, but longer-range interactions may subvert such constraints. Starting from the ground state of the Kitaev Majorana chain, we modify the wave function by an imaginary-time evolution generated by a quadratic Hamiltonian with power-law couplings that enhance pairing correlations, typically of the form $1/r^α$, where $r$ is the distance between two sites. As the state remains Gaussian, entanglement and correlation functions can be computed analytically. We find that the decay exponent $α$ controls three distinct infrared regimes: for $α>1$, the deformation produces only smooth crossovers at finite deformation strength, while the topological regime is reached only asymptotically as the deformation strength tends to infinity. At $α=1$, the deformation induces an immediate flow to the topological phase: an infinitesimal deformation strength drives the system to a topological regime, and in a particular case, an emergent Kramers-Wannier symmetry enforces Ising-like scaling at long distances. For $α<1$, the deformed state shows the same critical-like behavior for all non-zero deformation strength. We observe that even with arbitrarily long-range interactions, these models do not display a sharp phase transition at non-zero deformation strength.

We present a Multi-task Soft Actor-Critic (SAC) Reinforcement Learning framework designed for open-system quantum control across diverse Hamiltonians, which learns optimal pulse sequences while simultaneously discovering problem-specific evolution time T and number of control pulse segments N. Experimental results across 51 Hamiltonian variations demonstrate that the multi-task SAC model is able to generate control pulses that can drive a system, under environment noise, from its initial state to its target state with high fidelities, establishing essential foundations for universal quantum control applicable to realistic noisy quantum devices. Through progressive expansion of the training Hamiltonian set, we investigate if a single multi-task model trained using a given number of sample Hamiltonians can successfully accomplish state-transfer tasks for Hamiltonians drawn from the same Hamiltonian space but not encountered during training. In addition, our Robustness Infidelity Measure (RIM) analysis reveals that SAC trained policies exhibit superior robustness to pulse amplitude perturbations and decoherence rate variations compared to GRAPE-optimized controls.

Quanta emitted by an open quantum system carry information about intrinsic parameters, enabling their estimation via continuous monitoring. In practice, however, only a fraction of the emitted quanta is detected, reducing the achievable sensitivity. Here, we consider few-level systems in which coherent couplings and dissipative processes compete, producing metastable dynamics characterized by emission intermittency or by the emergence of a dark state. We show that both phenomena can be beneficial for sensing but their relative performance depends strongly on the achievable detection efficiencies. Intermittent emission, marked by long alternating bright and dark periods, allows to achieve robustness with respect to inefficient detection and dephasing, whereas dark states yield significantly higher sensitivity at unit detection efficiency. Yet the latter are highly susceptible to losses. We quantify the impact of inefficient detection through the classical Fisher information of the emission record and benchmark it against the ultimate sensitivity encoded in the joint system-environment state. Finally, we demonstrate that maximum-likelihood estimators based on the observed emission record can effectively approach this sensitivity. We focus here on trapped-ion systems, however, the results extend to other quantum platforms in which similar emission dynamics can be observed.

We study the extreme points of the convex set $\mathcal{C}(ρ_1,ρ_2)$ of bipartite quantum states with fixed marginals $ρ_1$ and $ρ_2$. We construct extreme points in $(d,\,d+m)$ dimension, of rank $d+m$, matching the highest possible value, for all $d\geq 3$, $m > \frac{d^2-2d-2}{2}$ (when $d=2$, $m\geq 1$). This proves the existence of extremal states with relatively large rank and also covers all the known examples. We further show that, in order to analyze the extreme points of $\mathcal{C}(ρ_1,ρ_2)$, it is sufficient to study the special case $\mathcal{C}(\mathcal{D}_1,\mathcal{D}_2)$, where the marginals are diagonal. Additionally, we observe that it is sufficient to consider $d_1\leq d_2$. Thus, our results show that apart from possibly a few finite cases, for each $d_1$, the maximal rank is achieved almost all times.

We study two complementary diagnostics of bipartite quantum channels, namely fidelity preservation across different classes of input states and entanglement generation from product inputs, given by properly defined entangling power for bipartite channels. We show that the fidelity averaged over any fixed Schmidt-coefficients local-unitary orbit for equal local dimensions is completely determined by average input-output fidelity and its restriction to product inputs. We also introduce concurrence- and negativity-based entangling power for 2-qubit channels, prove their convexity and monotonicity under local postprocessing, and show that, unlike the previously proposed linear-entropy quantity, they vanish for all separable channels. Examples of non-separable channels are investigated. Finally, we generalize our definitions of entangling power to non-product inputs, and provide an analytical lower bound for the concurrence-based entanglement variation, showing its effectiveness with specific examples.

The no-cloning theorem prohibits the creation of identical copies of quantum information, imposing fundamental constraints on quantum technologies. A recently proposed protocol, encrypted cloning, introduced by Yamaguchi and Kempf, showed that perfect qubit clones can be produced if they are simultaneously encrypted with a single-use key. They also observed a connection between this scheme and quantum secret sharing (QSS). However, it remained an open question whether encrypted cloning could be generalised to arbitrary dimensions, and the broader relationship between the two schemes had not been formally established. In this work, we address both questions by framing encrypted clones as Absolutely Maximally Entangled (AME) states. In parallel with recent work by Ceará that utilises Zadoff-Chu sequences, we independently develop a complementary framework for arbitrary dimensions based on Weyl-Heisenberg displacement operators, both tracing back to the original qubit construction by Yamaguchi and Kempf. We analytically compute the encrypted state and prove that an encrypted qudit system comprising two signal-noise qudit pairs is equivalent to a five-party AME state in any dimension, provided the input state is uniform. We then formalise the connection to QSS by proving that a threshold QSS scheme can achieve the fundamental objectives of encrypted cloning, establishing QSS as the natural general framework within which encrypted cloning can be contextualised.

Dipolar interactions are a major source of decoherence in dense ensembles of color centers in diamond. Current protocols demand using bias magnetic fields detrimental in many scenarios. We present ZENITH (Zero-field Ensemble Neutralization via Interleaved Trilevel Handling), a pulsed sequence to cancel dipolar interactions among V-degenerate spin-1 systems. We reveal excellent coherence survival, compatibility with existing sensing sequences, and improved DC detection, advancing a general framework to control interacting degenerate multilevel systems, of broad interest in quantum technologies.

The continuous spontaneous localization (CSL) model is one of the most promising approaches to address the wave function collapse problem in the measurement process of standard quantum mechanics. In this work, the effect of the CSL model on a Bragg atom interferometer was investigated. A Bragg interferometer achieving high fringe contrast of 99$\%$ has been demonstrated, maintaining this performance level at interrogation time up to $T=60~\mathrm{ms}$. The primary factors responsible for fringe contrast loss in the atom interferometer were systematically analyzed and corrected. This improvement established a new upper limit of $λ_{\rm CSL}=1.27\times10^{-5}~\mathrm{s}^{-1}$ at $r_C=10^{-5}~\mathrm{m}$ for the CSL collapse rate, representing approximately 4 times enhancement over previous atom-interferometric constraints.

Continuum-buried defect states in semiconductors are generally expected to be optically inactive due to their strong coupling to continuum bands. Here, we show that such defects can instead host radiative electronic bound states in the continuum (BICs), using the silicon G-center as a prototypical example. Hybrid-functional first-principles calculations with a Hubbard $U$ correction reveal that a localized defect state, initially buried below the valence band maximum (VBM) in the ground state, undergoes exchange-driven energy-level reordering under optical excitation and shifts above the VBM. This exchange-induced transition suppresses nonradiative decay and enables robust radiative emission. By computing temperature-dependent nonradiative lifetimes and comparing them with experimental photoluminescence (PL) lifetimes, we quantitatively reproduce the observed temperature dependence of the emission. These results uncover a stabilization mechanism for continuum-embedded defect states and establish electronic BICs as a general paradigm for designing defect-based optical systems, including quantum emitters and qubits.

We address the problem of identifying non-Markovian quantum time evolutions of an open quantum system by only performing measurements of the system's energy. We demonstrate that violations of CP-divisibility are always witnessed by non-positive values of the energy-change Kirkwood-Dirac quasiprobability distribution associated with the system's Hamiltonian, evaluated at consecutive times. The link between non CP-divisibility and non-positivity of the system's energy-change distribution is stronger when the system-environment interactions are energy-preserving. The witness works whenever anomalous energy fluxes, due to non-Markovianity, are realized. Anomalous fluxes are also detected by the non-Markovianity measure built over the quantum mutual information between the states of the open system and of a quantum correlated reference.

Scaling wide-band-gap semiconductors to the ultrathin limit offers a transformative pathway for power electronics, with gallium nitride (GaN) representing a cornerstone material in this class. However, the operational resilience and functional tunability of its two-dimensional form (g-GaN) remain underexplored. This work shifts the focus from idealized systems to the complex materials behavior under realistic conditions, investigating how the synergistic effects of point vacancy defects, strain, and external electric fields govern its electronic, magnetic, and sensing landscapes. We demonstrate that these factors are not merely perturbations but are fundamental to modulating the material response. Our first-principles calculations suggest g-GaN maintains electronic stability under intense electric fields; notably, gallium vacancies are predicted to further extend the theoretical stability limit. While in-plane tension preserves the band gap evolution under an electric field, in-plane compression facilitates low-field metallization. Using nitrogen monoxide (NO) adsorption as a prototype, we find that the interaction is defect-modulated and potentially tunable by electric fields. Analysis of adsorption energetics and diffusion barriers suggests the gallium vacancy may act as a thermodynamic trap for NO. Targeted hybrid-functional (HSE06) validation confirms the reliability of observed adsorption trends and theoretical metallization thresholds, while revealing that precise electronic-exchange treatment is critical for capturing the magnetic ground state of nitrogen vacancies. By systematically examining the geometry, energetics, band structure, density of states, magnetic response, and charge transfer, this study clarifies the interplay between defects and external electric fields, providing insights into theoretical upper bounds for property tuning and semiconductor device engineering.

We consider the non-Hermitian XY spin chain with open boundary conditions when the anisotropy parameter is extended to complex values. By analyzing the quasi-Hamiltonian matrix, we demonstrate that the free-fermion structure of the quasi-energy spectrum coincides with that of the Hermitian model and construct the corresponding biorthogonal fermionic basis away from exceptional points (EPs). We make use of an explicit Chebyshev-polynomial representation of the open-boundary eigenvectors in which the quasi-energy $\varepsilon$ is the natural spectral variable. This quasi-energy polynomial form is particularly useful at EPs, because EPs correspond to repeated roots of the same boundary polynomial, making the construction of generalized eigenvectors by $\varepsilon$-differentiation transparent. At EPs, where the quasi-Hamiltonian becomes defective, we derive the Jordan normal form and construct the associated generalized eigenvectors, which yields the correct counting of independent many-body eigenstates. We further show that EPs act as branch points in the complex anisotropy plane, leading to the characteristic permutation of eigenenergies and eigenstates upon encirclement. The branch-cut structure of the biorthogonal eigenstates provides direct evidence for the exchange of eigenstates when an EP is encircled. These results provide an analytically controlled many-body platform for studying EP physics and non-Hermitian topology beyond momentum-space descriptions.

Sequential sharing of quantum nonlocality (SSQN) is crucial for device-independent tasks in quantum information processing, wherein relaying the post-measurement qubit through a local quantum channel to a subsequent observer constitutes an essential operational step. Here we present a theoretical analysis of noise robustness of sequential sharing for bipartite Bell nonlocality and tripartite Mermin nonlocality under the influence of local phase-flip, bit-flip, and depolarizing quantum channels. It is established that arbitrarily many independent observers can sequentially share the quantum nonlocality of Bell, Greenberger-Horne-Zeilinger, and W states via specific noise-immune channels, whereas this feature of SSQN is destroyed under other noisy quantum channels. Furthermore, we demonstrate that the noise-immune channel enabling unbounded SSQN can be switched by employing our newly designed measurement strategies assisted by local operations on the initial entangled states. Moreover, as illustrative examples, we propose two concrete schemes for sharing bipartite Bell nonlocality and tripartite Mermin nonlocality with two sequential local observers on one side subject to local noisy channels. Our work establishes a practical framework for realizing the SSQN under noisy quantum channels, and reveals the connection between noise robustness and measurement strategies.

Inhomogeneous ensembles of two-level systems are important for both fundamental light-matter physics and quantum-network applications. Here we develop a general waveguide model that provides an intuitive and analytical description of collective dynamics in such systems by mapping the subradiant modes to an effective waveguide with well-defined input-output relations. For echo-based quantum memories, the model reveals the physical origin of noisy-echo suppression by adiabatic pulses and shows that inhomogeneous light-matter coupling can be harnessed as a resource for noiseless storage. For entanglement generation, the same mechanism exposes a previously unexplored limitation of robust control pulses and leads to a new composite-pulse protocol that overcomes it. These results establish the waveguide model as a practical bridge between fundamental collective physics and quantum-network protocol design, with direct implications for high-fidelity memories and robust entanglement generation in inhomogeneous ensembles.

We study the finite-temperature Casimir effect for a massless scalar field confined between two parallel plates in a Schwarzschild-like wormhole spacetime. Imposing Dirichlet boundary conditions, we compute the renormalized Casimir free energy in the comoving frame. We find that the thermal correction to the renormalized Casimir free energy decreases gradually with the temperature and becomes independent of the background geometry in this frame. Thermodynamic quantities derived from the Casimir free energy, namely, the renormalized Casimir entropy, internal energy, and heat capacity at constant volume, exhibit distinct temperature dependence. At low temperatures, all thermodynamic quantities recover the expected behavior, consistent with the fundamental laws of thermodynamics. These results provide a compact framework for analyzing quantum vacuum forces in gravitational backgrounds.

Clock synchronization is critical for maintaining low error rates in quantum key distribution. Here, we describe how a frequency mismatch between the transmitter and receiver clocks affects the quantum bit error rate in quantum key distribution, and derive from this model a simple synchronization algorithm together with clock stability requirements for practical operation. Our algorithm continuously compensates for both frequency mismatch and time-offset fluctuations directly from detection timestamps. It does not require a dedicated synchronization channel or auxiliary qubit sequence, converges from a large frequency mismatch within approximately one second of photon acquisition, and remains effective in low-photon-count regimes (more than 30 dB of channel loss) using standard hardware. We validate our approach by demonstrating successful key exchange over 100 km of fiber and continuous operation over 24 hours in a 16 km metropolitan network using commercial systems, with performance equivalent to using a service channel for clock synchronization.

We develop a theoretical and computational framework for estimating and correcting non-Abelian geometric distortions in time-bin photonic qudit processing when the relevant encoded object is a transported logical subspace rather than a collection of independent rays. In such settings, for example under mode mixing, multiplexed routing, or effective degeneracies, the geometric contribution is naturally matrix-valued and is described by a Wilczek-Zee holonomy on a rank-$m$ sub-bundle of the ambient Hilbert space. The framework generalises prior Abelian time-bin Pancharatnam-Berry feed-forward calibration, in which geometric distortions are represented by bin-resolved scalar phases, to the non-Abelian, matrix-valued case. We construct a gauge-covariant discrete estimator from overlap matrices between successive subspace frames: the polar factor of each overlap gives a unitary backward frame comparator, and the adjoint comparators compose to approximate the forward path-ordered exponential of the Wilczek-Zee connection. We prove gauge covariance under frame changes, polar optimality of the local comparator, consistency under partition refinement, and perturbative stability under well-conditioned overlap errors. We then formulate left- and right-acting feed-forward correction rules for removing the estimated holonomy from an effective logical operation. The work does not assume a device-specific transfer matrix, loss model, detector model, or experimental calibration pipeline; numerical studies use synthetic non-Abelian transport models to validate covariance, convergence, conditioning dependence, and correction fidelity.

A formal development of the hypoequilibrium (HE) state concept within the Steepest-Entropy-Ascent Quantum Thermodynamics (SEAQT) framework is presented, emphasizing its rigorous mathematical formulation. Using a general decomposition of the Hilbert space, HE states are defined in operator language and the reduced evolution of the associated intensive parameters for the regime where the dissipative dynamics commutes with the Hamiltonian is derived. It is proved that the $M$-th order HE family (where $M$ is the number of spectral sectors) constitutes an invariant manifold under the SEAQT equation of motion, ensuring that states initially representing a ``mixture of canonicals'' maintain this structure throughout their evolution. Furthermore, a formal connection is established between the HE ansatz and the rate-controlled constrained equilibrium (RCCE) method, identifying HE variables as constraint potentials. Finally, the model is extended to non-Hamiltonian SEAQT (NH-SEAQT) interactions to describe thermodynamically consistent energy and entropy exchanges between subsystems and heat baths. This work provides the formal foundation for reduced-order modeling of far-from-equilibrium relaxation and transport processes, and supports a methodology previously applied across various physical and chemical systems.

We determine the bipartite entanglement bounds of two interacting electrons in deeply interlocked Hopf-linked quantum rings via exact diagonalization of the unexpanded 3D Coulomb interaction. This identifies an exact continuous spatial symmetry that geometrically isolates the positive-parity Bell state, preventing classical interaction-driven localization. A non-coplanar geometric tilt ($α> 0$) is essential to lift the exchange degeneracy and maintain this maximally entangled manifold as a state of frozen entanglement. However, a higher-order Schrieffer-Wolff transformation demonstrates this geometric protection is fundamentally bounded; uncancelled inter-orbital momentum transitions inevitably induce dynamical parity mixing. This defines a critical interaction threshold ($λ_{crit}$) for irreversible entanglement collapse. Our analysis shows that the resulting bounding conditions reveal scaling limitations in mesoscopic semiconductor architectures, dictating the necessity of synthetic macroscopic platforms to achieve robust topological protection.

Multi-asset option pricing under local- and stochastic-volatility models leads naturally to high-dimensional parabolic PDEs. We develop an end-to-end quantum PDE framework for European option pricing under local-volatility Black--Scholes and Heston models. The framework takes classical contract and model data as input and returns classical estimates of selected option values. We solve the pricing PDEs after finite-difference discretization on spatial grids. For $N=2^n$ grid points per spatial direction and $d$ assets, the end-to-end gate complexity for single-point recovery, counted in elementary CNOT gates and one-qubit Pauli-axis rotations, has leading grid-size dependence $\widetilde{O}(d^2 N^{2+d/2})$ for local-volatility Black--Scholes and $\widetilde{O}(d^2 N^{d+2})$ for Heston. Relative to grid-based finite-difference baselines, these scalings correspond to polynomial improvement factors $N^{d/2}$ and $N^d$, respectively. These estimates translate to Clifford+T resources via standard compilation. We complement the complexity analysis with numerical benchmarks against standard classical methods. In the Heston setting, the framework recovers option prices across strikes together with the associated implied-volatility smile/skew. Overall, this work provides a complete end-to-end quantum pricing pipeline with explicit resource accounting and theoretical performance guarantees.

Analytic continuation from imaginary-time Green's functions to real-frequency spectra is a central ill-posed inverse problem in quantum many-body physics. We show that the thermal kernel admits an analytical generalized singular-value structure once its purely dynamical part is separated from the statistical weight imposed by the heat bath. The dynamical kernel is the imaginary-bandwidth continuation of Slepian's finite Fourier transform and is governed by the same Sturm-Liouville algebra that yields prolate spheroidal wave functions. Fermionic and bosonic statistics then enter as gauge transformations of the frequency-space inner product, producing self-adjoint effective potentials but no numerical kernel diagonalization. The Shannon number, $N_c=β\wmax/π$, fixes the upper information capacity of this pure Laplace channel. Finally, the optimal sampling points are obtained as eigenvalues of a Legendre colleague matrix, giving a deterministic compressed-sensing grid without iterative root searches.

Scalable generation of nonclassical light sources on an integrated platform is a key requirement for photonic quantum information processing. In particular, realizing multiple indistinguishable squeezed light sources on a single chip is an essential step toward continuous-variable quantum computing. Here, we demonstrate the fabrication of two indistinguishable and independently controllable optical parametric oscillators on a thin-film lithium niobate (TFLN) platform. The device design focuses on reproducibility, independent tunability, and compatibility with larger telecom-wavelength continuous-variable photonic circuits. We observe up to 0.5 dB of directly measured squeezing below the shot-noise level from each source. By interfering the two modes on a beam splitter, we generate an EPR-type two-mode squeezed state and verify continuous-variable entanglement through violation of the Duan-Simon inseparability criterion. This is the first demonstration of two independently tunable squeezed-light sources on a single TFLN chip and their use for generating continuous-variable entanglement.

Recursive QAOA (RQAOA) solves combinatorial optimization problems by using shallow quantum circuits to estimate pairwise correlations and recursively eliminate variables until a classical solver can handle the residual instance. Each elimination step requires measurement shots, and the total shot cost grows with the number of recursive stages. On near-term quantum devices, increasing shot counts can translate directly into greater exposure to hardware-level noise sources such as readout errors and decoherence, making shot-efficient execution not merely a cost-reduction measure but a factor with direct implications for solution reliability. While shot reduction has been studied broadly across NISQ algorithms, step-wise measurement control inside the recursive loop of RQAOA has received little attention. We formulate this step-wise allocation as a sequential decision problem and propose two strategies for depth-1 RQAOA on weighted Max-Cut instances. A hand-crafted heuristic assigns shots based on local indicators of step difficulty, and a tabular Double Q-learning agent learns a residual policy that adjusts this baseline under a Lagrangian-constrained objective. Both methods are evaluated under a fixed-cap fairness protocol that equalizes the per-step budget across all strategies, and the elimination rule itself is kept unchanged so that the contribution of adaptive measurement control can be isolated. On a diverse set of weighted graph instances spanning a range of sizes and structures, the heuristic reduces total shots by approximately 23% relative to uniform allocation, and the RL policy achieves a 36% reduction with a lower effective shots per success ratio than both baselines. The improvement persists on problem sizes not seen during training, suggesting that reinforcement learning can discover efficient, instance-adaptive measurement strategies in recursive quantum optimization.

We study entanglement harvested by Unruh DeWitt detectors following Rindler trajectories in compactified and superposed Minkowski spacetime. We consider different directions of acceleration (both parallel and antiparallel), separation between detectors and direction of spatial compactification mutually perpendicular to each other. Using the standard entanglement harvesting protocol, we analyze how these features influence the extracted correlations. When detector separation is perpendicular to the direction of acceleration, the harvested entanglement is uniformly suppressed due to increased spacelike separation. Compactification enhances field correlations leading to an increased concurrence and an extended harvesting range at higher accelerations. Additionally, we show that spacetime superposition introduces interference effects that further enlarge the entanglement harvesting region in parameter space, particularly in the high acceleration regime. We also find that the effect of antiparallel acceleration yielding significantly higher entanglement than parallel acceleration prevails in compactified and superposed spacetime.

Narrow-linewidth lasers with absolute frequency anchoring are essential for precision metrology, coherent sensing, and emerging quantum technologies beyond laboratory environments. Optical cavities and interferometers provide exceptional short-term spectral purity but lack intrinsic absolute frequency references. Atomic transitions, in contrast, provide stable frequency anchors but offer limited discrimination sensitivity. Recent hybrid approaches have demonstrated the combination of compact optical resonators with atomic references, yet achieving the Hz-level regime remains challenging. Here, we present a hybrid architecture that enables simultaneous realization of Hz-level linewidth and atomic-referenced frequency stability. An external-cavity diode laser is first stabilized to a fiber interferometer to achieve Hz-level spectral purity, while the interferometer is subsequently anchored to an 87Rb D2 transition via modulation transfer spectroscopy to suppress long-term drift and define the laser frequency relative to the atomic transition. This dual-stabilization scheme realizes a compact atomic-referenced laser with a 3.4-Hz linewidth (1-rad integrated-phase method), a minimum fractional frequency stability of 3.4x10-14 at 0.56 s, and 9x10-13 at 100 s. This architecture establishes a practical and scalable route toward compact and field-deployable atomic-referenced narrow-linewidth lasers for precision metrology and quantum technologies.

The eigenstate thermalization hypothesis (ETH) provides a fundamental mechanism for emergent statistical mechanics in isolated chaotic quantum systems, asserting that individual energy eigenstates behave as pseudorandom vectors within an energy window. This enables a complete characterization of nontrivial correlations among matrix elements in the energy eigenbasis, as described by the full ETH ansatz. Nevertheless, this description breaks down in systems exhibiting quantum many-body scars, which host non-thermal eigenstates with extensive energy. In this Letter, we address this problem by formulating the \textit{scar full ETH}, which captures correlations among matrix elements involving scar states. The corresponding scaling forms and factorization properties are established using typicality arguments. Multi-time correlation functions for scar states are then organized in terms of both thermal and scar cumulants, providing a nontrivial reorganization of higher-order correlations. We numerically demonstrate the validity of this framework in the paradigmatic model of quantum scars, the PXP model. Our results pave the way for a systematic understanding of intriguing correlations in systems with quantum many-body scars.

Quantum-enhanced multiparameter sensing is often associated with distributed architectures or 2-anticoherent states, whereas squeezing in a single collective ensemble is typically limited to single-parameter metrology. Here, we show that a single ensemble can support simultaneous multiparameter squeezing when each sensor is promoted from a qubit to a qudit (i.e., spin with $d$ energy levels). We develop a general framework in which the optimal product probe state, the corresponding global readout observables, and the associated squeezing parameters are all determined from the single-site quantum Fisher information matrix. We then present a minimal qudit construction for two-parameter vector magnetic field sensing with local dimension $d=3$. We further identify a collective twisting-like interacting Hamiltonian that generates such multiparameter-squeezed states and numerically demonstrate scalable metrological gain. In particular, for a trapped-ion qutrit chain with power-law interactions, we obtain up to 12 dB enhancement in two-parameter sensing for $N=256$ sensors. Our results establish qudit-enabled multiparameter squeezing in a single ensemble as a distinct route to multiparameter quantum metrology with global readout, and highlight its potential advantage over distributed multi-ensemble strategies in the fixed-sensor-budget regime.

Quantum complementarity is a fundamental feature of quantum systems and has captivated the physics research community for nearly a century, with significant advancements emerging in recent decades. This review traces the historical evolution of the concept of complementarity, beginning with Bohr's original formulation. It then explores its modern quantification through complementarity relations and its profound connection to the foundational postulates of quantum theory. Furthermore, it delves into key related developments, such as the operational definition of complementarity in the context of incompatible observables, its potential links with quantum uncertainty relations and contextuality, its various applications, and other pertinent topics. This review aims to serve physicists interested in quantum resources, quantum correlations, and the foundational principles of quantum mechanics.

Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical Hamiltonians are rarely exactly commuting, which naturally motivates the study of almost commuting Hamiltonians. Despite their relevance, the implications of approximate commutation are only poorly understood. In this work, we show how to efficiently approximate any almost commuting $2$-local qubit Hamiltonian by a commuting one: we give a locality-preserving algorithmic rounding technique that maps any $2$-local Hamiltonian $H=\sum_{i=1}^m h_i$ with $\|[h_i,h_j]\| \leq ε$ to a nearby Hamiltonian $\hat{H}$ whose terms pair-wise commute, and which is within overall distance $\|H-\hat{H}\| = O(m\,ε^{1/6})$. As a consequence, we show that $δ$-approximations to the ground energy for $ε$-almost commuting $2$-local qubit Hamiltonians lie in $\mathsf{NP}$ when $δ\gg mε^{1/6}$, extending the classical containment well beyond the commuting setting. Finally, we present two applications of our rounding framework: Gibbs sampling and fast Hamiltonian simulation for almost commuting systems.

Even in cases where quantum linear solvers provide significant speedup compared to their classical counterparts, their performance depends on some of the same parameters. In particular, the condition number of the matrix which is to be inverted is a decisive parameter. A well known classical, and now quantum, remedy is to precondition the linear system $A x = b$ by premultiplying it by a matrix $H$ in such a way that the condition number of $HA$ is significantly smaller than the condition number of $A$. In this work, we focus on a family of preconditioners called domain decomposition. First, we prove that it is feasible to apply quantum domain decomposition. We provide upper bounds for the block-encoding parameters of the Poisson problem discretized by the finite element method and preconditioned by the two-level Additive Schwarz preconditioner (one of the most fundamental domain decomposition techniques). From these bounds, we deduce the complexity of the quantum linear system solver. Second, we focus on a particular choice of local solver within the domain decomposition preconditioner by applying recent work by [Deiml and Peterseim, \textit{Math. Comput.}, 2025] on the Bramble--Pasciak--Xu (BPX) preconditioner. Finally, we provide details on how the operators are implemented.

We study Krylov complexity in BMN Plane Wave Matrix Model at large mass deformation. We consider various consistent reductions of the matrix model that allow us to perform a Hamiltonian analysis which leads to different notions of the Krylov complexity. In the first part of the paper, we study the Krylov state complexity considering systematic reduction of $N=3$ and $N=4$ representations of the matrix model, which reveals a universal characteristic scaling for the Lanczos coefficients and fix them completely in terms of the mass deformation parameter. In the second part of the paper, we study the Krylov operator growth in the matrix model and compute the corresponding Lanczos coefficients. In both cases, we observe a \emph{linear} scaling of Lanczos coefficients with the mass parameter. The early time growth in Krylov complexity receives quadratic correction due to the presence of the massive deformation in the matrix model. Our analysis reveals that such massive corrections appear at same order in time for both the notion of the Krylov complexity.

Simulating fermionic systems on qubit hardware involves many nonlocal interactions, and efficient routing of these interactions is critical to the overall cost of fermionic simulation algorithms. Recent works reduce this Jordan-Wigner routing overhead to polylogarithmic depth under all-to-all connectivity, but degrade to $O(\sqrt{N}\,\mathrm{polylog}\,N)$ for $N$ fermionic modes on 2D nearest-neighbor architectures. We present a fermionic permutation protocol tailored to 2D grid architectures that achieves the optimal $O(\sqrt{N})$ depth with $O(N\sqrt{N})$ nearest-neighbor gates and no ancilla qubits, mid-circuit measurements, or classical feedforward. This matches the $Ω(\sqrt{N})$ lower bound, which holds even when $O(N)$ ancillas and classical feedforward are permitted. We further construct an $O(\sqrt{N})$-depth transformation between the Jordan-Wigner, Bravyi-Kitaev, and Parity encodings on the 2D grid via a Hilbert-curve layout, extending our result to all three encodings. Benchmarks on the fermionic fast Fourier transform and Trotter simulation of sparse SYK model demonstrate consistent reduction in depth, spacetime volume, and infidelity for system sizes $N \gtrsim 100$ in the early fault-tolerant regime.

We propose a training-free quantum generative paradigm, which is fundamentally different from current generative models, which demand substantial computational power, face practical scalability limits, and often function as opaque black boxes, despite their remarkable success. We enable image and text generation without parameter training, by constructing a local parent Hamiltonian whose ground state encodes the target distribution and then solving the global Hamiltonian. Rooted directly in quantum mechanical principles, this approach establishes a new pathway for generative modeling that leverages superposition and entanglement to maintain global consistency.

Quantum computing is transitioning from experimental prototypes to commercially available turnkey systems, making architecture-agnostic performance metrics essential for cross-platform comparison. Peaked Random Circuits (PRCs) have recently been proposed as a viable path to demonstrate quantum advantage on NISQ devices: a quantum processor can reliably detect a single, peaked output state amid background noise, yet the circuits' characteristics render classical simulation infeasible. In this paper, we repurpose PRCs as a system-level fidelity benchmark. By successively running a matrix of PRCs with varying qubit counts and circuit depths, we quantify a system's ability to identify the deterministic peak despite cumulative noise, gate errors, and connectivity constraints. We apply the benchmark on IQM's superconducting and AQT's trapped-ion architectures. Our results show that PRCs provide a high-precision metric comparable to Quantum Volume while exhibiting greater sensitivity to interference effects. Consequently, PRCs enable a robust framework for assessing the computational reliability of NISQ hardware across platforms.

Processing large Pauli sums is a significant bottleneck in quantum chemistry, Pauli propagation, and Pauli-based compilation. Existing frameworks often suffer from Python interpreter overhead or utilize hash-map data structures that hinder SIMD vectorization and complicate multi-threaded merging. We present PauLIB, a header-only C++20 library designed to eliminate these bottlenecks through three key architectural choices. A bit-packed binary symplectic representation that encodes each qubit in two bits, reducing Pauli multiplication to a bitwise XOR and a population count; a sorted array layout that replaces hash maps to enable branch-predictable SIMD bulk operations; and a struct-of-arrays (SoA) memory layout that exposes contiguous word arrays for explicit SIMD vectorization. Benchmarks at 500 qubits show that single Pauli string multiplication runs at 25ns per operation-14 times faster than PauliEngine and 660 times faster than Qiskit-flat across all pair counts tested. Hamiltonian outer-product multiplication is approximately 10 times faster than PauliEngine and 45 times faster than Qiskit at all tested sizes. Greedy commutation grouping, the dominant preprocessing cost in variational algorithms, achieves up to 21,000 times speedup over PennyLane, driven by the compact bit-packed representation. The compact layout reduces the memory footprint of a one-million-term Hamiltonian at 500 qubits from 1,036MB (Qiskit) to 142MB, a 7.3 times reduction that directly enables larger problem sizes within a fixed memory budget. PauLIB is open source and provides C++ and Python interfaces.

We generalise the quantum mechanical toy model for gravitationally induced decoherence presented in Xu, Blencowe (2022) and Domi et al. (2024). In contrast to earlier formulations, in which the Hamiltonian of the system of interest is linearly coupled to the position operators of the oscillators in the environment, we consider an interaction formulated in terms of Weyl elements of the environment's position operators. This extension is motivated by polymer quantum mechanics, in which Weyl elements are fundamental operators, as well as by the possibility of generating non-linear interactions through suitable truncations of the exponential Weyl elements. Here we focus on a sinus-like coupling that is still quantised using the Schrödinger representation and, in the limit of a small Weyl parameter, reproduces the conventional linear interaction. To derive the corresponding master equation, we developed two complementary methods for the analytical calculation of the environmental correlation functions. The first utilises Wick's theorem for thermal expectation values in conjunction with annihilation and creation operators, while the second is based on the short-time Fourier transform and completely avoids the use of annihilation and creation operators, making it more readily transferable and generalisable to a polymer quantisation. Both approaches yield identical results. We further generalise the spectral density required for the exponential coupling structure. A numerical analysis shows that the environmental correlation functions decay rapidly with time, which supports the validity of the Markov approximation. Using a Taylor expansion in the Weyl parameter, we show that the first-order term reproduces the decoherence model of Xu, Blencowe (2022) and Domi et al. (2024). Finally, we derive the solution to the renormalised master equation.

Recent demonstrations of non-Abelian braiding of graph vertices on noisy intermediate-scale quantum (NISQ) superconducting processor, and the experimental realization of topological order in general on various quantum hardware platforms necessitate an important question: when does a native (topological) fusion readout genuinely help for topological anyonic Hamiltonians implemented on NISQ hardware? We use the Fibonacci anyons chain as a concrete model for understanding the trade-off between measurement cost and compilation cost in that setting. The comparison is made against a simple grouped-Pauli baseline, and is scored by a covariance-aware mean-squared-error (MSE) of the full energy estimator. We based our benchmark on two different important classes of quantum circuits, namely Floquet time-evolved and variational quantum eigensolver quantum circuits, with the underlying Hamiltonian consisting of both braiding and fusion interaction. Our analysis found that there is not a uniform best method across both problems: the fusion readout method performed better on Floquet-type circuits on both the MSE and covariance-aware sampling variance, while the grouped Pauli method performed better on VQE on the MSE but worse on sampling variance. We derive scaling laws, and compute shot-budget crossover points, where one method is operationally favored above the other. The relevance of this work extends beyond Fibonacci chains to two-dimensional topological models compiled on superconducting and other qubit-native platforms, and can be used as a guide in answering the question of when one should measure in the native operator basis of the target physics, or when it is better to fall back on Pauli-basis reconstruction.

General-purpose programmable photonic processors provide a flexible foundation for integrating various functionalities within a single chip. A two-dimensional bricks waveguide mesh of Mach Zehnder interferometers has been demonstrated to possess considerable potential in the domain of photonic neural networks and quantum signal processing. In this article, we propose an expansion of the available applications of recirculating bricks mesh architecture to distillation protocols necessary for quantum signal processing. These protocols are essential for the heralding of the output of single photons, which is characterized by a reduced distinguishability error rate. The demonstration will be made of a single programmable optical system's ability to realize various distillation protocols with reduced computational resource costs. The present study will concentrate on cascaded quantum interferometers and Fourier transform-based schemes. It will demonstrate that the bricks mesh can implement such schemes, which are unattainable using feed-forward networks, without the need for complex out-of-plane integration. The propagation of the signal in any direction, along with the utilization of all ports as both input and output, facilitates the execution of such transformations with minimal optical depth of the circuit and in time scales shorter than the decoherence time.

Complex zeros of wavefunctions represented as entire functions in Bargmann--Fock space encode structural information about the underlying quantum state. Prior work employed zero galleries of randomly generated polynomial superpositions of Fock states as visual fingerprints suitable for classification. Here we examine whether Bargmann zeros of physically realized eigenstates of one-dimensional anharmonic and double-well Hamiltonians carry a recognizable signature of the tunneling transition in the symmetric double well. Ground and first-excited eigenstates are obtained from a variational ansatz consisting of a physically motivated symbolic envelope multiplied by a small flexible correction network, trained by Rayleigh--Ritz minimization of the finite-difference Hamiltonian expectation value and validated to reproduce energies to within $\sim 10^{-5}\,\mathrm{Ha}$. The resulting wavefunctions are projected onto the harmonic-oscillator basis and the complex zeros of the truncated Bargmann polynomial are located by numerical root-finding. For harmonic and quartic-anharmonic potentials the zeros show no preferred orientation. For double-well eigenstates, by contrast, the zeros condense onto the imaginary axis. A sweep of the barrier parameter $a$ from $0.5$ to $2.3$ reveals a continuous migration of zeros toward the imaginary axis, concurrent with the exponential collapse of the tunneling splitting $Δ(a) = E_1 - E_0$ over $3.5$ decades. This condensation is traced to a sign-alternation pattern in the Fock-coefficient spectrum that is characteristic of bimodally localized wavefunctions. The complex zero set of the Bargmann-represented wavefunction thereby provides a compact, purely analytic diagnostic for the tunneling regime of one-dimensional double-well Hamiltonians, extending the random-polynomial zero-image framework to physical eigenstates.

This text introduces geometric quantization on orbifolds. After reviewing the necessary background, it develops new treatments of prequantization, polarizations, and metaplectic correction for symplectic orbifolds.

The expressions of the eigenfunctions of the Hawton photon position operator in the configuration space are derived for several classes of wave function, including the Riemann-Silberstein and Landau-Peierls cases. Although these eigenfunctions have a simple form in momentum space, the explicit characterization of their representations in the configuration space is rather more involved. We provide closed expressions of these eigenfunctions in terms of linear combinations of the complete elliptic integrals $K(κ)$ and $E(κ)$ with modulus $κ$ depending on trigonometric functions of the polar angle. We show that they diverge not only at the value $\mathbf q$ of the position eigenvalue, but also on a plane containing $\mathbf q$ and that they decay as inverse powers of the distance from $\mathbf q$.

Measurements can drive quantum many-body systems into nontrivial steady states and induce interesting dynamical phase transitions, rendering measurement-only quantum circuits a useful platform for exploring quantum many-body phases beyond those of equilibrium Hamiltonian systems. Here we study a class of long-range measurement-only quantum circuits with competing two-qubit and three-qubit measurements. We demonstrate that these circuits exhibit rich steady-state structure and uncover a strong influence of the measurement range on the resulting phases. In particular, states with symmetry-protected topological (SPT) order can emerge with sufficiently short-range measurements beyond the nearest-neighbor limit. These states feature robust topological edge modes, which can also be detected from circuit dynamics. With longer-range measurements, an extended parameter regime emerges in which conventional order parameters are suppressed while spatial correlations remain nontrivial. Moreover, we show that in this circuit model sufficiently long-range measurements can produce significant entanglement with scaling beyond an area law despite the absence of any unitary evolution.

Dissipation engineering has attracted growing interest as an approach to controlling open quantum systems through engineered system-environment interactions. Standard variational quantum circuits are usually built from unitary operations and therefore explore only a restricted family of states. To go beyond this limitation, we introduce a variational dissipative framework in which ancilla-assisted engineered dissipation is incorporated into parameterized quantum algorithms. In this framework, system-only variational layers are combined with trainable dissipative modules, so that the circuit can prepare a broader class of mixed states through ancilla-assisted nonunitary transformations. Within this framework, the same ancilla-assisted dissipative block is used in two representative settings with different objectives. For ground-state search, it is integrated into a dissipative variational quantum eigensolver to improve the convergence toward low-energy states. For state recovery, it is trained as a recovery channel to suppress preparation noise and enhance fidelity with the target state. In both cases, the block is realized through parameterized system-ancilla couplings followed by ancilla reset and trace-out. Our results show that engineered dissipation can be incorporated into variational quantum circuits as a reusable trainable primitive rather than treated only as a source of noise. In this sense, the proposed framework identifies ancilla-assisted dissipative channels as a concrete variational resource that can support both optimization and recovery tasks within a unified design.

Open quantum systems are central to quantum optics, condensed matter, and chemistry, yet their simulation remains challenging for both classical and near-term quantum hardware. In this work we implement and execute utility-scale quantum circuits that accurately reproduce the dissipative dynamics of interacting qubits. We consider a one-dimensional chain of many qubits weakly coupled to a common Markovian bath. The Markovian time evolution of the system is implemented through Trotterized evolution with the introduction of ancilla-assisted dissipative channels, including single-qubit and two-qubit dissipators to capture collective decay. Mid-circuit measurements, conditional gates, and hardware-aware transpilation significantly reduce circuit depth. We further implement a biased Clifford data regression (biased CDR), an error mitigation strategy that outperforms the uniform Cliffordization baseline and a variety of zero-noise extrapolation protocols. We execute large-scale quantum experiments of the dynamics of chains comprising up to 86 emitters on the IBM System Two \texttt{ibm\_basquecountry}. In order to do so, we use 129 total qubits (including ancillas), with the largest circuits contain about 8000 two-qubit gates. To validate these experiments we develop a classical Monte Carlo-Time-Evolving Block-Decimation (MC-TEBD) tensor-network method that incorporates reset operations through stochastic pure-state trajectories, obtaining very good agreement. The approach presented here opens a practical route for utility-scale quantum simulation of dissipative dynamics, enabled by dynamic circuits, targeted error mitigation, and tensor-network validation, and enables to tackle complex dynamics of systems such as quantum emitters in dissipative optical cavities.

Quantum wave mixing on a single superconducting qubit produces a hierarchy of coherent side peaks associated with elastic multiphoton scattering pathways. In a cascaded source--probe geometry these pathways become sensitive to the photon statistics of the radiation emitted by the source qubit. We develop an analytical theory of this effect starting from the cascaded master equation in the weak-driving regime. In the coherent-filtering limit $γ_{\rm s}\ggγ_{\rm pr}$, the standard coherent--coherent wave-mixing hierarchy is recovered. In the opposite limit $γ_{\rm pr}\ggγ_{\rm s}$, side peaks associated with multiphoton absorption from the antibunched source field are parametrically suppressed. Numerical solutions confirm the analytical scaling laws. The resulting sideband hierarchy provides a frequency-domain fingerprint of antibunched itinerant microwave light.

We formulate a one-dimensional flux-controlled anomalous Floquet quantum walk and show that it admits a direct microscopic realization in a driven bipartite lattice. The walk consists of a coin-dependent drift step and a momentum-dependent coin mixing step, so the same evolution operator governs quasienergy bands, boundary modes, and bulk dynamics in real space. Because the walk is chiral, the quasienergy gaps at $0$ and $π/T$ carry independent topological information, which organizes trivial, $0$-only, $π$-only, and coexistence sectors in the $(M,φ)$ plane. In the coexistence sector, a $0$ mode and a $π$ mode reside on the same edge and span a natural boundary logical subspace. One Floquet period acts there as a relative phase operation and produces a clear $2T$ response in local boundary observables. In the bulk, the same anomalous Floquet structure is probed dynamically in two complementary ways. Frame-resolved mean chiral displacements approach the two winding numbers in the clean pre-reflection window of the symmetric time frames, while selected benchmark cuts at a representative $0$ gap closing and a representative $π$ gap closing exhibit distinct local stroboscopic responses, with the $π$ gap benchmark showing a much stronger odd-even alternation. The boundary logical subspace and the bulk dynamical probes are therefore organized within one flux-controlled anomalous Floquet quantum walk, suggesting a symmetry-protected route to quantum-walk information primitives in driven microstructured lattices.

Quantum federated learning (QFL) on NISQ hardware is highly sensitive to backend heterogeneity: some clients contribute informative updates, while others contribute noise-dominated drift that uniform averaging cannot distinguish. We propose Q-RAIL (Quantum Reliability-Aware Federated Inference and Learning), a circuit- and calibration-aware aggregation method for hardware-heterogeneous QFL. Q-RAIL computes a client-specific effective noise budget from backend calibration metadata together with transpiled circuit statistics. This budget is converted into stabilized aggregation weights using temperature scaling, uniform mixing, and a minimum-weight floor. Q-RAIL was evaluated across multiple experimental settings, including an ablation study, and benchmarked against state-of-the-art methods on three datasets: MNIST, Fashion-MNIST, and OrganAMNIST. On the primary MNIST benchmark under strong hardware skew, Q-RAIL improves final test accuracy from FedAvg's 0.777 to 0.877, a +10.0-point gain corresponding to about 44.8% relative error reduction, while also exceeding the strongest wpQFL baseline (0.833). At the same time, test loss drops from 0.722 to 0.585, and test AUC rises from 0.920 to 0.973. Under non-IID MNIST, Q-RAIL reaches 0.813 vs 0.722 for FedAvg. It also outperforms FedAvg in 12/12 ansatz/CX-fold stress configurations and remains stronger at 4, 10, and 15 qubit setups. Overall, the results support calibration-driven, circuit-aware aggregation as a practical path toward robust QFL on heterogeneous quantum hardware.

Hybrid quantum neural networks (HQNNs) integrate parameterized quantum circuits (PQCs) within classical networks, where the behavior of the underlying PQCs is often the primary focus of analysis. In this context, expressibility and trainability are widely used to characterize PQC's performance and are commonly assumed to exhibit a trade-off, where highly expressive circuits are more susceptible to barren plateaus. However, the validity of this relationship in HQNNs remains unclear. In this paper, we systematically analyze the expressibility--trainability relationship in HQNNs across varying circuit depths, qubit counts, entanglement topologies. We consider different training configurations, including pure PQCs, quantum-only training in hybrid setting, and full end-to-end training of hybrid models. Our results show that pure PQCs exhibit only a weak and regime-dependent trade-off, while hybrid architectures increasingly disrupt and can eliminate this relationship under full hybrid training. This indicates that classical components reshape the optimization landscape, decoupling trainability from PQC expressibility. We further propose a multi-objective neural architecture search (NAS) framework that jointly optimizes expressibility, trainability, and task performance over a combined classical--quantum design space, revealing different Pareto-optimal solutions under full end-to-end and quantum only training in hybrid setting. different trainability definitions. Our results suggest that hybridization is not just an implementation detail, but a defining factor in the performance of quantum machine learning models.

We investigate the dynamics of a qubit chain locally coupled to a thermal reservoir, modeled through repeated collisions with particles drawn from a heat bath. Under suitable conditions, the resulting Lindblad equation is thermodynamically consistent -- it drives the system toward thermal equilibrium -- while remaining local at short times. This framework reveals a crossover between the global Lindblad equation derived from the secular approximation in weak-coupling theory and the local dissipative models often employed in the literature, which generally fail to ensure thermodynamic consistency.

Photons in a two-path interferometer best embody wave-particle duality (WPD), which is a core concept of quantum theory. So far, the WPD relation is commonly written as $V^2+D^2 \leq 1$, where $V$ is the interference fringe visibility and $D$ is path distinguishability, i.e., the distinguishability of which path a photon passed. This inequality is saturated only when the which-way marker (WWM), which embodies which-path information (WPI) via an internal degree of freedom of photons, such as polarization, is in a pure state. For mixed-state WWM, conventionally defined distinguishability underestimates the amount of WPI and thus does not saturate the WPD relation. Here, we introduce a generalized measure of distinguishability $D$ that properly quantifies the WPI and saturates the WPD relation for all pure- and mixed-state WWM within a purification-based framework. To this end, mixed-state WWM is treated as a result of entanglement formation between the WWM and an external degree of freedom, e.g., environment, and $D$ is defined so that it incorporates the total WPI shared between the WWM and the environment. We show that $D$ thus defined is experimentally quantifiable, independently of $V$, without access to the environment. We experimentally evaluate $V$ and $D$ using true single photons generated in the completely mixed (unpolarized) state, and thus verify the saturated WPD relation.

The permutation model is a classical spin system where elements of the symmetric group interact with one another. The partition function of this model is directly related to the entanglement structure of random quantum circuits and random tensor networks. In these contexts, the entanglement entropy undergoes a transition between area-law and volume-law scaling, depending on the model parameters. This transition point has attracted considerable attention. In the present work, we investigate the ferromagnetic-paramagnetic phase transition of the permutation model, which corresponds to the entanglement entropy transition. Using exact real-space renormalization group calculations on self-dual hierarchical lattices, we numerically determine finite-replica critical points for (q=mn=2,...,6). We compare the results with the duality prediction based on the Fourier transform of the symmetric group and then extrapolate the b=3 data toward the replica limit $mn\to0$, where the effective dimension is two. The comparison supports the duality-based estimate while also clarifying the systematic uncertainty associated with the extrapolation formula.

Boundary time crystals exhibit spontaneous breaking of continuous time-translation symmetry through persistent periodic oscillations in driven-dissipative many-body systems. Here, we show that multilevel interference provides a natural route beyond periodic order, enabling dissipative time quasicrystals without externally imposed quasiperiodic driving. We consider a collectively driven-dissipative four-level ensemble with two degenerate excited states and two degenerate ground states. In the thermodynamic limit, the exact mean-field dynamics reduces to an irrational flow on a two-dimensional torus, yielding quasiperiodic order parameters with discrete spectra generated by two incommensurate fundamental frequencies. Vanishing maximal Lyapunov exponents demonstrate that the nonlinear self-consistent dynamics remains nonchaotic. Our results establish a minimal interference-induced mechanism for time-quasiperiodic order and open a route toward higher-dimensional quasiperiodic dynamics in multilevel systems.

Photonic hyperentanglement enables increased information capacity and enhanced functionality for quantum communication and networking. However, synchronization of hyperentangled photon pairs requires maintaining correlations simultaneously across multiple degrees of freedom (DOFs). The preservation of polarization and energy-time entanglement in hyperentangled photon pairs is demonstrated using a free-space optical delay line based on nested Herriott cells. After a delay of 647 ns, a two-photon interference visibility of 93.9(3)% is observed in the energy-time DOF, while a CHSH parameter of 2.758(5) is obtained in the polarization DOF. These results confirm that entanglement correlations in both DOFs are preserved after propagation through the delay line. They demonstrate that free-space optical delay lines are compatible with complex photonic quantum states and provide a promising route toward delay-based memories for synchronization and multiplexing in quantum networks.

We investigate the fidelity susceptibility, which quantifies the sensitivity of single-particle eigenstates to perturbations, in the three-dimensional Anderson model. As a function of disorder strength $W$, it exhibits two distinct peaks. The first peak signals a crossover at weak disorder strength from plane-wave states to single-particle quantum chaos, and its position shifts toward $W\to 0$ in the thermodynamic limit. The second peak emerges, to high numerical accuracy, at the critical disorder strength associated with the Anderson localization transition. We further show that the divergence of the first peak is maximal, scaling as the square of the inverse frequency cutoff, whereas the divergence of the second peak is submaximal. We relate the latter suppression to the fractal structure of single-particle eigenstates at criticality. We discuss two distinct scenarios that give rise to the peaks in the fidelity susceptibilities. Moreover, studying the scaling of typical fidelity susceptibilities above the Anderson transition, we find evidence of two distinct regimes of nonergodic behavior.

We investigate the renormalized fermion-gluon vertex, the fermion effective mass, and the fermion condensate when the fermion propagates in an external Yang-Mills gauge field. We use an exact Green's function for the Dirac operator in a non-Abelian plane-wave gauge field to construct the renormalized vertex function, calculate the on-shell fermion self-energy, and the background-dependent condensate. We consider both the background and operator fields in the axial gauge $k^{μ} \mathcal{A}_{μ}^{a}=0$, thereby preserving the gauge. Its applications to strong-field QCD and non-Abelian Schwinger physics are discussed.

Variational quantum algorithms (VQAs) rely on parameterized quantum circuits (PQCs), whose performance is governed by expressibility and trainability. Existing studies typically evaluate these properties at the logical circuit level, implicitly assuming that designed PQCs remain unchanged during hardware execution. In practice, however, hardware-aware transpilation modifies circuit structure through qubit mapping, routing, and basis decomposition, potentially altering PQC behavior. In this paper, we perform a systematic hardware-aware analysis of expressibility and trainability by comparing logical and transpiled PQCs across multiple ansatz families, qubit counts, and circuit depths. Expressibility is measured using fidelity-based KL divergence, while trainability is quantified through gradient variance. Our results show that transpilation acts as an implicit architectural perturbation, producing strongly ansatz-dependent effects. Expressibility deviations exceed upto 125% in some cases, while trainability variations reach up to 25%. Structured ansatzes are generally more robust, whereas highly entangled architectures are more sensitive to transpilation-induced transformations. We further show that transpilation can alter the commonly assumed expressibility-trainability trade-off, demonstrating that logical-level analyses may not reliably predict hardware-level behavior. These findings highlight the importance of hardware-aware evaluation for accurate characterization of VQAs.

Correlations distributed by a mediator are usually valued for the coordination they enable between authorized agents, but in adversarial settings a more decisive property is whether the same coordination can be inherited by an outside colluder without disturbing the authorized marginal. Classical shared randomness is freely copyable, so a hidden seed coordinating two agents can be duplicated for a third; entanglement is constrained by monogamy, which can forbid such lossless extensions in strongly nonlocal regimes. We turn this asymmetry into an operational resource for private-information games. For a fixed authorized behavior $P_{12}$, we define its \emph{collusive shadow} as the set of relabelled behaviors a colluder can reproduce in any admissible tripartite extension preserving $P_{12}$, and we identify \emph{strategic non-shareability} with the distance from this shadow. We prove that, on finite alphabets, the game-optimized anti-collusion capacity equals the total-variation distance to the shadow; a fixed game provides a task-specific separating witness, while optimization over relabelled games recovers the full distance. In the CHSH score slice, Toner--Verstraete monogamy yields the exact certified frontier, so the Bell local bound $S_{12}=2$ is the sharp onset of positive certified anti-collusion power, saturating at $1/(2\sqrt{2})$ for the maximally entangled CHSH strategy. Classical hidden-variable mediators have zero capacity in this slice. We complement these results with two operational tools: a Hoeffding-based finite-data certification protocol that turns observed Bell scores into confidence-bounded anti-collusion certificates, and a level-2 NPA semidefinite relaxation that extends certified upper envelopes to tilted Bell inequalities. These results recast entanglement monogamy as a measurable shareability deficit for quantum-mediated strategic networks.

Quantum technologies have become a powerful paradigm for quantum information and simulation, while quantum chaos plays a key role in understanding complex quantum dynamics. Integrated photonics offers unique advantages for quantum applications, including high-speed operation, scalability, and programmable unitary transformations. However, probing quantum chaos on integrated photonic platforms remains largely unexplored because a clear connection between programmable photonic dynamics and established chaos diagnostics is still lacking. In this work, we establish Fock-state boson sampling as a practical probe of quantum chaos by exploiting the sensitivity of multiphoton interference to the random-matrix properties of underlying single-particle unitary dynamics. More importantly, we design and fabricate a programmable silicon quantum photonic chip to experimentally implement this framework, achieving the first integrated-photonic demonstration of quantum-chaos probes based on boson sampling. Experimental results show that the three complementary probes proposed in this work, namely the distance to Porter-Thomas statistics, Shannon entropy, and Out-of-Time-Ordered-Correlator-equivalent observables, exhibit close agreement with theoretical predictions and consistently distinguish chaotic and integrable dynamics. Our work provides a scalable route for investigating complex quantum dynamics on programmable photonic platforms while leveraging the intrinsic advantages of boson sampling through multiphoton interference and complex output statistics.

The non-Hermitian skin effect (NHSE) is a hallmark of non-Hermitian system, yet its generalized Brillouin zone (GBZ) description is restricted to periodic systems. We develop a site-resolved theory via a local scaling transformation (LST), introducing local twisting $T_n$ to quantify metric operator $ξ$ nontriviality. This elucidates the NHSE's origin and uncovers the generalized multiple-channel skin effect (MCSE). Exploiting $T_n$'s translational independence, we define the Zahlen-Brillouin Zone (ZBZ), extending non-Hermitian band theory to nonperiodic and disordered lattices. Furthermore, we unify the $ξ$ with GBZ Riemannian geometry, establishing the metric and state correspondence (MSC) as the principle for real-space localization. With a global skin index $\mathbfΓ$ for phase transitions, our results provide a universal paradigm for non-Hermitian physics in both crystalline and amorphous media.

Transformer now underpins modern AI as its core infrastructure. Its defining capability-dynamically focusing on the most relevant information in complex inputs-is bounded above by the self-attention scoring function. Quantum computing, with its superposition, entanglement, and probabilistic outputs, offers a fundamentally distinct computational framework for exploring beyond the design constraints of classical scoring functions. While quantum attention mechanisms have shown initial promise, existing works remain largely confined to redefining feature similarity measures, leaving the systematic use of parameterized quantum circuits (PQCs) as scoring functions largely unexplored; a substantial portion of existing schemes further rely on purely quantum architectures, precluding effective encoding of high-dimensional image inputs in the Noisy Intermediate-Scale Quantum era. We propose the Quantum Parameterized Self-Attention Network (QPSAN), implementing the self-attention scoring function via PQCs with only 5 trainable quantum parameters per layer. QPSAN computes query-key attention scores through quantum state encoding and joint measurement, yielding naturally bounded outputs without the explicit scaling of classical dot-product attention. We further establish a theoretical framework of the mathematical properties of this scoring function, demonstrating its potential to capture complex nonlinear query-key interactions, and quantifying the structural constraints of the encoding layer via effective degrees of freedom analysis. Experiments on four vision datasets show that QPSAN significantly outperforms the Vision Transformer (ViT) baseline, with the quantum representational advantage amplifying as data complexity increases. Ablation studies indicate that the performance gains may stem from the structural inductive bias of the quantum circuit rather than from parameter scale.

Large language models (LLMs) are dominated by dense linear transformations, whose storage, memory and computational overheads hinder efficient adaptation and deployment while masking the functional impacts of structural simplification. Here we present Tensor Mixture (MixT), a general tensor-structured compression scheme that replaces targeted dense linear layers with natively executable mixtures of tensor operators. Operating directly on generic linear projections instead of model-specific components, MixT is potentially applicable across Transformer-based LLMs and other dense neural mappings. We evaluate MixT on Qwen3-8B and LLaMA2-7B under a unified recovery protocol, identifying a broad compressible regime in which MMLU accuracy is largely preserved before an abrupt transition at model-specific boundaries. This transition coincides with coordinated shifts in output entropy, prediction entropy and inter-layer geometry. At the LLaMA2-7B transition boundary, MixT reduces full-model parameters by 47.5\%, inference FLOPs by 37.1\%, training FLOPs by 52.1\% and peak inference memory by 60.4\%, demonstrating its practical potential for lower-cost LLM compression.

Nondispersive wave packets in driven helium are long-lived quantum states that follow classical resonant orbits without spreading. Their identification typically requires detailed analysis of phase-space structures and extensive exploration of parameter regimes. In this work, we introduce an unsupervised learning approach to automate the identification of physically relevant states in the driven helium atom. Using a Floquet-based description, quantum states are computed and represented as probability distributions in configuration and phase space, which serve as input to a convolutional neural network that constructs a low-dimensional embedding of the data. Clustering in the embedding space reveals distinct classes of quantum states. By combining geometric analysis, physical parameter inspection, and time-evolution studies, we identify clusters corresponding to frozen planet states and nondispersive wave packets. The method successfully recovers known NDWP regimes without prior labeling, demonstrating that the learned representation captures physically meaningful structures in a systematic and automated manner. These results establish unsupervised representation learning as an effective tool for the systematic analysis of complex quantum datasets.

We present a microscopic statistical-mechanical foundation for interpreting the horizon area of a scrambling black hole as coherent information, equivalently negative conditional quantum entropy, in Hawking's pair-creation picture. We derive the entropy increase induced in a black hole when an infalling object is absorbed and scrambled into its microscopic degrees of freedom. Up to finite-reservoir corrections, this increase takes a canonical form at the Hawking temperature, regardless of the entropy carried by the infalling object. Applying this entropy formula to an incoming mode paired by time reversal with an outgoing Hawking radiation mode, we show that their partition-function contributions cancel in the coherent-information balance associated with the horizon area. The resulting area response is then determined only by the energy flux, in agreement with the black-hole first law.

Recent developments in the formalisation of quantum causal structures have made it possible to test and compare hypotheses about causal structure empirically, rather than being a-priori assumptions. Such differences in causal structure may be leveraged to distinguish between the processes they belong to, akin to distinguishing between quantum states known to belong to different eigenspaces of an observable. So how far this analogy can be pushed? Can causal order be interpreted as a kind of observable? Can it be measured? To this end we construct a completely operational definition of observables in terms of `discrimination tasks'. This begins with some base set of classes (analogous to a quantum observable's eigenspaces) before we impose three conditions on how these classes relate under discrimination tasks. These conditions recover the properties of a standard observable, letting us apply this definition to non-state entities such as quantum processes, which naturally encode causal structure. These conditions can be described in plain language as (1) `members of any class are perfectly distinguishable from members of any other' (i.e. our classes are `sharp'), (2) `entities perfectly distinguishable pairwise are all perfectly distinguishable by a joint intervention', and (3) `if all members of a class are perfectly distinguishable from an entity, then the whole class is perfectly distinguishable from it jointly'. By analysing classes of quantum processes having strict causal orders, we find causal classes which are sharp but violate condition 2, and classes which violate condition 3. This implies that causal order cannot be an observable. We note cases in the literature which claim to prove the opposite, and discuss them. We find their analyses presume special circumstances equivalent to conditions (2) and (3), and so do not contradict our own findings.

Accurate prediction of molecular correlation energies from first principles requires resolving the {O}(N^4) electron repulsion integral (ERI) tensor. Existing graph neural network approaches to the electronic structure problem often compress this tensor into low-rank scalar features, discarding higher-order interaction structures relevant to electron correlation. In this work, we demonstrate that tensor factorization of the ERI naturally induces a structured bipartite message-passing architecture that preserves access to higher-order interaction structure more effectively than compressed orbital representations. By utilizing the density-fitted Cholesky decomposition of the ERI tensor, we derive a bipartite graph network that models orbital degrees of freedom and auxiliary interaction nodes as distinct sets, maintaining interaction topology at a reduced theoretical complexity of {O}(N^3). Evaluated on 132 geometries of six diatomic molecules with Full Configuration Interaction (FCI) reference energies, our factorized representation achieves an in-distribution Mean Absolute Error (MAE) of 0.0296 Ha under five-fold cross-validation, a substantial improvement over compressed-integral baselines. Leave-one-molecule-out validation reveals that zero-shot generalization varies by nearly a factor of four across molecular species and correlates with the structural similarity of the held-out molecule's orbital environment to the training distribution, rather than with nuclear charge asymmetry alone.

We argue that the SYK model provides a conditional realization of Cryptographic Censorship in JT gravity. By using the Weingarten calculus and random matrix universality, we prove that the SYK disorder ensemble is an approximate unitary $k$-design for all $k=\poly(N)$, with deviation controlled by the spectral form factor. We then formulate the planted-SYK hardness conjecture and provide evidence from spectral universality and the low-degree polynomial framework. Under this conjecture, the approximate design becomes a gravitationally pseudorandom unitary. Together with the efficient causal wedge reconstruction in JT gravity, this leads to the conclusion that typical states in the SYK microcanonical window must have event horizons in their bulk duals, with the horizonless fraction doubly exponentially small. We further identify the regularized geodesic length of the maximal interior slice as the explicit distinguishing operator. Its prediction gap grows linearly with time due to the stretching of the black hole interior, linking Cryptographic Censorship to the complexity equals volume conjecture.

Solid-state quantum sensors based on ensembles of nitrogen-vacancy (NV) centers in diamond have emerged as powerful platforms for high-precision metrology. Coupling the NV ensemble to a microwave cavity mode in a cavity quantum electrodynamics (cQED) configuration enables spin readout that surpasses the limitations of conventional optical detection, achieving sub-picotesla magnetic sensitivities. However, existing continuous-wave cQED approaches remain far from the intrinsic spin-projection-noise limit due to spin saturation and power broadening. Here, we introduce a dispersive cQED readout technique to overcome these fundamental limitations in NV ensemble sensing. We develop a comprehensive theoretical framework describing the dispersive interaction and analyze the time-domain dynamics of a strongly-coupled NV-cavity system. Our results indicate near-unity inverse readout fidelity and femtotesla-level sensitivity using a commercially available diamond NV ensemble. Importantly, the dispersive readout exhibits a distinct sensitivity scaling that improves as 1/N with increasing number of spins N, providing a practical pathway toward approaching the standard quantum limit for solid-state spin-ensemble sensors.

This paper introduces the Quantum Covariance Embedding, which embeds Positive Operator-Valued Measures into a tensor product of a Reproducing Kernel Hilbert Space and the quantum state space via a tensorized Bochner integral. This construction induces the Quantum Maximum Discrepancy that metrizes the space of quantum measurements. Applying this framework to Quantum State Tomography, we reformulate density estimation as a tensorized kernel regression, enabling optimal inference without the basis-dependent sparsity constraints that restrict existing methods. We develop a unified geometric design theory for quantum Gram superoperators, establishing that Unitary Designs are strictly E-optimal experimental designs and thus statistically superior to Pauli observables. For general structure-free estimation, we derive the exact minimax lower bound and prove that our tensorized estimators achieve this optimal rate. Furthermore, we introduce the QUAntum Regression with Kernels (QUARK) estimator to accommodate the spectral geometry of physical implementations, deriving central limit theorem and concentration inequalities. To facilitate practical estimation, we establish the exactness of trace-preserving projections and demonstrate efficient estimation under mutually unbiased bases via the fast Walsh-Hadamard transform.

In this thesis, I explore whether it is possible to build a unified Quantum Internet architecture that supports different types of quantum repeaters -- especially the two most distinct and seemingly incompatible ones: memory-based quantum repeaters and all-photonic, memoryless repeaters. These technologies have traditionally been developed with the aim of becoming the single dominant solution, but I ask: Can they work together in the same network? What kind of architecture would support both? And how can simulation help us understand what is needed to manage such a network at scale? To address these questions, I propose an architecture based on an existing recursive network design and programmable RuleSet-based protocols that can coordinate diverse hardware components. I introduce a new emitter-photon building block to bridge memory-based and all-photonic segments, and show how classical networking abstractions can be extended to manage quantum operations. While I have developed a simulation tool grounded in these architectural principles and validated it against existing simulators and analytical models, a full-scale investigation of the resource trade-offs and performance implications remains future work. Nevertheless, the results so far suggest that a unified, heterogeneous quantum network is not only possible but increasingly practical with current technologies -- though ongoing experimental progress will be essential to fully realize this vision.

With coupled detuned oscillators, either individual or collective oscillations are observable. The latter is used in quantum information processing in linear Paul traps. Here, we study the transition from collective radial modes at stronger axial confinements into individual radial oscillations at low axial confinements in a tapered Paul trap. The eigenmodes are experimentally studied in detail in the transition regime and compared with theoretical predictions. The features studied will enable investigation of modified heat transport phenomena and defect formation in trapped ions.

Identifying spatial quantum correlations in mixed states is challenging because thermal mixed-state contributions obscure the entanglement encoded in subsystem entropy. Here, we introduce the entanglement projected entropy, a diagnostic for extracting boundary-sensitive quantum correlations from mixed fermionic Gaussian states. By resolving subsystem entropy into Gaussian entanglement channels and projecting their purification partners onto the physical complement, we obtain a closed-form expression in terms of the physical covariance matrix. In a one-dimensional free-fermion chain, it removes the volume-law mixed-state background and recovers the zero-temperature conformal scaling with the $c/3$ coefficient. In a two-dimensional half-filled $π$-flux model, it reveals a universal finite-temperature scaling collapse governed by an effective Dirac infrared length. These results establish entanglement projected entropy as a Gaussian spatial filter for boundary-sensitive quantum correlations hidden in mixed-state entropy.