Quantum Physics Paper Analysis

Solving the Elliptic Curve Discrete Logarithm Problem (ECDLP) is critical for evaluating the quantum security of widely deployed elliptic-curve cryptosystems. Consequently, minimizing the number of logical qubits required to execute this algorithm is a key object. In implementations of Shor's algorithm, the space complexity is largely dictated by the modular inversion operation during point addition. Starting from the extended Euclidean algorithm (EEA), we refine the register-sharing method of Proos and Zalka and propose a space-efficient reversible modular inversion algorithm. We use length registers together with location-controlled arithmetic to store the intermediate variables in a compact form throughout the computation. We then optimize the stepwise update rules and give concrete circuit constructions for the resulting controlled arithmetic components. This leads to a modular inversion circuit that uses $3n + 4\lfloor \log_2 n \rfloor + O(1)$ logical qubits and $204n^2\log_2 n + O(n^2)$ Toffoli gates. By inserting this modular inversion component into the controlled affine point-addition circuit, we obtain a space-efficient algorithm for the ECDLP with $5n + 4\lfloor \log_2 n \rfloor + O(1)$ qubits and $O(n^3)$ Toffoli gates. In particular, for a 256-bit prime-field curve, our estimate reduces the logical-qubit count to 1333, compared with 2124 in the previous low-width implementation of Häner et al.

In trapped-ion chains, multipartite GHZ states can be prepared natively with the help of a single bichromatic laser pulse. However, higher-order terms in the expansion in the Lamb-Dicke parameter $η$ limit the GHZ state preparation infidelity for rectangular and bell-like pulses to the order of $η^4$. For tens of ions, the infidelity caused by out-of-Lamb-Dicke effects can reach several percents. We propose an amplitude and phase-modulated pulse shape, an "echoed lemniscate pulse", which cancels this contribution into error in the leading order. For the proposed pulse, the infidelity scales as $η^6$. The improved scaling is achieved because of a special phase trajectory of a collective motional mode following the figure-eight curve (lemniscate). We demonstrate that the lemniscate pulse allows achieving lower infidelity than bell-like pulses, which can be as low as $10^{-4}$ for $20$-ion chains.

We investigate the quantum algorithms for dynamic programming by Ambainis et al. (SODA'19). While giving provable complexity speedups and applicable to a variety of NP-hard problems, these algorithms have a notable drawback: they require a large amount of Quantum Random Access Memory (QRAM), which potentially could be very challenging to implement in a physical quantum computer. In this work, we study how we can improve the space complexity by trading it for time, while still retaining a speedup over the classical algorithms. We show novel quantum time-space tradeoffs, which we obtain by adjusting the parameters of these algorithms and combining them with "quantized" classical strategies.

Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited connectivity. In this work, we explore a non-Pauli stabilizer code that can be used to complete a universal gate set on topological toric and surface codes in strictly two dimensions. Fault-tolerant syndrome extraction for the non-Pauli code requires mid-circuit $X$ corrections, a key difference to conventional Pauli codes. We construct and benchmark a just-in-time (JIT) matching decoder to reliably decide these corrections. Under a phenomenological error model with equally likely physical and measurement errors, we find a high threshold of $\approx 2.5\,\%$, close to the $\approx 2.9\,\%$ of a decoder with access to the full syndrome history. We also perform a finite-size scaling analysis to estimate how the logical error rate scales below threshold and verify an exponential suppression in both physical error rate and in the system size. A second global decoding step for $Z$ errors is required and the non-Clifford gates in the circuit reduce the threshold from $\approx 2.9\,\%$ to $\approx 1.8\,\%$ with a naive decoder. We show how $Z$ decoding can be improved using knowledge of the $X$ corrections, pushing the threshold to $\approx 2.2\,\%$. Our results suggest non-Clifford logic in 2D codes could perform comparably to 2D quantum memory. Our formalism for efficient benchmarking and decoding directly generalizes to a broader family of CSS codes whose $X$ stabilizers are twisted by diagonal Clifford operators, and spacetime versions thereof, defined by CSS-like circuits enriched by $CCZ$, $CS$, and $T$ gates.

We exhibit nontrivial transversal logical multi-controlled-$Z$ gates on $[\![N,Θ(N),\tildeΘ(N)]\!]$ quantum low-density parity-check codes and $[\![N,Θ(N),\tildeΘ(N)]\!]$ quantum locally testable codes with soundness $\tildeΘ(1)$, combining nearly optimal code parameters with fault-tolerant non-Clifford gates for the first time. Remarkably, our proofs are almost entirely algebraic-topological, showing that such presumably intricate logical gates naturally arise as a fundamental topological phenomenon. We develop a general framework for constructing a rich new family of homological invariant forms which we call ''cupcap gates'' that induce transversal logical multi-controlled-$Z$ and, building on insights from [Li et al., arXiv:2603.25831], covering space methods to certify their nontriviality. The claimed almost-good code results follow immediately as examples.

We introduce a twisted fiber-bundle construction of quantum CSS codes over group algebras \(R=\mathbb F_2[G]\), where each base generator carries a generator-dependent \(R\)-linear fiber twist satisfying a flatness condition. This construction extends the untwisted lifted product code, recovered when all twists are identities. We show that invertible twists (satisfying a flatness condition) give a complex chain-isomorphic to the untwisted one, so the resulting binary CSS codes have the same blocklength \(n\) and encoded dimension \(k\). In contrast, singular chain-compatible twists can lower boundary ranks and increase the number of logical qubits. Examples over \(R=\mathbb F_2[D_3]\) show that the twisted fiber bundle code can outperform the corresponding untwisted lifted-product code in \(k\) while keeping the same \(n\) and, in our examples, the same minimum distance \(d\).

Utility-scale quantum computing requires the integration and operation of a large-scale qubit register. Semiconductor spin qubits are a primary candidate for this, due to the prospects of building integrated hybrid quantum-classical architectures. However, scaling spin-qubit systems while preserving performance and control has remained a challenge. Here, we demonstrate the operation of an 18-qubit array in germanium based on an extendable 2xN architecture. We achieve simultaneous initialization, control, and readout across the entire array, enabled by parallel operation of modular unit cells. Across the array, we achieve average and median single-qubit gate fidelities of 99.8% and 99.9%, respectively. Finally, we characterize the nearest-neighbor exchange couplings throughout the device and implement high-quality controlled-Z gates to generate a three-qubit Greenberger-Horne-Zeilinger (GHZ) state. These results demonstrate that spin-qubit arrays can be scaled while maintaining high-fidelity operation and establish a modular, extendable architecture for planar semiconductor quantum processors.

We present Tsim, an open-source high-throughput simulator for universal noisy quantum circuits targeting quantum error correction. Tsim represents quantum circuits as ZX diagrams, where Pauli channels are modeled as parameterized vertices. Diagrams are simplified via parameterized ZX rules, and then compiled for vectorized sampling with GPU acceleration. After the one-time compilation, one can sample detector or measurement shots in linear time in the number of Clifford gates and exponentially only in the number of non-Clifford gates. Tsim implements the Stim API and fully supports the Stim circuit format, extending it with T and arbitrary single-qubit rotation instructions. For low-magic circuits, Tsim throughput can match the sampling performance of Stim.

Quantum gates executed on physical hardware are inevitably degraded by environmental noise. While state purification effectively distills static quantum resources, the dynamic execution of quantum algorithms requires a higher-order approach to mitigate errors on the operations themselves. In this work, we investigate unitary purification: the task of utilizing a quantum higher-order operation to partially restore the ideal action of an unknown unitary corrupted by a known noise model. Focusing on canonical depolarizing noise, we first reveal a fundamental operational obstruction. We prove that within the indefinite causal order framework, no nontrivial 2-slot higher-order operation can universally purify the set of single-qubit unitaries. Overcoming this strict limitation, we establish that a 3-slot architecture provides the minimal realization for non-trivial universal purification. We analytically derive the optimal average fidelity for the 3-slot regime, demonstrating that it strictly surpasses trivial strategies by systematically utilizing ancillary qubits as a quantum memory to absorb errors. Furthermore, we provide a concrete quantum circuit construction for this optimal higher-order operation. Our results establish the strict theoretical boundaries of distilling clean operations from noisy gates, offering immediate architectural insights for robust gate design.

With code and syndrome-extraction schedule fixed, can routed geometry alone change the correlated fault model enough to impact logical performance? Starting from a geometry-conditioned same-tick interaction Hamiltonian, we derive a controlled retained single-and-pair data-fault model for bivariate-bicycle (BB) layouts. Two geometry metrics emerge in two kernel regimes: under a crossing-local diagnostic kernel, a matching argument reduces the support-level effective fault weight; when every support pair appears in at least one retained round with finite same-round separation, strictly positive kernels saturate the support graph, and weighted exposure becomes the discriminating quantity. Circuit-level Monte Carlo on the $[\![72, 12, 6]\!]$ and $[\![144, 12, 12]\!]$ benchmarks confirms that a biplanar bounded-thickness layout suppresses the monomial single-layer embedding penalty, with weighted exposure tracking logical error rate across 101 operating points (Spearman correlation 0.893). A single-layer logical-family optimization on BB72 reduces worst-case exposure by 26.11% and lowers logical error rate in the tested power-law window. Routed geometry should be optimized together with code, schedule, and decoder.

In the context of finite Abelian groups two problems are presented and solved using quantum computing techniques. The first is the well--known Hidden Subgroup Problem, originally solved by Simon in a landmark work. The second is the Fully Balanced Image Problem, originally introduced by the authors (joint with J. Ossorio--Castillo), which is related to a certain class of mappings (which contains strictly, for instance, the family of group morphisms). Both problems are tackled using a combination of two techniques: first, a conversion into Boolean objects, better suited for quantum computing arguments, and subsequently a custom--tailored algorithm which takes advantage of the Generalised Phase--Kick Back technique.

Neutral atom quantum computers (NAQCs) are among the most promising computational platforms for quantum computing. Controlling and measuring individual atoms and their states, which often requires multiple imaging and image-analysis procedures, is typically the most time-consuming task during computation and contributes significantly to overall cycle times. To resolve this challenge, we propose a highly-parallel atom-detection accelerator for tweezer-based NAQCs. Our design builds on an existing state-reconstruction method and combines an algorithm-level optimization with a Field Programmable Gate Array (FPGA) implementation to maximize parallelism and reduce the run time of the image-analysis process. We identify and overcome several challenges for an FPGA implementation, such as introducing a prefetching mechanism to improve scalability and customizing bus transfers to support large bandwidths. Tested on a Xilinx UltraScale+ FPGA, our design can analyze a 256x256-pixel fluorescence image in just 115mus, achieving 34.9x and 6.3x speedups over the original and optimized CPU baseline, respectively. Moreover, our accelerator can maintain consistent resource utilization across various atom array sizes, contributing to the ongoing efforts toward scalable and fully integrated FPGA-based control systems for NAQCs.

The impending arrival of cryptographically relevant quantum computers (CRQCs) threatens the security foundations of modern software: Shor's algorithm breaks RSA, ECDSA, ECDH, and Diffie-Hellman, while Grover's algorithm reduces the effective security of symmetric and hash-based schemes. Despite NIST standardising post-quantum cryptography (PQC) in 2024 (FIPS 203 ML-KEM, FIPS 204 ML-DSA, FIPS 205 SLH-DSA), most codebases lack automated tooling to inventory classical cryptographic usage and prioritise migration based on quantum risk. We present Quantum-Safe Code Auditor, a quantum-aware static analysis framework that combines (i) regex-based detection of 15 classes of quantum-vulnerable primitives, (ii) LLM-assisted contextual enrichment to classify usage and severity, and (iii) risk scoring via a Variational Quantum Eigensolver (VQE) model implemented in Qiskit 2.x, incorporating qubit-cost estimates to prioritise findings. We evaluate the system across five open-source libraries -- python-rsa, python-ecdsa, python-jose, node-jsonwebtoken, and Bouncy Castle Java -- covering 5,775 findings. On a stratified sample of 602 labelled instances, we achieve 71.98% precision, 100% recall, and an F1 score of 83.71%. All code, data, and reproduction scripts are released as open-source.

Reducing the non-Clifford cost of fault-tolerant quantum circuits is a central challenge in quantum compilation, since T gates are typically far more expensive than Clifford operations in error-corrected architectures. For Clifford+T circuits, minimizing T-count remains a difficult combinatorial problem even for highly structured algebraic optimizers. We introduce VarTODD, a policy-parameterized variant of FastTODD in which the correctness-preserving algebraic transformations are left unchanged while candidate generation, pooling, and action selection are exposed as tunable heuristic components. This separates the quality of the algebraic rewrite system from the quality of the search policy. On standard arithmetic benchmarks, fixed hand-designed VarTODD policies already match or improve strong FastTODD baselines, including reductions from 147 to 139 for GF(2^9) and from 173 to 163 for GF(2^10) in the corresponding benchmark branches. As a proof of principle for automated tuning, we then optimize VarTODD policies with GigaEvo, an LLM-guided evolutionary framework, and obtain additional gains on harder instances, reaching 157 for GF(2^10) and 385 for GF(2^16). These results identify policy optimization as an independent and practical lever for improving algebraic T-count reduction, while LLM-guided evolution provides one viable way to exploit it.

In this paper, we construct several new quantum Floquet codes on compact, orientable, as well as non-orientable surfaces. In order to obtain such codes, we identify these surfaces with hyperbolic polygons and examine hyperbolic semi-regular tessellations on such surfaces. The method of construction presented here generalizes similar constructions concerning hyperbolic Floquet codes on connected and compact surfaces with genus $g \geq 2$. A performance analysis and an investigation of the asymptotic behavior of these codes are also presented.

Quantum computing is expected to become a foundational technology for solving problems that exceed the capabilities of classical systems. As quantum algorithms and hardware technologies continue to advance, the need for scalable architectures becomes increasingly clear. Distributed quantum computing offers a promising path forward by interconnecting multiple smaller processors into a larger, more powerful system. However, distributed quantum computing introduces significant circuit depth overhead, as logical operations are typically decomposed into sequential physical procedures that require entanglement generation. These sequential operations limit the reliability of quantum algorithms in the NISQ era due to noise. In this work, we present a compiler that integrates logical-to-physical decomposition with depth-aware rescheduling to reduce the execution cost of distributed quantum circuits. The compiler identifies sequences of logical CNOT gates that share a control or target qubit, reschedules them into parallel instruction groups, and applies decompositions that allow multiple gates to be executed simultaneously using distributed shared entanglement resources. An algorithm is proposed that ensures parallelism is created when possible while keeping logical equivalence and that circuit depth is never increased. Benchmark results demonstrate that the compiler consistently reduces circuit depth for circuits containing inherently sequential CNOT structures, while leaving already-parallel circuits unchanged. These results highlight the value of combining scheduling and hardware-aware decomposition, and establish the compiler as a practical tool for improving the fidelity of distributed quantum computations.

Superconducting quantum processor units (QPUs) are incapable of producing massive datasets for quantum error correction (QEC) because of hardware limitations. Thus, QEC decoders heavily depend on synthetic data from qubit error models. Classic depolarizing error models with polynomial complexity present limited accuracy. Coherent density matrix methods suffer from exponential complexity $\propto O(4^n)$ where $n$ represents the number of qubits. This paper introduces PAEMS: a precise and adaptive qubit error model. Its qubit-wise separation framework, incorporating leakage propagation, captures error evolvements crossing spatial and temporal domains. Utilizing repetition-code experiment datasets, PAEMS effectively identifies the intrinsic qubit errors through an end-to-end optimization pipeline. Experiments on IBM's QPUs have demonstrated a 19.5$\times$, 9.3$\times$, and 5.2$\times$ reduction in timelike, spacelike, and spacetime error correlation, respectively, surpassing all of the previous works. It also outperforms the accuracy of Google's SI1000 error model by 58$\sim$73\% on multiple quantum platforms, including IBM's Brisbane, Sherbrooke, and Torino, as well as China Mobile's Wuyue and QuantumCTek's Tianyan.

We define the class of register-logic graphs and prove that any uniformly deterministic measurement-based quantum computation (MBQC) where the inputs coincide with the outputs must be driven on such graphs by measurements in the $YZ$ plane of the Bloch sphere. This observation is revisited in the context that goes beyond uniform determinism, where we present a universal $YZ$-plane-only measurement pattern and establish a connection between $YZ$-plane-only and $XZ$-plane-only patterns. These results conclude the line of research on universal patterns with measurements restricted to one of the principal planes of the Bloch sphere. We further demonstrate, within the framework of the Parity Architecture, that $YZ$-plane patterns with the register-logic graph can be embedded into another graph with purely local interactions, and we extend this case to the scenario of universal quantum computation.

Quantum computers have the potential to perform computational tasks beyond the reach of classical machines. A prominent example is Shor's algorithm for integer factorization and discrete logarithms, which is of both fundamental importance and practical relevance to cryptography. However, due to the high overhead of quantum error correction, optimized resource estimates for cryptographically relevant instances of Shor's algorithm require millions of physical qubits. Here, by leveraging advances in high-rate quantum error-correcting codes, efficient logical instruction sets, and circuit design, we show that Shor's algorithm can be executed at cryptographically relevant scales with as few as 10,000 reconfigurable atomic qubits. Increasing the number of physical qubits improves time efficiency by enabling greater parallelism; under plausible assumptions, the runtime for discrete logarithms on the P-256 elliptic curve could be just a few days for a system with 26,000 physical qubits, while the runtime for factoring RSA-2048 integers is one to two orders of magnitude longer. Recent neutral-atom experiments have demonstrated universal fault-tolerant operations below the error-correction threshold, computation on arrays of hundreds of qubits, and trapping arrays with more than 6,000 highly coherent qubits. Although substantial engineering challenges remain, our theoretical analysis indicates that an appropriately designed neutral-atom architecture could support quantum computation at cryptographically relevant scales. More broadly, these results highlight the capability of neutral atoms for fault-tolerant quantum computing with wide-ranging scientific and technological applications.

Fault-tolerant quantum computing requires large-scale superconducting processors, yet monolithic architectures face increasing constraints from wiring density, crosstalk, and fabrication yield. Modular superconducting platforms offer a scalable alternative, but achieving high-fidelity entangling gates between distant modules remains a central challenge, particularly for highly coherent fixed-frequency qubits. Here, we propose a distributed hardware architecture designed to overcome this bottleneck by employing a pair of double-transmon couplers (DTCs). By synchronously controlling the two DTCs stationed at opposite ends of a macroscopic cable, our scheme strongly suppresses residual static inter-module coupling while enabling on-demand activation of a non-local cross-Kerr interaction with an on/off ratio exceeding $10^6$. Through comprehensive system-level numerical simulations incorporating realistic hardware parameters, we demonstrate that this mechanism can realize a remote controlled-Z (CZ) gate with a fidelity over 99.99\% between fixed-frequency transmons housed in separate packages interconnected by a 25 cm coaxial cable. These results establish a highly viable, hardware-efficient route toward high-performance distributed superconducting processors.

Adiabatic quantum algorithms must evolve slowly enough to suppress non-adiabatic transitions while remaining fast enough to be practical. In open systems, this trade-off is reshaped by decoherence. For Hamiltonians subject to dephasing Lindbladians, Avron et al. [1] showed that a unique timetable exists that maximizes the fidelity with a target state. This optimal schedule is characterized by a constant tunneling rate along the adiabatic path. In this work, we revisit their analysis and apply it to the adiabatic Grover search framework, obtaining closed-form expressions for the optimal evolution schedule, the minimum runtime, and the resulting achievable fidelity. Moreover, by invoking an energy-time uncertainty argument, we identify a critical dephasing threshold, beyond which further noise-assisted acceleration is prohibited, thereby defining the physically realizable boundaries for dephasing-based adiabatic quantum search protocols.

Protecting information in systems that have more than two basis states (qudits) not only offers a promising route for reducing the number of individual quantum locations that must be protected, while more accurately reflecting the structure of realistic quantum hardware, but also has some possibly enticing foundational strengths. While work in the past has largely focused on protecting information in quantum devices with locations that are some consistent local structure, this work considers coding-theoretic constraints on devices constructed from locations which may vary in their local structures -- these are mixed-register quantum devices. In this work we provide some general results for mixed-register Pauli operators, then identify some stabilizer encoded information forms that are forbidden. Building on these insights, we construct coding-theoretically optimal mixed-register stabilizer codes from sets of codes defined on coprime local-dimensions. The construction of such codes results in codes with logical subspaces that do not directly correspond to any of the constituent local-dimensions.

We study Anderson localization in a one-dimensional disordered system with long-range correlated hopping decaying as $1/r^{a}$ with complex hopping amplitudes that break time-reversal symmetry in a tunable fashion by varying their argument. We find analytically a corelation-induced algebraic localization that is robust to a finite strength of the time-reversal-symmetry-breaking parameter, beyond which all states delocalize. This establishes a localization--delocalization transition driven by the interplay between long-ranged correlated hopping and time-reversal symmetry breaking. In addition to obtaining the static localization phase diagram, we also investigate the dynamical phase diagram through the lens of wavepacket spreading. We find that the growth in time of the mean-squared displacement of a wavepacket, which is subdiffusive for the time-reversal symmetric case, becomes diffusive for any finite value of the time-reversal-symmetry-breaking parameter.

Single-photon sources with high single-photon purity and high brightness are key elements of many future quantum technologies. While photon blockade (PB) is widely exploited in the development of such sources, achieving the coexistence of high purity and high brightness remains a long-standing challenge. Here, we identify a novel mechanism for high-brightness PB and demonstrate that near-ideal purity and near-ideal brightness can be simultaneously achieved in an extended nondegenerate two-photon Jaynes-Cummings model with two-body and three-body interactions. This mechanism is underpinned by a distinctive energy-level structure arising from the combined action of the two interactions. The energy levels in the multi-excitation manifold essentially retain a harmonic ladder of degenerate doublets, whereas in the single-excitation subspace the doublet degeneracy is lifted, with a finite splitting between the two levels. Consequently, when one bosonic mode is driven by a coherent continuous-wave pump, the former degeneracy enables the other bosonic mode to exhibit near-perfect PB even in the strong driving regime, while the latter splitting allows the mean photon number of that mode to approach unity. Our proposed scheme overcomes the outstanding challenge and offers a promising pathway toward realizing ideal single-photon sources.

We investigate the semiclassical regularity of thermal equilibria in the presence of a harmonic potential at low temperature; that is, we obtain the asymptotic behavior of the Schatten norms of commutators of the one-body operators associated with these equilibria and the position and momentum operators. We also obtain upper bounds in the magnetic field case for the Fock-Darwin Hamiltonian. Our estimates, in particular, allow us to observe several regimes depending on the joint behavior of the Planck constant, the temperature, and the strength of the magnetic field.

Organising the space of entanglement structures of a multipartite quantum system is a much more challenging task than its bipartite version: while the local unitary (LU) orbit of a bipartite pure state can be conveniently characterized by its entanglement spectrum, invariants of multipartite entanglement structures are comparatively difficult to define and work with. The root cause of this difference is that the bipartite problem can be reduced to the analysis of matrix invariants, while its multipartite version is governed by a much richer space of tensor invariants. The present work explores the latter through the lens of so-called trace-invariants, which are in one-to-one correspondence with combinatorial objects known as colored graphs. We first explain why trace-invariant evaluations can serve as labels of LU-orbits of multipartite pure states, how this strategy extends to random states, and how the effect of local operations (LO) can be analyzed through such data. We then focus on entanglement classification within an (infinite-dimensional) subspace of reference states, whose basic building blocks are GHZ states of various dimensions. We show that relatively simple subclasses of trace-invariants are sufficient to separate the LU-orbits of reference states, and enable a complete (resp. an incomplete) characterization of their relations in the LO (resp. LOCC) resource theory of entanglement. Finally, we investigate how a (still infinite) subclass of reference states of local dimension N can be efficiently distinguished at leading and subleading orders in an asymptotic large-N expansion (among themselves, or from Haar-random states). This analysis relies crucially on combinatorial quantities associated to colored graphs, some of which have already played instrumental roles in the recent literature on random tensors. Results of broader relevance are reported along the way.

We present a detailed computational and algebraic study of Mutually Unbiased Bases (MUBs) in finite-dimensional Hilbert spaces, with a particular focus on dimensions 2, 3, 4, and the challenging case of 6. Starting from the Hadamard-phase parametrization, we derive explicit analytical conditions for mutual unbiasedness in dimension 4, providing a tractable system of trigonometric constraints on the phase parameters. We then explore a tensor-product construction via Pauli operators, highlighting the algebraic and group-theoretical origin of MUBs in two-qubit systems, and demonstrating how these constructions yield a complete set of 5 MUBs in dimension 4. Extending our approach, we investigate the Fourier-family method in dimension 6, where the absence of a prime-power structure imposes strong rigidity constraints and limits the known constructions to sets of 3 MUBs. We provide a systematic computational framework for testing candidate phase vectors, bridging the gap between analytical insight and numerical exploration. Finally, we generalize the discussion to arbitrary prime-power dimensions, emphasizing the role of finite-field structures, Heisenberg-Weyl operators, and discrete symmetries in generating complete sets of MUBs. Our work offers a transparent, line-by-line verification methodology, highlighting both the geometric and algebraic richness of MUBs, and clarifying why certain dimensions resist full analytical constructions. This study serves as a comprehensive resource for researchers seeking both theoretical understanding and practical construction of MUBs in quantum information science.

Ultra-narrow-linewidth lasers with suppressed high-frequency phase noise are critical for quantum control and precision metrology. While optical phase locking (OPL) is the standard technique for cloning the coherence of such sources, its effectiveness is often limited at high frequencies by feedback latency. We present a robust feedforward architecture that overcomes this limitation by recycling and demodulating the existing master-slave beat signal to drive a single electro-optic modulator for near-instantaneous noise cancellation. This approach eliminates the extraneous sidebands and transmission losses typical of more complex modulators. Through active stabilization of the beat amplitude and demodulation phase, we demonstrate robust suppression exceeding 30 dB from 10 kHz to 10 MHz. This hardware-efficient framework is readily compatible with standard OPL setups, offering a scalable solution for high-fidelity coherent control.

Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum mechanics by understanding how we have applied it. We should not seek agreement on the nature of the world it represents, because this theory does not itself represent the physical world (though its applications do help us to represent it better). When applied to a quantum state, quantum mechanics yields probabiities for physical events: both state and probability are objective--not because they represent elements of phyiscal reality, but because each exerts norrmative authority over the beliefs of anyone who accepts quantum mechanics and applies it relative to a physical situation they may (but need not) occupy. These events may be described by statements that are meaningful in an appropriate environmental context, and quantum mechanics can help one to say when that is. Measurement creates an appropriate context, so here the Born rule indirectly yields probabilities of measurement outcomes. The quantum state of a system does not "collapse" on measurement: a new state must be assigned relative to a physical situation in which information about the outcome is accessible. Understood this way, there is no measurement problem, and violations of Bell inequalities does not demonstrate "spooky" non-local action. Quantum field theories have no physical ontology of their own: a quantum field is a mathematical object in a model whose application helps us to improve and extend our descriptions of the world in other terms. We cannot realise the scenario of Wigner's friend and its recent extensions: but the data that provide overwhelming evidence for quantum mechanics are objective in the same sense as the relative measurement outcomes described in those scenarios.

Powerful approaches to squeeze the motional state of a harmonic oscillator rely on the stepwise modulation of its resonance frequency. Such protocols can be limited by forces that vary slowly between experimental runs but are constant during a single experimental shot. Such shot-to-shot noise gives rise to a spread in experimental outcomes that masks the uncertainty intrinsic to quantum theory. Taking inspiration from spin-echo protocols, we propose a decoupling technique that, under ideal conditions, perfectly cancels shot-to-shot force noise in squeezing experiments based on parametric modulation. We implement the protocol using an optically levitated nanoparticle, where shot-to-shot force noise arises from slowly varying stray fields acting on the charge carried by the particle. Using our oscillator-echo protocol, we demonstrate shot-to-shot noise suppression to the measurement-backaction limit.

Distributing arbitrary graph states across quantum networks is a central challenge for modular quantum computing and measurement-based quantum communication. I introduce the phase quantum walk (PQW), a discrete-time quantum walk in which the conventional position-permuting shift operator is replaced by a diagonal conditional phase (CZ) gate, enabling distribution of arbitrary graph states, not merely GHZ states, from elementary two-qubit resources. The Byproduct Lemma shows that each walk step teleports edge entanglement with a correctable Pauli byproduct; the Coin Invariance Theorem proves that the optimal fidelity F*(C,E) = F*(H,E) for all unitary coins C and noise channels E, with closed-form expressions F_dep = (1 - 3p/4)^k and F_pd = ((1 + sqrt(1 - p))/2)^k. Analytical correction formulas are derived for tree graphs (general theorem) and ring graphs (C4 case study), with F = 1.0 verified across eight topologies (up to 4096 outcomes). Hardware validation on ibm marrakesh (IBM Heron r2, CZ-native) yields F_cl = 0.924 for |GHZ4> and 0.922 for |L4>, statistically identical, providing the first experimental confirmation that fidelity is independent of graph topology as predicted by the Coin Invariance Theorem.

Q2NS is an open-source quantum network simulator built on ns-3, the de facto standard for classical network simulation. By inheriting ns-3's mature classical stack and event-driven execution model, Q2NS enables faithful co-simulation of quantum-network dynamics and classical signaling, a core requirement for the functioning of any quantum network. Its modular architecture is designed for extensibility, with pluggable quantum-state backends (state-vector, density matrix, stabilizer) and a clean separation between network control and node-level operations. Q2NS comes with a quantum network visualizer Q2NSViz, supporting interactive inspection of both physical- and entanglement-induced connectivity graphs, helping users interpret protocol behavior and entanglement manipulation processes. We present a demonstration of Q2NS, highlighting its ability to capture and simulate the coexistence of quantum and classical communication. The proposed demonstration presents quantum communication scenarios of increasing complexity: from entanglement distribution basics to multipartite graph-state manipulation, complemented by pre-loaded examples in Q2NSViz that require no prior quantum communication or coding experience.

The Quantum Approximate Optimization Algorithm (QAOA) is a leading hybrid heuristic for combinatorial optimization, but efficiently handling hard constraints remains a significant challenge. XY-mixers successfully confine quantum state evolution to a feasible subspace, such as the Hamming-weight-1 sector for one-hot constraints. On the contrary, warm-starting biases the search toward promising regions based on preliminary solutions. Combining these two techniques requires maintaining the essential alignment between the initial state and the mixer Hamiltonian to preserve convergence guarantees. Previous work demonstrated warm-starting with XY-mixers via a biased initial state, but relying only on standard mixer Hamiltonians. Consequently, the initial state is no longer a ground state of the mixer. In this work, we overcome these limitations by formulating a warm-started XY-mixer Hamiltonian for one-hot constraints and proving its ground-state properties. Furthermore, we provide a shallow circuit implementation suitable for NISQ implementations. We embed the warm-starting into a classical heuristic that iteratively updates the bias based on previous samples, called Iterative Warm-Starting (IWS). Extensive numerical simulations on Max-$k$-Cut and Traveling Salesperson Problem instances demonstrate that IWS-QAOA significantly accelerates the solution-finding process, increasing the probability of sampling optimal solutions by orders of magnitude compared to standard XY-QAOA. Finally, we validate our approach on the ibm_boston QPU using hardware-tailored 144-qubit problem instances. By coupling IWS-QAOA with a greedy steepest-descent post-processing strategy to repair infeasible measurements caused by hardware noise, we successfully identify optimal solutions on actual quantum devices.

Quantum information processing, communication, and sensing networks are being developed with various qubit platforms that use different encoding schemes. Connecting quantum network nodes to distribute entanglement requires matching photon qubit basis encoding. In this work, we implement an interconversion protocol which converts photon qubit encoding from the polarization basis to the time-bin basis, transmits the photons through a transport fiber with large fluctuations in polarization, and converts back to polarization encoding for ease of measurement. This interconversion scheme faithfully transmits a polarization Bell state across the transport fiber by converting sources of infidelity to changes in transmission rate. These results illustrate a practical approach for interfacing distinct qubit platforms to enable modular and flexible operation in heterogeneous quantum networks.

The quantum information content of Hawking radiation holds the key to understanding black-hole evaporation and the fate of unitarity. Motivated by recent advances in cold-atom experiments, we develop a lattice-regularization approach aimed at simulating the coarse-grained entanglement scaling of a quantum field in a 1+1D analogue black-hole background. We provide the first concrete demonstration that logarithmic negativity -- an entanglement monotone that typically exhibits a UV-divergent log-scaling for the conformal vacuum -- acquires a UV-finite volume term from the nonlocal correlations seeded by Hawking radiation. We show that this volume term encodes both the number density and spatial distribution of entangled Hawking pairs along the black-hole interior and exterior. We highlight its prospective detection in currently realizable experiments as well as its implications beyond the analogue paradigm, in particular for black-hole thermodynamics.

We provide here a universal approximation theorem with precise quantitative error bounds for noisy quantum neural networks. We focus on applications to Quantitative Finance, where target functions are often given as expectations. We further provide a detailed numerical analysis, testing our results on actual noisy quantum hardware.

We demonstrate that strong-field ionization of atoms in circularly polarized laser fields generates a photoelectron spin texture with toroidal topology in momentum space. Using time-dependent Schrödinger equation simulations, spin-resolved classical-trajectory Monte Carlo calculations, and an extended spin-resolved strong-field approximation including intermediate excitation pathways, we show that the rotation angle of this spin torus provides access to attosecond relative time delays associated with photoelectron wave packets released by tunneling from the counter-rotating and co-rotating \(p\)-orbital channels. When intermediate-state dynamics become significant, the torus develops a clear splitting. These results establish photoelectron spin textures as a complementary source of dynamical information beyond conventional momentum spectroscopy, and identify spin polarization as a robust internal degree of freedom for self-referenced attosecond metrology.

Auxiliary Field Quantum Monte Carlo (AFQMC) has emerged as a powerful framework for treating strongly correlated electronic systems, offering a favorable balance between computational cost and accuracy. In this paper, we present a novel AFQMC method that uses the isometric tensor hypercontraction (ITHC) technique to diagonalize the two-body Coulomb interaction of molecular electronic Hamiltonians by introducing additional fictitious fermionic modes. Our method shows reduced theoretical complexity and better practical performance for both propagation and local energy evaluation compared to the standard AFQMC method. We demonstrate the efficacy of this approach by computing the ground-state energies of a linear $\ce{H10}$-chain and the benzene molecule. Our results show that the extended-basis AFQMC recovers many-body correlations with a precision comparable to that of high-level wavefunction methods such as Coupled Clusters (CC) or Density Matrix Renormalization Group (DMRG), while offering significantly improved scaling.

We introduce a novel quantum algorithm for similar subgraph identification in form of an NP-hard cardinality-constrained binary quadratic optimization problem. Given a weighted reference graph with Laplacian $\boldsymbol{B}$, our algorithm determines the subgraph featuring Laplacian $\boldsymbol{B'}$ on the same vertex set, but $x$ out of $N$ inactive edges, minimizing the Frobenius distance $||\boldsymbol{B} - \boldsymbol{B'}||_\mathrm{F}^2$. We represent the $\binom{N}{x}$ graph topologies by an equal-weight superposition in form of a Dicke state, enabling controlled transformations applied to the quantum state associated with the vectorized Laplacian of the reference graph. Combined with amplitude estimation and a minimum finding approach, our algorithm provides a polynomial speed up $\mathcal{O}(\sqrt{N^{x}/x!}N\log\log N)$ compared to $\mathcal{O}(N^{x+1}/x!)$ of classical brute-force search algorithms. We demonstrate the application of our method on standard test cases, which represent electric power grids, by reconstructing $||\boldsymbol{B} -\boldsymbol{B'}||_\mathrm{F}^2$ from measurements and show how our approach can be additionally used to calculate energy functional like quadratic forms of the Laplacians with respect to a given vector.

I take a pragmatist perspective on quantum theory. This is not a view of the world described by quantum theory. In this view quantum theory itself does not describe the physical world, nor our observatons, experiences or opinions of it. Instead, the theory offers reliable advice on when to expect an event of one kind or another, and on how strongly to expect each possible outcome of that event. The actual outcome is a perspectival fact: a fact relative to a physical context of assessment. Measurement outcomes and quantum states are both perspectival. By noticing that each must be relativized to an appropriate physical context one can resolve the measurement problem and the problem of nonlocal action. But if the outcome of a quantum measurement is not an absolute fact, then why shoud the statistics of such outcomes give us any objective reason to accept quantum theory? One can describe extensions of the scenario of Wigner's friend in which a statement expressing the outcome of a quantum measurement would be true relative to one such context but not relative to another. However, physical conditions in our world prevent us from realizing such scenarios. Since the outcome of every actual quantum measurement is certified at what is essentially a single context of assessment, the outcome relative to that context is an objective fact in the only sense that matters for science. We should accept quantum theory because the statistics these outcomes display are just those it leads us to expect.

Entangled photon pair sources are a key enabling technology for quantum communication and networking, yet their deployment beyond laboratory environments is hindered by system-level complexity, limited operational stability, and insufficient industry compatibility. Here, we demonstrate a rack-based, mobile quantum light source architecture based on a semiconductor quantum dot emitter that directly addresses these challenges through modular system integration and automated operation. The source generates polarization-entangled photon pairs with an entanglement negativity 2n of up to $0.98(1)$, confirming near-maximal entanglement quality. In continuous, hands-off operation over a six-hour time window, the system achieves an average single-photon emission rate of $697(8)$ kHz and a maximum rate of $740(7)$ kHz, while maintaining 2n-value of more than $95$ $\%$. These results are enabled by the integration of optical excitation, collection, cryogenic operation, and control electronics within a standardized rack footprint, together with automated monitoring. By demonstrating simultaneously high entanglement quality, sustained brightness, and long-term operational stability in an industry-aligned system architecture, this work advances semiconductor quantum dot sources toward deployable entangled photon sources for applied quantum photonics.

We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H$_2$, LiH, BeH$_2$, H$_2$O, and NH$_3$. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ansätze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H$_2$ and HeH$^+$ using both STO-3G and 6-31G basis sets, and for LiH and BeH$_2$ in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32 $\times$ 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.

In this article, we propose a practical construction of Lie group-equivariant and permutation-invariant functions of $N$ variables from the knowledge of a one-particle basis that is stable with respect to the group action. The construction is generic for any linear Lie group and relies on building a matrix constructed from the Lie algebra whose kernel is spanned by a group-equivariant and permutation-invariant basis. In particular, this construction does not require the knowledge of Clebsch--Gordan coefficients and instead directly builds generalized Clebsch--Gordan coefficients. For specific groups such as $SO(3)$ and $SU(2)$, we exploit the Lie algebra structure to simplify the matrix, which then allows us to derive an explicit formula for the exact dimension of the group-equivariant and permutation-invariant space. Numerical simulations are provided to show that the proposed method scales linearly instead of exponentially for existing methods in the literature. We also show that for large values of $N$, the number of rotation-equivariant and permutation-invariant basis functions is of a comparable order as the number of permutation-invariant basis functions, while pre-asymptotically, a large gain can be achieved by explicitly enforcing rotation-equivariance on top of permutation-invariance.

We propose a geometry-driven quantum-inspired classification framework that integrates Correlation Group Structures (CGR), compact SWAP-test-based overlap estimation, and selective variational quantum decision modelling. Rather than directly approximating class posteriors, the method adopts a geometry-first paradigm in which samples are evaluated relative to class medoids using overlap-derived Euclidean-like and angular similarity channels. CGR organizes features into anchor-centered correlation neighbourhoods, generating nonlinear, correlation-weighted representations that enhance robustness in heterogeneous tabular spaces. These geometric signals are fused through a non-probabilistic margin-based fusion score, serving as a lightweight and data-efficient primary classifier for small-to-moderate datasets. On Heart Disease, Breast Cancer, and Wine Quality datasets, the fusion-score classifier achieves 0.8478, 0.8881, and 0.9556 test accuracy respectively, with macro-F1 scores of 0.8463, 0.8703, and 0.9522, demonstrating competitive and stable performance relative to classical baselines. For large-scale and highly imbalanced regimes, we construct compact Delta-distance contrastive features and train a variational quantum classifier (VQC) as a nonlinear refinement layer. On the Credit Card Fraud dataset (0.17% prevalence), the Delta + VQC pipeline achieves approximately 0.85 minority recall at an alert rate of approximately 1.31%, with ROC-AUC 0.9249 and PR-AUC 0.3251 under full-dataset evaluation. These results highlight the importance of operating-point-aware assessment in rare-event detection and demonstrate that the proposed hybrid geometric-variational framework provides interpretable, scalable, and regime-adaptive classification across heterogeneous data settings.

Non-Hermitian systems driven along slow parametric loops undergo non-adiabatic transitions whose outcome depends sensitively on the driving speed, yet no explicit formula has been available for the critical timescale $T_{\mathrm{cr}}$ at which these transitions develop. Using a $2\times 2$ Hamiltonian with circular parameter trajectories, we derive $T_{\mathrm{cr}} = \mathcal{G}\,\ln(1/|Δ|)$ in closed form for non-encircling loops, phase-shifted loops, offset loops, and loops encircling exceptional points, where $\mathcal{G}$ is a geometry-dependent growth factor and $Δ$ is the instability seed. This formula sharply separates the regime where the system remains in the averagely dominant eigenstate ($T< T_{\mathrm{cr}}$) from the superadiabatic regime where the instantaneous dominant eigenstate takes over ($T> T_{\mathrm{cr}}$), resolving the apparent tension between the previous literature. We identify two competing seeds: a geometric Stokes multiplier and the finite-precision floor. When the geometric seed vanishes, precision alone governs the transition, yielding $T_{\mathrm{cr}} \propto m\lnβ$, linear in the number of precision bits $m$. This provides a purely forward-evolution manifestation of precision-induced irreversibility (PIR)~\cite{PIR}, demonstrating that the fundamental limit identified through echo protocols also controls the outcome of slow non-Hermitian dynamics without requiring time reversal. For PT-symmetric energy spectra, $T_{\mathrm{cr}}$ additionally determines the onset of chirality: the dynamics is non-chiral for $T< T_{\mathrm{cr}}$ and chiral for $T> T_{\mathrm{cr}}$.

The realization of the Quantum Internet promises transformative capabilities in secure communication, distributed quantum computing, and high-precision metrology. However, transitioning from laboratory experiments to a scalable, multi-tenant network utility introduces deep orchestration challenges. Current development is often siloed within physics communities, prioritizing hardware, while the classical networking community lacks architectural models to manage fragile quantum resources. This tutorial bridges this divide by providing a network-centric view of quantum networking. We dismantle idealized assumptions in current simulators to address the "simulation-reality gap," recasting them as explicit control-plane constraints. To bridge this gap, we establish Software-Defined Quantum Networking (SDQN) as a prerequisite for scale, prioritizing a symbiotic, dual-plane architecture where classical control dictates quantum data flow. Specifically, we synthesize reference models for SDQN and the Quantum Network Operating System (QNOS) for hardware abstraction, and adapt a Quantum Network Utility Maximization (Q-NUM) framework as a unifying mathematical lens for engineers to reason about trade-offs between entanglement routing, scheduling, and fidelity. Furthermore, we analyze Distributed Quantum AI (DQAI) over imperfect networks as a case study, illustrating how physical constraints such as probabilistic stragglers and decoherence dictate application-layer viability. Ultimately, this tutorial equips network engineers with the tools required to transition quantum networking from a bespoke physics experiment into a programmable, multi-tenant global infrastructure.

Inspired by the work of McGlynn and Simenel [Phys. Rev. C {\bf 102}, 064614 (2020)], this study investigates the quantum tunneling of two interacting distinguishable particles in two potential wells. We first benchmark the system by reproducing key established results: the exact quantum solution and the spurious self-trapping effect that arises in the real-time mean-field dynamics for strong interactions. To exactly capture the tunneling dynamics, we apply the time-dependent generator coordinate method (TDGCM) to the model. Numerical simulations demonstrate that the TDGCM, by utilizing the real-time mean-field states as generator states, successfully overcomes the self-trapping effect, yielding tunneling dynamics in excellent agreement with the exact solution. Furthermore, we explore the expectation values of the generator coordinates from the correlated TDGCM many-body wave function. While different methods for calculating expectation values show consistent results in some cases, significant discrepancies are observed in others, providing critical insights into the emergence of collective and single-particle behaviors in interacting systems. This work also verifies the TDGCM as a robust framework for describing collective quantum tunneling and opens avenues for its application to more complex and realistic systems.

We present a loop-shaping approach to coherent feedback (CF) control. By formulating the coupling between a quantum system and its environment in terms of the noise power spectrum, our method enables direct manipulation of the effective dissipation coefficients through spectral shaping. A systematic design framework for CF controllers is also developed, in which transfer functions are shaped to realize desired spectral responses. Applying this framework to optomechanical sideband cooling, we demonstrate that suppression of the Stokes process and enhancement of the anti-Stokes process can be simultaneously achieved, enabling ground-state cooling even in the unresolved-sideband regime. This loop-shaping framework provides an intuitive and general foundation for the design of CF controllers and can be extended to a wide class of quantum systems in which interactions with environments are characterized by noise power spectra.

Nonreciprocity, characterized by direction-dependent signal propagation, is fundamental to technologies such as isolators, signal routing, and precision sensing. This letter theoretically demonstrates nonreciprocal phonon transport and the conversion between photon and acoustic phonon signals in coupled optomechanical cavities via phase-dependent driving. It is demonstrated that, in contrast to nonreciprocal phonon transport, which necessitates both dissipation and phase-induced violation of time reversal symmetry, the nonreciprocity in photon-phonon conversion can occur without violating time reversal symmetry. We demonstrate that such nonreciprocity arises due to the path-dependent asymmetry in photon-phonon conversion. Furthermore, we demonstrate that the nonreciprocity of photon-phonon conversion can be further enhanced, achieving isolation levels of up to 40 dB by suitably modifying the phase difference of the driving lasers.

While QKD ensures information-theoretic security at the link level, real-world deployments depend on trusted repeaters, creating potential vulnerabilities. In this paper, we thus introduce a topology-hiding connectivity assurance protocol to enhance trust in quantum key distribution (QKD) network infrastructures. Our protocol allows network providers to jointly prove the existence of a secure connection between endpoints without revealing internal topology details. By extending graph-signature techniques to support multi-graphs and hidden endpoints, we enable zero-knowledge proofs of connectivity that ensure both soundness and topology hiding. We further discuss how our approach can certify, e.g., multiple disjoint paths, supporting multi-path QKD scenarios. This work bridges cryptographic assurance methods with the operational requirements of QKD networks, promoting verifiable and privacy-preserving inter-network connectivity.

A classical particle under spatial constraints is strictly confined to live on a specific space manifold or path, but this assumption is incompatible with the zero-point fluctuations of a quantum particle. One way to describe quantum mechanics under constraints is the confinement potential approach (CPA). For a non-relativistic particle, the CPA maps the problem onto the solution of a Schrödinger-type equation in an isometrically embedded Riemannian submanifold of Euclidean space while the motion along orthogonal directions are decoupled and spatially confined. This approach respects quantum uncertainty, and one of its key results is the appearance of geometry- and metric-induced potentials that affect the stationary states and the dynamics of the particle. For particles constrained to different spaces, such as structures hosting sharp bents, vertices, wedges, conical apices, tips, or self-intersections, a formalism beyond the CPA is needed. Here, a step towards a CPA extension for irregular spaces is presented. After classifying the possible geometric irregularities concerning the CPA formalism, the presentation is focused on a sharply bent quantum wire modeled as an embedded curve with singular (but absolute integrable) curvature. For a subclass fulfilling the additional requirement that the geometric potential is a distribution of first order, a solution scheme for the confined Schrödinger equation is presented based on singular Sturm-Liouville theory and operator theoretic methods. The analytical considerations and numerical simulations evidence the existence of curvature-induced bound states with non-differentiable wave functions localized around the singular point, with an extension well beyond the singularity. Furthermore, a multitude of scattering states appear that may affect the transport and optical properties of the system.

Secure long-distance communication in quantum key distribution (QKD) networks depends on trusted repeater nodes along the entire transmission path. Consequently, these nodes will be subject to strict auditing and certification in future large-scale QKD deployments. However, trust must also extend to the network operator, who is responsible for fulfilling contractual obligations -- such as ensuring certified devices are used and transmission paths remain disjoint where required. In this work, we present a path validation protocol specifically designed for QKD networks. It enables the receiver to verify compliance with agreed-upon policies. At the same time, the protocol preserves the operator's confidentiality by ensuring that no sensitive information about the network topology is revealed to users. We provide a formal model and a provably secure generic construction of the protocol, along with a concrete instantiation. For long-distance communication involving 100 nodes, the protocol has a computational cost of 1-2.5s depending on the machine, and a communication overhead of less than 70kB - demonstrating the efficiency of our approach.

We propose a general scheme to controllably distribute pairwise entanglement in a quantum network of qubits by exploiting environmental ancilla qubits interacting with the network nodes through tunable Hamiltonians. Our approach leverages collision models, in which a quantum syatem interacts sequentially with ancilla units. We explore two distinct scenarios within this framework: one in which the ancilla is reset to its initial coherent state after each interaction (the traditional collision model), and another where the ancilla is not reset but its state is simply carried over to the next interaction, which we dub the repeated interaction model. In both scenarios, we ensure that the system-ancilla correlations are discarded between steps. We also demonstrate how varying the ancilla-system interaction patterns enables selective generation of entanglement between different qubit pairs, including non-neighbouring nodes that do not directly interact. The scheme is analyzed in networks up to three qubits under both collision and repeated interaction dynamics, revealing the genaration of maximally entangled bell pairs even in configurations where the interacting ancilla couples to only a single node. Our results provide a systematic and physically implementable route to entanglement distribution, offering potential applications in quantum communication, metrology and modular quantum computing.

We theoretically investigate the control of the Goos-Hänchen shift (GHS) of a reflected weak probe field in both parity-time ($\mathcal{PT}$)-symmetric and conventional optomechanical systems. The proposed scheme consists of a single optomechanical platform where a passive optical cavity is coupled to an active mechanical resonator, in contrast to standard passive-passive configurations. Analysis of the eigenfrequency spectrum reveals the emergence of an exceptional point under balanced gain-loss conditions at a tunable effective optomechanical coupling strength. Using the transfer-matrix method combined with stationary-phase analysis, we examine the GHS across broken and unbroken $\mathcal{PT}$ phases and compare it with that in the conventional system. The lateral shift exhibits strong phase dependence: it is markedly enhanced in the unbroken regime relative to both the broken phase and the passive configuration. We further show that the GHS can be actively tuned through the cavity detuning and the intracavity medium length. These results provide a controlled means for manipulating beam shifts in optomechanical systems and suggest pathways toward tunable photonic components and precision optical sensing.

Magnetic Resonance Spectroscopy (MRS) offers a unique non-invasive window into metabolic processes, yet its potential remains strictly constrained by severe spectral congestion and intrinsic insensitivity. Traditional pulse sequence design, tethered to human intuition, predominantly targets simple quantum states, thereby overlooking the vast majority of the exponentially scaling operator space which consists of complex spin superpositions. Here, we introduce a spectrum-driven, end-to-end differentiable physical framework that transcends these heuristic limitations. By integrating physical laws with automatic differentiation algorithm, our approach directly navigates the high-dimensional spin dynamics space, bypassing the intractable inverse problem of state preparation. This enables the discovery of non-intuitive, complex mixed states that simultaneously satisfy the dual objectives of selective excitation and interferometric signal enhancement. We validate this paradigm by achieving the robust separation of Glutamate and Glutamine, which is a longstanding neuroimaging challenge, in the human brain at 3T, demonstrating spectral fidelity superior to conventional methods. By unlocking the "dark" informational content of nuclear spin ensembles, our work establishes a generalizable paradigm for goal-driven quantum state engineering in magnetic resonance and beyond.

Non-Hermitian skin effect (NHSE) is one of the most fascinating phenomena in non-Hermitian systems, which refers to enormous eigenstates localize at the boundary exponentially under open boundary condition (OBC). For typical NHSE, the localization length for a skin mode is independent of the system's size. Recently, some studies have revealed that for specific $1$-dimensional model, the localization length for eigenstates are proportional to the system's length under generalized boundary condition (GBC), and such phenomenon is dubbed as scale-free skin effect (SFSE). Further, SFSE is discovered in $1$-dimensional Hermitian chain with pure imaginary impurity at the end. In this work, we propose a mechanism for SFSE in 1-dimensional systems, which is model-independent. Our work provide a viewpoint for researching SFSE and shed new light on understanding finite size effect in non-Hermitian systems.

We propose a privacy-aware hybrid framework for federated medical image classification that combines tensor-network representation learning, MPC-secured aggregation, and post-aggregation quantum refinement. The framework is motivated by two practical constraints in privacy-aware federated learning: MPC can introduce substantial communication overhead, and direct quantum processing of high-dimensional medical images is unrealistic with a small number of qubits. To address both constraints within a single architecture, client-side tensor-network frontends, Matrix Product State (MPS), Tree Tensor Network (TTN), and Multi-scale Entanglement Renormalization Ansatz (MERA), compress local inputs into compact latent representations, after which a Quantum-Enhanced Processor (QEP) refines the aggregated latent feature through quantum-state embedding and observable-based readout. Experiments on PneumoniaMNIST show that the effect of the QEP is frontend-dependent rather than uniform across architectures. In the present setting, the TTN+QEP combination exhibits the most balanced overall profile. The results also suggest that the QEP behaves more stably when the qubit count is sufficiently matched to the latent dimension, while noisy conditions degrade performance relative to the noiseless setting. The MPC benchmark further shows that communication cost is governed primarily by the dimension of the protected latent representation. This indicates that tensor-network compression plays a dual role: it enables small-qubit quantum processing on compressed latent features and reduces the communication overhead associated with secure aggregation. Taken together, these results support a co-design perspective in which representation compression, post-aggregation quantum refinement, and privacy-aware deployment should be optimized jointly.

A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over the possible states expressible by this ansatz, one can alternatively formulate the problem as a noncommutative polynomial optimization problem. This optimization problem can then be addressed using a hierarchy of semidefinite programming relaxations. In contrast to variational calculations, the semidefinite program can provide lower bounds for ground state energies and upper and lower bounds on observable expectation values. However, this approach typically suffers from severe scalability issues, limiting its applicability to small-to-medium-scale systems. In this article, we demonstrate that leveraging the inherent structures of the system can significantly mitigate these scalability challenges and thus allows us to compute meaningful bounds for quantum spin systems on up to $16\times16$ square lattices.

Single-shot measurement learning (SSML) learns a compensation unitary from a one-bit success/failure record and halts after a prescribed run of consecutive successes. We recast SSML as an adaptive estimator on a parameterized sensing manifold and ask what role it can play in quantum-enhanced sensing. First, we show that the terminal run itself furnishes an intrinsic certificate of local alignment: longer terminal runs certify smaller infidelity, and near the optimum this becomes a Fisher-calibrated certificate of parameter error. Second, for compensation-type sensing families, the Bernoulli success/failure record is locally matched to the probe quantum Fisher information (QFI), so SSML preserves the probe's metrological content despite using only one classical bit per copy. In this sense, SSML makes the quantum enhancement carried by the probe operationally available in an online self-terminating protocol. Applied to GHZ/NOON probes of depth $m$, SSML retains the familiar square-root entanglement gain over product probes at fixed total resource, while an ideal multiscale architecture remains compatible with Heisenberg scaling. Monte Carlo simulations of photonic NOON-state phase sensing show the expected near-inverse decay of terminal infidelity with entangled shots, SQL-like total-resource scaling at fixed entanglement depth, the corresponding fixed-resource entanglement gain, the global limitation of a single fringe scale, and the recovery of Heisenberg-compatible behavior under ideal multiscale hand-off. These results identify SSML as a Fisher-preserving, self-certifying estimator layer for quantum-enhanced sensing.

We study the computational complexity of estimating the normalized trace $2^{-n}Tr[f(A)]$ for a log-local Hamiltonian $A$ acting on $n$ qubits. This problem arises naturally in the DQC1 model, yet its complexity is only understood for a limited class of functions $f(x)$. We show that if $f(x)$ is a continuous function with approximate degree $Ω({\rm poly}(n))$, then estimating $2^{-n}Tr[f(A)]$ up to constant additive error is DQC1-complete, under a technical condition on the polynomial approximation error of $f(x)$. This condition holds for a broad class of functions, including exponentials, trigonometric functions, logarithms, and inverse-type functions. We further prove that when $A$ is sparse, the classical query complexity of this problem is exponential in the approximate degree, assuming a conjectured lower bound for a trace variant of the $k$-Forrelation problem in the DQC1 query model. Together, these results identify the approximate degree as the key parameter governing the complexity of normalized trace estimation: it characterizes both the quantum complexity (via efficient DQC1 algorithms) and, conditionally, the classical hardness, yielding an exponential quantum-classical separation. Our proof develops a unified framework that cleanly combines circuit-to-Hamiltonian constructions, periodic Jacobi operators, and tools from polynomial approximation theory, including the Chebyshev equioscillation theorem.

Topological phase transitions in generic multiband systems are mediated by band-touching defects whose codimension -- the number of momentum directions along which the gap closes linearly -- varies across universality classes. Although singular behavior of fidelity susceptibilities and quantum Fisher information (QFI) has been computed for specific models, no unifying principle connecting these results has been identified: it has remained unclear whether the controlling variable is spatial dimensionality, band structure, or an intrinsic geometric property of the defect. We resolve this question by showing that the singular contribution to the QFI with respect to the tuning parameter $m$ obeys a universal power-law scaling $\sim |m|^{p-2}$ for $p \neq 2$, with a logarithmic divergence $\sim \ln(1/|m|)$ at the marginal codimension $p = 2$, where $p$ denotes the codimension of the band-touching defect. This exponent is independent of spatial dimensionality, anisotropies, ultraviolet regularization, and additional gapped bands, and is protected by renormalization-group arguments at the linearized fixed point. The result unifies previously isolated observations for SSH chains ($p=1$), Chern insulators ($p=2$), and Weyl semimetals ($p=3$) as instances of a single codimension-dependent universality class, and reveals that only defects with $p \leq 2$ generate divergent information-geometric responses. This establishes a direct and previously missing link between topological classification in momentum space and quantum distinguishability in parameter space, with implications for metrological sensitivity near topological transitions and for the experimental detection of topological criticality via quantum geometric observables.

Let $G$ be a strongly regular graph of prime order $p$ with connection degree $k \geq 6$. We prove that the \emph{quantum walk characteristic polynomial} $χ_q(G,λ) \coloneqq \det(λI - U_G)$, where $U_G$ is the coined quantum walk operator on $G$, completely determines $G$ up to isomorphism within the class of strongly regular graphs of the same order. The proof proceeds in three steps. First, we show that $U_G$ block-diagonalizes under the discrete Fourier transform over $\Z_p$, yielding $p$ blocks $U_G^{(j)}$ of size $k \times k$. Second, we prove an explicit formula \[ χ_q\!\bigl(U_G^{(j)}, λ\bigr) = (λ-1)^{(k-2)/2}(λ+1)^{(k-2)/2} \!\left(λ^2 - \tfrac{2\widehat{A}_G(j)}{k}\,λ+ 1\right), \] from which the Fourier coefficient $\widehat{A}_G(j)$ is recovered as the unique real part of an eigenvalue of $U_G^{(j)}$ distinct from $\pm 1$. Third, the inverse discrete Fourier transform recovers the connection set $S$ of $G$, and Turner's theorem (1967) identifies $G$ up to isomorphism. As a consequence, graph isomorphism is decidable in polynomial time within this class using the quantum walk spectrum, without resorting to the general quasi-polynomial algorithm of Babai (2016).

Characterising multi-time quantum processes is essential for analysing temporally correlated noise and for designing effective control and mitigation strategies. A complete operational description through multi-time process tomography requires an informationally complete set of probes, which necessarily includes non-deterministic intermediate operations. On present-day quantum devices, such operations are commonly implemented using mid-circuit measurements and reset, which are technologically limited and can introduce noise and overhead in terms of ancilla requirement. In this work, we study the minimal ancillary dimension required for complete characterisation of multi-time processes. We show that sequential interactions with a single qubit ancilla can generate an informationally complete family of correlated probes for processes of arbitrary length, without requiring mid-circuit measurements or reset. Our result provides a resource-efficient route for complete multi-time process tomography and establishes that one qubit of coherent ancillary memory suffices for full reconstruction of arbitrary multi-time dynamics.

Classical shadows (CS) has recently emerged as an important framework to efficiently predict properties of an unknown quantum state. A common strategy in CS protocols is to parametrize the basis in which one measures the state by a random group action; many examples of this have been proposed and studied on a case-by-case basis. In this work, we present a unified theory that allows us to simultaneously understand CS protocols based on sampling from general group representations, extending previous approaches that worked in simplified (multiplicity-free) settings. We identify a class of measurement bases which we call "centralizing bases" that allows us to analytically characterize and invert the measurement channel, minimizing classical post-processing costs. We complement this analysis by deriving general bounds on the sample-complexity necessary to obtain estimates of a given precision. Beyond its unification of previous CS protocols, our method allows us to readily generate new protocols based on other groups, or different representations of previously considered ones. For example, we characterize novel shadow protocols based on sampling from the spin and tensor representations of $\textsf{SU}(2)$, symmetric and orthogonal groups, and the exceptional Lie group $G_2$.

This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of which is known only to a single noisy intermediate-scale quantum (NISQ) computer. Each NISQ computer communicates with certain other quantum computers in the same row and column of the block partition, where the communication patterns are described by the row- and column-neighbor graphs, both of which are connected. The proposed algorithm integrates a variant of the variational quantum linear solver at each computer with distributed classical optimization techniques. The derivation of the quantum cost function provides insight into the design of the distributed algorithm. Numerical quantum simulations demonstrate that the proposed distributed quantum algorithm can solve linear systems whose size scales with the number of computers and is therefore not limited by the capacity of a single quantum computer.

Commutativity gadgets provide a technique for lifting classical reductions between constraint satisfaction problems to quantum-sound reductions between the corresponding nonlocal games. We develop a general framework for commutativity gadgets in the setting of quantum homomorphisms between finite relational structures. Building on the notion of quantum homomorphism spaces, we introduce a uniform notion of commutativity gadget capturing the finite-dimensional quantum, quantum approximate, and commuting-operator models. In the robust setting, we use the weighted-algebra formalism for approximate quantum homomorphisms to capture corresponding notions of robust commutativity gadgets. Our main results characterize both non-robust and robust commutativity gadgets purely in terms of quantum polymorphism spaces: in any model, existence of a commutativity gadget is equivalent to the collapse of the corresponding quantum polymorphisms to classical ones at arity $|A|^2$, and robust gadgets are characterized by stable commutativity of the appropriate weighted polymorphism algebra. We use this characterisation to show relations between the classes of commutativity gadget, notably that existence of a robust commutativity gadget is equivalent to the existence of a corresponding non-robust one. Finally, we prove that quantum polymorphisms of complete graphs $K_n$ have a very special structure, wherein the noncommutative behaviour only comes from the quantum permutation group $S_n^+$. Combining this with techniques from combinatorial group theory, we construct separations between commutativity-gadget classes: we exhibit a relational structure admitting a finite-dimensional commutativity gadget but no quantum approximate gadget, and, conditional on the existence of a non-hyperlinear group, a structure admitting a quantum approximate commutativity gadget but no commuting-operator gadget.

The thermodynamic resourcefulness of quantum channels primarily depends on their underlying causal structure and their ability to generate quantum correlations. We quantify this interplay within the resource theory of athermality for bipartite quantum channels in the presence of a side channel acting as memory, referred to as the resource theory of conditional athermality. For channels with trivial output Hamiltonians, we characterize the optimal one-shot rates for distilling the identity gate from a given channel, as well as the cost of simulating the channel using the identity gate, under conditional Gibbs-preserving superchannels. We show that these rates have a direct trade-off relation with the conditional channel entropies, attributing operational significance to signaling in quantum processes. Furthermore, we establish an equipartition property for the conditional channel min-entropy for classes of channels that are either tele-covariant or no-signaling from the non-conditioning input to the conditioning output. As a consequence, we demonstrate asymptotic reversibility of the resource theory for these channels. The asymptotic conditional athermality capacity of a tele-covariant channel is half the superdense coding capacity of its Choi state. Our work establishes the conditional channel entropy as a primitive information-theoretic concept for quantum processes, elucidating its potential for wider applications in quantum information science.

Quantum phase estimation is a central primitive in quantum algorithms and sensing, where performance is governed by the sensitivity of measurement signals to the target parameter. While existing methods have developed increasingly sophisticated inference and adaptive design strategies, the signal family used for phase learning is often largely pre-specified. Here we propose a programmable signal design framework for quantum phase estimation based on quantum signal processing, which enables the measurement signal to be tailored to the current uncertainty region. We cast phase estimation as a max-min optimization problem over admissible signals and introduce a sensitivity efficiency parameter that quantifies information gain per query depth. The resulting iterative algorithm combines optimized quantum signal transformations with structured classical inference, retaining Heisenberg-limited scaling while improving sensitivity efficiency and practical resource prefactors. Numerical results show reduced estimation variance compared with standard protocols such as robust phase estimation. Our framework also extends to Hamiltonian eigenvalue estimation in higher dimensions and establishes a quantum-classical co-design paradigm through programmable signal shaping.

Learning quantum states from measurement data is a central problem in quantum information and computational complexity. In this work, we study the problem of learning to generate mixed states on a finite-dimensional lattice. Motivated by recent developments in mixed state phases of matter, we focus on arbitrary states in the trivial phase. A state belongs to the trivial phase if there exists a shallow preparation channel circuit under which local reversibility is preserved throughout the preparation. We prove that any mixed state in this class can be efficiently learned from measurement access alone. Specifically, given copies of an unknown trivial phase mixed state, our algorithm outputs a shallow local channel circuit that approximately generates this state in trace distance. The sample complexity and runtime are polynomial (or quasi-polynomial) in the number of qubits, assuming constant (or polylogarithmic) circuit depth and gate locality. Importantly, the learner is not given the original preparation circuit and relies only on its existence. Our results provide a structural foundation for quantum generative models based on shallow channel circuits. In the classical limit, our framework also inspires an efficient algorithm for classical diffusion models using only a polynomial overhead of training and generation.

We develop a rigorous and implementable framework for Gibbs sampling of infinite-dimensional quantum systems governed by unbounded Hamiltonians. Extending dissipative Gibbs samplers beyond finite dimensions raises fundamental obstacles, including ill-defined generators, the absence of spectral gaps on natural Banach spaces, and tensions between implementability and convergence guarantees. We overcome these issues by constructing KMS-symmetric quantum Markov semigroups on separable Hilbert spaces that are both well-posed and efficiently implementable on qubit hardware. Our generation theory is based on the abstract framework of Dirichlet forms, adapted here to the case of algebras of bounded operators over separable Hilbert spaces. Leveraging the spectral properties of our self-adjoint generators, we establish quantitative convergence results in trace distance, including regimes of fast thermalization. In contrast, we also identify Hamiltonians for which a naive choice of generators guaranteeing implementability generally comes at the cost of losing convergence of the associated evolutions, thereby establishing a strong trade-off between implementability and convergence. Our framework applies to a wide class of models, including Schrödinger operators, Gaussian systems, and Bose-Hubbard Hamiltonians, and provides a unified approach linking rigorous infinite-dimensional analysis with algorithmic Gibbs state preparation.

We study the impact of a minimal length, implied by generalized uncertainty principles and quantum gravity models, on unbounded (scattering) trajectories in the Kepler problem. The analysis is based on the precession of the Hamilton vector, which serves as a sensitive probe of orbital perturbations. Within the framework of the deformed Heisenberg algebra, we derive the correction to the trajectory arising from minimal length effects. It is shown that these quantum-gravitational corrections lead to a reduction in the scattering angle. In particular, for massless particles such as photons, the quantization of space results in a weakening of the gravitational lensing effect. Using available experimental data from the observation of the Einstein ring, we estimate the deformation parameter and the corresponding minimal length for the electron and Mercury. These findings highlight potential observational signatures of minimal length scenarios in high-energy astrophysics and gravitational optics.

The strategic demand for quantum hardware currently outpaces the availability of near-term devices, necessitating high-performance software emulators to validate novel protocols. We introduce Hyperion, a massively parallel, GPU-accelerated quantum emulator architected to bypass the classical memory walls inherent in strongly correlated quantum chemistry simulations. Hyperion leverages custom-optimized Sparse Matrix-Sparse Vector (SpMspV) kernels to natively accelerate exact matrix-vector multiplications, enabling strictly accurate State-Vector (SV) ADAPT-VQE simulations for up to 32 qubits on multi-node platforms. To scale beyond this hardware limit, we address the trade-off in pure Matrix Product State (MPS) emulators, where standard compression yields severe truncation errors and strict compression triggers intractable tensor rank explosions. We propose a novel partitioned emulation, namely the SV-MPS strategy: by routing non-interacting terms into an exact sparse SV core and delegating interacting terms to the MPS engine, this approach achieves emulation of 36 to 40 qubits with controlled approximations. This partitioning significantly reduces GPU resource requirements while maintaining robust accuracy across ADAPT-VQE iterations. Ultimately, Hyperion offers a high-fidelity platform dedicated to the development of new quantum algorithms for chemistry, enabling the modeling of realistic chemical systems at accuracies approaching the exact Full Configuration Interaction (FCI) / Complete Basis Set (CBS) limit.

We introduce a variational method for simulating the dynamics of interacting open quantum spin systems. The method is based on the spin phase-space representation and variationally targets the Husimi-$Q$ function with an ansatz based on a multi-dimensional mixture of spin-coherent states. Crucially, the mixture coefficients are allowed to take negative values, enabling the faithful capture of quantum correlations beyond semiclassical descriptions. The resulting equations of motion are derived from the Dirac-Frenkel variational principle and can be evaluated efficiently without resorting to Monte Carlo sampling by exploiting the analytical structure of the ansatz. As a first application, we demonstrate that this approach accurately captures both the full quantum dynamics and the non-equilibrium steady states of the transverse-field quantum Ising model, in excellent agreement with exact diagonalization. Furthermore, we show that the method scales efficiently to large two-dimensional lattices, a regime that remains challenging for other techniques.

We investigate entanglement in and out of equilibrium in a one-dimensional Bose gas in its low-energy Bogoliubov regime. In this Gaussian setting, the state is fully characterized by its covariance matrix, which allows us to detect and quantify entanglement using a covariance-based framework and associated entanglement monotones. For thermal states, we determine the optimal entanglement witness arising from the covariance matrix criterion and show that it has a remarkably simple mode-resolved structure: it is diagonal in the normal-mode basis and admits a simple analytic form that can be expressed as a product of only two normal-mode uncertainties. We then study out-of-equilibrium dynamics induced by unitary compression and show that entanglement can be generated even from initially separable thermal states. When the evolution is fully adiabatic, the optimal witness retains the same two-mode structure as in the thermal case. Departing from this regime, i.e., performing increasingly rapid compression, the optimal witness becomes genuinely more intricate. Our methods and results provide a unified and physically intuitive picture of how entanglement emerges and evolves in 1D quantum Bose gases, and identify an optimal witness structure relevant more broadly to the analysis of entanglement in quadratic bosonic models and its role in thermodynamic cycles.

We propose a novel superconducting quantum circuit that should be robust against both relaxation and dephasing over a wide and experimentally accessible parameter range. The circuit consists of a parallel arrangement of a large inductance, a small capacitor, and a well-transmitting Josephson weak link. Protection against relaxation arises from the hybridization between the fermionic degree of freedom associated with Andreev levels in the weak link and the bosonic electromagnetic mode of the LC circuit, hence its name: FerBo. Furthermore, as in the fluxonium qubit, delocalization of the wavefunctions in phase space provides resilience against dephasing.

We study non-equilibrium quantum dynamics by performing principal component analysis on the data sets of wavefunction snapshots. We show that a specific transformation of the data sets maximizes the information content in the largest principal component and further enables its connection to certain observables. This connection enables us to explain the dynamical features revealed by such a dimensionality-reduction scheme. We demonstrate this using quantum dynamics of the Heisenberg spin chain, starting from different initial states, and further extend the approach to extract higher-order correlations. Our framework should also be applicable to other unsupervised machine-learning methods based on dimensionality-reduction schemes and is highly relevant to experiments with quantum simulators, including those in higher dimensions.

Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite all atomic frequency references having more than two energy-levels, the commonly used model for evaluating their ultimate limits assumes a two-level atom. This leads to frequency interrogation protocols and theoretical stability bounds that are suboptimal for a true multi-level atom. The most fundamental stability bound assumes two noise sources - quantum projection noise and spontaneous decay from the excited state. In this work, we analyze a model that includes these noise types and is generalized beyond the two-level assumption, where spontaneous decay can branch to more than a single ground state. This model allows for detection and exclusion of atomic frequency interrogations in which the atom decayed, leading to a frequency stability improvement of up to $\approx 4.5 \text{ dB}$ compared with the two-level model. Furthermore, we identify an even greater stability enhancement of $\approx 5.4 \text{ dB}$ for frequency comparisons between atoms in an odd parity Bell state. These enhancements are particularly relevant for the numerous trapped-ion optical clock species that operate close to lifetime-limited stability. We calculate new stability limits for those cases and provide a detailed experimental protocol for frequency interrogation with an $^{27}\text{Al}^{+}$ optical ion clock.

One hundred years after the creation of quantum theory, there is no consensus on the kind of reality that is described by the theory. Here, I attribute the lack of progress to the prevailing interpretative methodology, which invariably takes the quantum formalism as the starting point for philosophical reflection and analysis. I argue that this methodology is particularly inappropriate, for it invariably marginalizes much of the theory's content, both that implicit in modelling heuristics and experimental practices, and that encapsulated in the mathematical structures of its formalism. In addition, the prevailing methodology offers little protection against undue influence by metaphysically-laden language which invariably accompanies the formalism. Here, I summarize an alternative methodology whose goal is to ensure that an interpretational project take into account all forms of theoretic content. The methodology harnesses the recent results of the quantum reconstruction program. These results distil the mathematical content of the quantum formalism into physical principles and assumptions, which are more readily philosophically digestible than the formalism itself, and bracket much of its metaphysically-laden language. As a case study of reconstruction-based interpretation, I describe the reconstruction of the identical particle formalism, and its step-by-step interpretation, highlighting the key questions that drive the interpretation forwards and the techniques and stances that are employed in each step. The interpretation yields a novel metaphysical profile for systems of identical particles as potential parts of a whole, which can be traced step-by-step to elementary experimental data and the reconstruction's physical postulates and assumptions. I also describe some of the pitfalls that one faces in any attempt to directly interpret the identical particle formalism.

Universal $T$-matrices, or Hopf algebra dual forms, for quantum groups are revisited, and their contraction theory is developed. As a first illustrative example, the (1+1) timelike $κ$-Poincaré $T$-matrix is explicitly worked out. Afterwards, motivated by recent results on the role of the Hopf algebra dual form of a quantum (1+1) centrally extended Galilei group as the algebraic object underlying non-relativistic quantum reference frame transformations, a new quantum deformation of the (1+1) centrally extended Poincaré Lie algebra is obtained, and its universal $T$-matrix is presented. Finally, the Hopf algebra dual form contraction is applied to this Poincaré $T$-matrix, showing that its corresponding non-relativistic counterpart is precisely the Galilei $T$-matrix associated with quantum reference frames. In this way, the Poincaré Hopf algebra dual form introduced here stands as a natural candidate for describing the symmetry structure of relativistic quantum reference frame transformations. In the appropriate basis, the associated quantum Poincaré group is recognized, remarkably, as a non-trivial central extension of the (1+1) spacelike $κ$-Poincaré dual Hopf algebra.

We introduce Simulated Bifurcation Quantum Annealing (SBQA), a quantum-inspired optimization algorithm that extends simulated bifurcation by incorporating inter-replica interactions to mimic quantum tunneling. SBQA retains the efficiency and parallelism of simulated bifurcation while improving performance on sparse and rugged energy landscapes. We derive its equations of motion, analyze parameter dependence, and propose a lightweight auto-tuning strategy. A comprehensive benchmarking study on both large-scale problems and smaller instances relevant for current quantum hardware shows that SBQA systematically improves on SBM in the sparse and rugged regimes where SBM is known to struggle, while remaining competitive and versatile across a diverse set of tested problem families. These results position SBQA as a practical quantum-inspired optimization heuristic and a stronger classical baseline for the sparse and rugged regimes studied here.

Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes are available that achieve high accuracy while preserving key qualitative properties of the underlying dynamical system, and are successfully used across a broad range of fields. In this work, we present a systematic analysis of both local and global errors arising from arbitrary splitting methods applied to unitary problems. Two complementary types of error estimates are derived. The first is expressed in terms of operator norms, while the second is formulated using norms of commutators and can, under suitable assumptions, be extended to certain classes of unbounded operators. Special attention is devoted to the case where only two operators are involved. The theoretical results are illustrated by deriving explicit error bounds for some representative schemes.

The $q$-multinomial coefficient, a classical object in enumerative combinatorics, counts permutations of multisets weighted by the number of inversions, with a single deformation parameter $q$. We introduce the twisted multinomial coefficient, in which each inversion between letters $i$ and $j$ carries a pair-dependent weight $ω_{ij}$ determined by a skew-symmetric matrix $Ω$. In general, no closed-form evaluation is known. Our main result is that under a natural structural condition on $Ω$ - predecessor-uniformity ($ω_{ij} = q_j$ for all $i<j$) - the twisted multinomial factorizes as a product of Gaussian ($q$-deformed) binomials with site-dependent parameters: $\binom{k}{k_1,\ldots,k_m}_Ω= \prod_j\binom{\ell_j}{k_j}_{q_j}$. This extends the standard product formula for the $q$-multinomial from a single parameter $q$ to $m-1$ independent parameters. The identity is purely combinatorial: it holds for arbitrary $q_j \in \mathbb{C}\setminus\{0\}$ without any algebraic constraints. We were led to this identity by studying pilot state preparation in Hamiltonian Decoded Quantum Interferometry (HDQI), a recently proposed quantum algorithm for preparing Gibbs and ground states. As an application, we show that the factorization yields an exact matrix product state (MPS) of bond dimension $k+1$ for the expansion coefficients of $h^k$ in a twisted algebra. We note that this addresses only one component of the HDQI pipeline (pilot state preparation); the full protocol additionally requires efficient decoding of the associated Hamiltonian code, and both components must work in conjunction for Hamiltonians of physical interest. Identifying such Hamiltonians remains an important open problem.

We study multiqubit variational quantum states that can be considered as weighted quantum graph states. These states are constructed as single-layer variational circuits with $RX$ rotations and $RZZ$ entangling gates, corresponding to graphs of arbitrary structure. In general case of quantum graph states of arbitrary structure we derive the geometric measure of entanglement and evaluate quantum correlators. It is shown that these quantities are directly related to the degrees of the corresponding vertices in graph. As an example, we analyze the state associated with the star graph $K_{1,4}$ using noisy quantum computing on the AerSimulator. The results are in good agreement with theoretical predictions. These findings demonstrate a connection between graph structure and quantum properties, enabling the study of classical graphs via quantum computing.

We report a proof-of-principle implementation of the quantum approximate optimization algorithm (QAOA) for the smallest nontrivial MAX-CUT instance on an NV-center-based quantum processor operating at room temperature. The two-qubit register is encoded in the electron spin and the ${}^{14}\mathrm{N}$ nuclear spin of a single NV$^-$ center. Using a minimization formulation of MAX-CUT, we implement a single-layer QAOA ansatz with native entangling and single-qubit control operations. Because the optical readout of the NV$^-$ center is not projective in the computational basis, we reconstruct computational-basis populations from averaged fluorescence signals and use them to determine the experimental QAOA cost landscape by scanning the variational parameters. These results show that the core elements of QAOA can be realized on this platform and establish a baseline for future improvements in phase tracking, coherence-preserving control, and scaling to larger problem sizes.

Variational autoencoders (VAEs) learn compact latent representations of complex data, but their generative capacity is fundamentally constrained by the choice of prior distribution over the latent space. Energy-based priors offer a principled way to move beyond factorized assumptions and capture structured interactions among latent variables, yet training such priors at scale requires accurate and efficient sampling from intractable distributions. Here we present Boltzmann-machine--prior VAEs (BM-VAEs) trained using quantum annealing--based sampling in three distinct operational modes within a single generative system. During training, diabatic quantum annealing (DQA) provides unbiased Boltzmann samples for gradient estimation of the energy-based prior; for unconditional generation, slower quantum annealing (QA) concentrates samples near low-energy minima; for conditional generation, bias fields are added to direct sampling toward attribute-specific regions of the energy landscape (c-QA). Using up to 2000 qubits on a D-Wave Advantage2 processor, we demonstrate stable and efficient training across multiple datasets, with faster convergence and lower reconstruction loss than a Gaussian-prior VAE. The learned Boltzmann prior enables unconditional generation by sampling directly from the energy-based latent distribution, a capability that plain autoencoders lack, and conditional generation through latent biasing that leverages the learned pairwise interactions.

We study continuous time quantum walk on a random comb graph with infinite teeth. Due to localization effects along the spine, the walk cannot go to infinity in the spine direction, while it can escape to infinity along the teeth of the comb. Starting from an initial vertex the walk has a nonzero probability to stay trapped in a finite region. These results are obtained by studying the spectrum and eigenstates of the random Hamiltonian for the graph and analysing its properties. We use both analytic and numerical methods many of which come from the theory of Anderson localization in one dimension.

We investigate the spectral properties of the Su-Schrieffer-Heeger (SSH) model with sublattice-dependent onsite nonlinearity. Two complementary approaches are employed in our studies. First, Bloch state solutions under periodic boundary conditions are assumed to enable semi-analytical treatment, which allows us to obtain the system's energy band structure and further derive a general expression of the Zak phase that incorporates nonlinearity-induced correction (referred to as nonlinear Zak phase). This analysis reveals that, at sufficiently high nonlinearities, a nonlinearity-induced topological phase transition occurs, marked by a discontinuity in the nonlinear Zak phase. The second approach amounts to numerically obtaining other (non-Bloch) solutions under open boundary conditions, employing the Self-Consistent Field Iterative Method. Its main results include the observation of an edge state's energy that is independent of a nonlinear parameter, a persisting band touching point that only shifts in the presence of perturbations reminiscent of Weyl points in a Weyl semimetal, as well as delocalized solutions that persist even at extreme nonlinearity strengths. These findings illuminate the rich interplay between topology and nonlinearity in lattice models with potential realization in optical/acoustic waveguide settings.

In this paper, we present a systematic study on the ground state computation of quantum droplets in homonuclear Bose-Bose mixtures, governed by the extended Gross-Pitaevskii equations (eGPEs) with Lee-Huang-Yang (LHY) corrections. This model captures the formation of self-bound droplets stabilized by the delicate balance between the attractive mean-field interaction and the repulsive quantum fluctuations. We formulate dimensionless energy functionals for both the general two-component system and the reduced single-component density-locked model. To compute the ground states efficiently, we adapt and benchmark various gradient flow discretization schemes, identifying a backward-forward sine-pseudospectral scheme based on the gradient flow with Lagrange multiplier method (GFLM-BFSP) as the robust solver for our simulations. Utilizing this method, we report three main numerical observations: (i) the density-locked model is quantitatively validated as a reliable approximation for ground state properties; (ii) the dimension-dependent convergence rates of the Thomas-Fermi approximation are established in the strong-coupling regime; and (iii) the critical particle number for self-binding in free space is numerically determined, providing a precise correction to the analytical prediction by Petrov [Phys. Rev. Lett. 115, 155302 (2015)].

A system of three or four particle can be entangled in a number of different ways. It may be the case that only subsets of the particles are entangled, and these subsets are not entangled with each other. It may also be the case that the state is the sum of states in which entanglement only exists within subsets. If this is not the case, the state is said to be genuinely entangled. GHZ states, for example, are genuinely entangled. Deciding whether a state is genuinely entangled is not simple, but conditions do exist to detect it. Here we would like to propose additional sufficient conditions based on one for bipartite entanglement.

We present a methodological study of quantum simulation of cranking in a Nilsson $+$ pairing Hamiltonian on a fixed deformation grid. The many-body Routhian is mapped to qubits via the Jordan--Wigner transformation and minimized using the Variational Quantum Eigensolver (VQE) in a truncated active space $(M)$. We employ a structured, number-conserving singles-and-doubles ansatz: double excitations implement pair transfer, while singles are restricted to the nonzero Coriolis-coupling graph of the active Nilsson basis. For $M=8$, this yields 42 parameters while preserving particle number exactly. Exact number conservation enforces $\langle P_k \rangle = 0$, so the conventional pairing gap $Δ_κ\propto G\left|\sum_k \langle P_k \rangle\right|$ vanishes identically. We instead introduce a fixed-$N$ pairing-coherence diagnostic, \[ Δ_{\mathrm{coh}} = G \sqrt{\sum_{k \neq l} \left| \langle P_k^\dagger P_l \rangle \right|}, \] used as a scalar measure of off-diagonal pair coherence rather than a BCS gap. We study even-even $^{80,82,84}$Zr. $^{80}$Zr shows a stable oblate minimum at $δ^\ast \approx -0.25$; $^{82}$Zr exhibits the strongest rotational evolution; $^{84}$Zr retains a robust prolate minimum with the largest neutron pairing coherence. These results reflect the present truncated model rather than converged spectroscopy. A cranked BCS calculation on the same grid serves as a qualitative baseline. Comparisons between $M=6$ and $M=8$ show stable trends but visible shifts, so no active-space convergence is claimed. The structured fixed-$N$ ansatz thus captures consistent isotope trends and provides a practical framework to analyze pairing via $Δ_{\mathrm{coh}}$.

Quantum computing has attracted the attention of the scientific community in the past few decades. However, despite some relevant advantages, near-term quantum devices remain severely limited by thermal effects, which induce decoherence and restrict coherent control at finite temperature. In this regard, this work reports a gate-based quantum algorithm that prepares the finite-temperature vacuum of Thermofield Dynamics (TFD) and tracks its real-time evolution. The circuit depth scales linearly with system size and requires only single-qubit rotations and nearest-neighbor CNOT gates, making it NISQ-friendly. We benchmark the protocol on the PennyLane simulator: magnetization of a spin-$1/2$ particle in a magnetic field agrees with the exact result $M(β)=\tanh(βω/2)$ to machine precision, and the coherent precession acquires a temperature-dependent damping that quantitatively matches the analytical TFD prediction. Our work provides a ready-to-deploy toolbox for thermal quantum simulations and opens a route to study dissipative phase transitions, quantum thermodynamics and thermal machine-learning models on near-term devices.

Optical circuits and light sources, such as lasers, undergo continuous miniaturization. In its extreme, nanolasers might be comprised of only a few molecules confined in plasmonic nanoresonators. Few-emitter lasers promise low energy requirements and fast responses in a footprint that can be inserted into any device or biological tissue. Utilizing the recently developed stacked hierarchy approach, informed from first principles, we demonstrate the impact of vibrational structure on lasing, using the example of few-molecule lasing in plasmonic cavities. Explicitly accounting for the entire vibrational manifold unveils resonances in the laser intensity that depend on the Stokes shift, drive strength, and the number of emitters. Our work identifies the limits of the omnipresent "incoherent drive"-approximation and paves the way for the understanding of nanolasers at the molecular scale.

The approximate coherent state rank is the minimal number of (classical) coherent states required to approximate a continuous-variable bosonic quantum state and directly relates to the classical complexity of simulating bosonic computations. Despite its importance, little is known about lower bounds on this quantity, even for basic families of states. In this work, we initiate a systematic study of lower bounds on the approximate coherent state rank. Our contributions are as follows. (i) We introduce a technique based on low-rank approximation theory yielding generic lower bounds on the approximate coherent state rank of arbitrary single-mode states. (ii) Using this technique, we find a complete characterization of all single-mode states of finite approximate coherent state rank, and we obtain in particular analytical expressions for the approximate coherent state rank of squeezed states and of finite superpositions of Fock states. (iii) We further show that our single-mode lower bounds can be lifted to multimode lower bounds for finite superpositions of multimode Fock states. (iv) Finally, we prove a super-polynomial lower bound on the approximate coherent state rank of the $n$-mode Fock state $|1\rangle^{\otimes n}$, by exploiting a connection to the permanent. To do so, we show that the algebraic complexity of approximate multi-linear formulas for the permanent is super-polynomial, building upon the proof of a lower bound for exact formulas due to [Raz, JACM 2009]. Our results establish an unconditional barrier to efficient classical simulation of Boson Sampling via coherent state decompositions and connect non-classicality of bosonic quantum systems to central questions in algebraic complexity.

Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold ground-state polar molecules are an ideal platform to encode synthetic dimensions, offering access to large Hilbert spaces of long-lived internal states associated with the rotational and hyperfine degrees of freedom, that can be coupled together with microwave fields to simulate tunnelling. Here, to benchmark the advantages of ultracold molecules, we encode a 1D synthetic lattice in the rotational states of ultracold RbCs molecules and use it to investigate the well-known Su-Schrieffer-Heeger (SSH) model, a minimal model displaying topological properties. To probe the system, we perform spectroscopy using an auxiliary rotational state and study the time dynamics after deterministic state preparation. We demonstrate long coherence times, typically ~500 times the lattice tunnelling period, even for a synthetic lattice using 8 rotational states. Observations of dynamics at long times with full site-resolved readout of the synthetic dimension allow us to test the effects of chiral and non-chiral perturbations on the topologically protected edge states. Our work lays the foundation for further quantum simulations using the rich internal structure of molecules, including dipolar string phases in interacting samples of molecules, and adiabatic state preparation of many-body Hamiltonians.

Random Number Generators (RNGs) are crucial for applications ranging from cryptography to simulations. Depending on the source of randomness, RNGs are classified into Pseudo-Random Number Generators (PRNGs), True Random Number Generators (TRNGs), and Quantum Random Number Generators (QRNGs). This work presents the end-to-end development of a high-speed, high-efficiency, phase-noise-based QRNG system that taps into the quantum phase noise of a single-frequency laser, with randomness originating from spontaneous emission. Using a self-heterodyne measurement with a semiconductor laser (linewidth $\approx$ 5.23 $GHz$) operated near threshold and a $\sim$48 $cm$ fiber delay line, a raw data generation rate of 2.0 $Gbps$ is achieved. To ensure uniform randomness in the QRNG output, robust extraction techniques developed in-house, such as the Toeplitz Strong Extractor (TSE), are used. Randomness validation using the NIST and Diehard test suites confirms that all statistical tests pass at standard confidence levels. The developed system achieves a post-processed generation rate of 1.0 $Gbps$ in operation and attains a Technology Readiness Level (TRL) of 7, approaching TRL 8, making it suitable for real-time secure applications such as cryptographic key generation and stochastic modeling.

We study a composite model of two $1D$ $PXP$ chains with dual constraints, forming a junction that acts as an infinite kinematic barrier to quantum information exchange. Moreover, the hard wall at the junction which acts as a perfect reflector, preventing any quantum information leakage between the two sides of the composite chain, can be made permeable by relaxing the constraint at the junction sites. Multiple frozen junctions shatter the Hilbert space into disjoint Krylov fragments, the number of which increases exponentially with the engineered defects. Furthermore, the energy level statistics in each symmetry-resolved sector are strictly Poissonian, demonstrating that the tensor sum of the disjoint Hamiltonians results in a pure superposition of the chaotic spectra of the sub- $PXP$ chains. We also find that a chirally protected zero-energy mode can exist which has local peaks at the physical edges and within the bulk near the junction sites. This state is protected from hybridization with bulk states induced by any chirality preserving disorder. Due to the tensor product structure of the eigenfunctions, the non-zero energy scar states also multiply in number. Finally, we introduce novel Fock states with spatially tunable thermal and athermal regions. This architecture can be readily realized in programmable Rydberg atom platforms using optical tweezers, addressing beams and facilitation techniques.

We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical behavior, our framework targets the inference of invariant algebraic structures underlying the effective Markovian evolution. Measurement limitations, symmetries, and superselection rules are incorporated through a $*$-algebraic description of accessible observables. The learning problem is formulated as maximum-likelihood estimation from multi-time measurement sequences, where the algebraic type of an invariant subalgebra - articularly a decoherence-free subalgebra - is treated as a discrete structural hypothesis. The feasibility of the approach is illustrated on multiple synthetic models and a waveguide quantum electrodynamics system, where nontrivial intermediate algebraic structures are identified directly from measurement data.

We establish a systematic framework of unbiased quantum sampling and estimation protocols for the classical Gibbs expectation. This framework generalizes existing approaches to the partition function estimation and has broader applications in various fields. We consider sampling and estimation for a wide class of non-log-concave distributions, particularly heavy-tailed ones, under relaxed assumptions beyond strong convexity, such as dissipativity. We develop an unbiased extension of quantum-accelerated multilevel Monte Carlo (QA-MLMC) to eliminate all biases from discretization and time truncation, together with introducing a change-of-measure approach and the Girsanov theorem via Radon-Nikodym derivatives. As a result, our approach achieves quantum complexity $\widetilde{\mathcal{O}}(ε^{-1})$ within error $ε$, whereas the classical MLMC requires $\widetilde{\mathcal{O}}(ε^{-2})$ and existing quantum algorithms yield biased estimators under stronger assumptions. Furthermore, our unified framework enables unbiased quantum sampling and estimation for certain heavy-tailed distributions after transformation. We provide several concrete applications of our approach in statistics, machine learning, and finance, towards more practical scenarios of the quantum acceleration of stochastic processes.

Nonlinear Thouless pumping has been established in periodic lattices; its counterpart in quasiperiodic lattices remains unexplored. Here, we show a nonlinear topological pumping of gap solitons in quasiperiodic lattices where the local nonlinear self-consistent potentials lead to a lattice potential reconstruction; as a result, an emergent topological structure induced by this local reconstruction governs the dynamics of the gap solitons. This enables solitons to adiabatically occupy a single topological band, realizing quasi-quantized Thouless pumping. In addition, the intrinsic lattice perturbations disrupt this band occupation, which drives solitons into a non-quantized drifting regime. However, even in this regime, we also find that the soliton transport is constrained by the topological properties of a critical rational approximant. Tuning nonlinearity or lattice scaling reveals a controllable switching among topological pumping, drifting, and localization. Our work uncovers a mechanism for nonlinearity-induced topological behavior in complex lattice potentials.

We present a theoretical study of the survival probability of a state initially prepared in the one-particle sector of a multi-qubit system. The motivation for our work is the ongoing laboratory development of multi-qubit platforms based on superconducting circuits. Using elementary concepts of random matrix theory, we obtain analytic expressions for the survival probability in mathematical models of platforms which, albeit stylized, have been previously shown to provide relevant benchmarks for experimental data. In particular, we show that the decay properties are sensitive to the property of the Hamilton operator to have extended states. The survival probability does not appear instead to depend on whether the interaction between qubits is described by a Gaussian orthogonal ensemble (often interpreted as a model of ''chaotic'' dynamics) or is modeled by an analytically solvable chain. We interpret this phenomenon as a manifestation of a general mechanism for the emergence of equilibration in purely unitary dynamics. Finally, under the same hypothesis of an initial preparation with projection on a large fraction of the extended eigenstates of the Hamilton operator, we show how to extend the classical Kac-Mazur-Montroll estimate of the return time to the quantum survival probability.

This study investigates the application of quantum machine learning (QML) to approximate the nonlinear component of the collision operator within the quantum lattice Boltzmann method (QLBM). To achieve this, we train a variational quantum circuit (VQC) to construct an operator $U$. When applied to the post-linear-collision quantum state $\ket{Ψ_i}$, this operator yields a final state $\ket{Ψ_f} = U\ket{Ψ_i}$ that successfully replicates the nonlinear collision dynamics derived from the Bhatnagar-Gross-Krook (BGK) approximation. Within this framework, we present two distinct architectures: the R1 model and the R2 model. The R1 model is designed for quantum simulations that involve multiple time steps without intermediate measurements, focusing on accurately capturing nonlinear dynamics in continuous evolution. In contrast, the R2 model is tailored to achieve the high-precision reconstruction of the nonlinear operator for a single time step with an unitary operator.

The breakdown of Lorentz invariance, a potential signature of quantum gravity, offers a window into physics beyond general relativity. We investigate how such a violation, embodied by the Einstein-Bumblebee black hole spacetime, influences the nonlocal quantum correlations. Specifically, we study the quantum steering and Bell nonlocality between modes trapped inside and outside the event horizon of an Einstein-Bumblebee black hole. Our analysis demonstrates that quantum steering for an initially correlated state is confined to a narrow region near the event horizon, with the Lorentz-violating parameter further constraining this domain. Notably, the degree of steering asymmetry is significantly modulated by both the distance from the horizon and the Lorentz-violating parameter, with the two spatially separated regions exhibiting opposite trends. Furthermore, the Bell nonlocality measurable by an external observer strengthens with increasing distance from the black hole. These findings confirm the persistence of nonclassical correlations in a Lorentz-violating gravitational background and and offer a novel perspective on the interplay between quantum information and fundamental spacetime symmetries.

The binary paint shop problem (BPSP) is an APX-hard optimization problem in which, given n car models that occur twice in a sequence of length 2n, the goal is to find a colouring sequence such that the two occurrences of each model are painted differently, while minimizing the number of times the paint is swapped along the sequence. A recent classical heuristic, known as the recursive star greedy (RSG) algorithm, is conjectured to achieve an expected paint swap ratio of 0.361, thereby outperforming the QAOA with circuit depth p = 7. Since the performance of the QAOA with logarithmic circuit depth is instance independent, the average paint swap ratio is upper-bounded by the QAOA, which numerical evidence suggests is approximately between 0.265 and 0.282. To provide hardware-relevant comparisons, we additionally implement the BPSP on a D-Wave Quantum Annealer Advantage 2, obtaining a minimum paint swap ratio of 0.320. Given that the QAOA with logarithmic circuit depth does not exhibit quantum advantage for sparse optimization problems such as the BPSP, this implies the existence of a classical algorithm that surpasses both the RSG algorithm and logarithmic depth QAOA. We provide numerical evidence that the Mean-Field Approximate Optimization Algorithm (MF-AOA) is one such algorithm that beats all known classical heuristics and quantum algorithms to date with a paint swap ratio of approximately 0.2799.

Traditional perturbation theory, based on local analyticity (Taylor expansion), often fails in many-body systems with exponentially small energy gaps and strong interactions. This work presents an alternative methodological framework built on two core principles: (1) starting from the pole expansion of the resolvent to directly capture the global analytic structure, and (2) treating local fluctuations statistically (in the spirit of the eigenstate thermalization hypothesis) to close the mean-field equations. Crucially, we go beyond the mean-field level by deriving an exact recursive re-expansion of the cross-correlated terms, which systematically generates higher-order corrections that control the distribution tails, branch splitting, and fluctuations. The framework is realized through a hierarchical ansatz strategy, solving self-consistent equations with Lorentzian, Gaussian, and hybrid forms to describe the bulk, tail, and full distribution, respectively. This methodology does not rely on weak-coupling assumptions and is applicable to the quantitative analysis of global properties such as entropy production and distribution functions in nonintegrable many-body systems. We detail its mathematical structure, the recursive expansion of fluctuations, conditions of validity, comparison with traditional methods, and provide a general implementation workflow.

This paper presents a quantum algorithm for solving the fractional Poisson equation \((-Δ)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system solvers to achieve exponential quantum advantage. The rational approximation represents the inverse fractional Laplacian as a weighted sum of standard resolvents, transforming the original nonlocal problem into a collection of shifted integer-order partial differential equations. These equations are consolidated into a single large linear system through a modified right-hand side construction that simplifies the quantum implementation. To enable practical implementation, we develop explicit quantum circuits via the Schrödingerization technique, which converts the non-unitary dynamics of the linear system into a higher-dimensional Schrödinger-type equation, allowing the use of standard Hamiltonian simulation. The circuit construction leverages the decomposition of shift operators to realize the discrete Laplacian and employs controlled operations to implement the select oracle. Under finite difference discretization, we provide detailed algorithmic procedures utilizing block-encoding techniques for the coefficient matrices. A comprehensive complexity analysis demonstrates that the quantum algorithm achieves a dependence on the inverse mesh size \(h^{-1}\) that is independent of the spatial dimension \(d\), in stark contrast to classical methods which suffer from exponential growth in high dimensions. This establishes an exponential quantum advantage for high-dimensional fractional problems, effectively overcoming the curse of dimensionality that limits classical approaches.

Vortex states of photons, electrons, and other particles are wave packets that carry intrinsic orbital angular momentum (OAM) and exhibit other features unavailable for plane waves. Collisions of high-energy vortex states can become a promising tool for nuclear and particle physics, once experimental challenges are overcome. An extensive literature exists on scattering processes involving vortex states; however, most works rely on assumptions that will be challenging to achieve in experiment. In this work, we initiate a systematic re-analysis of vortex-state scattering processes using paraxial Laguerre-Gaussian (LG) wave packets colliding at a non-zero impact parameter $b$. Since the total final transverse momentum $P_\perp$ is no longer fixed, we focus on how the differential cross section depends on $P_\perp$. We emphasize that non-trivial $P_\perp$-dependent features can originate either from the shape of the LG wave packets or from the dynamics of the scattering process under interest. Here, we focus on the former source and explore in detail these universal kinematic features, while the study of process-specific modifications, along with the novel insights they may bring, is delegated to a future work. Interestingly, the non-zero impact parameter $b$ plays a key role in many $P_\perp$-dependent effects, making it a useful probe of vortex states, not a nuisance factor as often assumed.

We investigate nonequilibrium dynamics of a triad of fermionic superfluids connected via Josephson junctions, following sudden switch-on of two-body loss in one of the three superfluids. By formulating the dissipative BCS theory for the Lindblad equation, we find that the superfluid order parameter exhibits a phase rotation, thereby giving rise to three types of dc Josephson currents corresponding to different junctions. We demonstrate that, when the tunneling amplitude $V_{31}$ between superfluids without two-body loss is weak, two-step nonequilibrium dynamical phase transition (NDPT) characterized by the vanishing dc Josephson currents occurs: dissipation first induces the NDPT by making one dc Josephson current finite, while further increasing dissipation makes this remaining dc Josephson current vanish. By contrast, when $V_{31}$ is strong, dissipation induces the NDPT in which all dc Josephson currents simultaneously vanish. An analytical study based on a simplified model further supports this observation.

Liquid crystalline defects in 3D can be viewed as geometric spinors, whose emergent properties are reminiscent of those of topological excitations in quantum condensed matter, such as Majorana quasiparticles. However, it is unclear how deep this analogy is, and whether this is a purely mathematical mapping, or it extends to key physical features, such as the exchange statistics or braiding behaviour. To address this question, here we consider a simple pattern made up of four nematic Majorana-like defect profiles, and ask how the defect profiles change as we braid them repeatedly around each other. Surprisingly, we find that in a large range of parameter space the defect profiles behave as classical analogues of non-Abelian anyons, which can be described in our case by defect bivectors moving on a Bloch-like hemisphere. Elastic interactions and dynamical effects enhance the complexity of the gates which can be performed by braiding these quasiparticles, making these liquid crystalline spinors promising candidates as components of topological computers.

Standard quantum phase estimation (QPE) has often been regarded as unsuitable for simultaneous detection of all eigenvalues, because it requires initial states with sufficient overlap with the target eigenstates. In this paper, we show that this limitation is not inherent to the QPE circuit itself. The output distribution of standard QPE can be written as a superposition of Fejér kernels weighted by the squared overlaps with the eigenmodes. We prove that, if the initial state is independently drawn at each shot from a 1-design (in particular, by random selection of computational basis states), these mode weights are equalized in expectation, yielding a state-averaged QPE distribution that exhibits peaks at every eigenphase location. In this sense, all eigenvalues become accessible without any modification of the standard QPE circuit; repeated eigenvalues appear through the aggregated weight of their eigenspaces. For distinct eigenphases satisfying a separation condition, we further establish a rigorous peak-detection theory and derive a sufficient shot-count estimate for detecting all peaks. We validate the theory through numerical experiments on a finite element method (FEM) matrix with 1,008 degrees of freedom arising from computer-aided engineering (CAE).

The Grothendieck constant $K_{G}$ is a fundamental quantity in functional analysis, with important connections to quantum information, combinatorial optimization, and the geometry of Banach spaces. Despite decades of study, the value of $K_{G}$ is unknown. The best known lower bound on $K_{G}$ was obtained independently by Davie and Reeds in the 1980s. In this paper we show that their bound is not optimal. We prove that $K_{G} \ge K_{DR} + 10^{-12}$, where $K_{DR}$ denotes the Davie-Reeds lower bound. Our argument is based on a perturbative analysis of the Davie-Reeds operator. We show that every near-extremizer for the Davie-Reeds problem has $Ω(1)$ weight on its degree-3 Hermite coefficients, and therefore introducing a small cubic perturbation increases the integrality gap of the operator.

We present a theoretical framework for recovering the amplitude and carrier phase of a single received RF field with a Rydberg-atom receiver, without injecting an RF local oscillator (LO) into the atoms. The key enabling mechanism is a static DC bias applied to the vapor cell: by Stark-mixing a near-degenerate Rydberg pair, the bias activates an otherwise absent upper optical pathway and closes a phase-sensitive loop within a receiver driven only by the standard probe/coupling pair and the received RF field. For a spatially uniform bias, we derive an effective four-level rotating-frame Hamiltonian of Floquet form and show that the periodic steady state obeys an exact harmonic phase law, so that the $n$th probe harmonic carries the factor $e^{inΦ_S}$. This yields direct estimators for the signal phase and amplitude from a demodulated probe harmonic, with amplitude recovery obtained by inverting an injective harmonic response map. In the high-SNR regime, we derive explicit RMSE laws and use them to identify distinct phase-optimal and amplitude-optimal bias-controlled mixing angles, together with a weighted joint-design criterion and a balanced compromise angle that equalizes the fractional phase and amplitude penalties. We then extend the analysis to nonuniform DC bias through quasistatic spatial averaging and show that bias inhomogeneity reduces coherent gain for phase readout while also reshaping the amplitude-response slope. Numerical examples validate the phase law, illustrate response-map inversion and mixing-angle trade-offs, and quantify the penalties induced by bias nonuniformity. The results establish a minimal route to coherent Rydberg reception of a single RF signal without an auxiliary RF LO in the atoms.

Interactive verification protocols for quantum computations allow to build trust between a client and a service provider, ensuring the former that the instructed computation was carried out faithfully. They come in two variants, one without quantum communication that requires large overhead on the server side to coherently implement quantum-resistant cryptographic primitives, and one with quantum communication but with repetition as the only overhead on the service provider's side. Given the limited number of available qubits on current machines, only quantum communication-based protocols have yielded proof of concepts. In this work, we show that the repetition overhead of protocols with quantum communication can be further mitigated if one examines the task of operating a quantum machine from the service provider's point of view. Indeed, we show that the test rounds data, whose collection is necessary to provide security, can indeed be recycled to perform continuous monitoring of noise model parameters for the service provider. This exemplifies the versatility of these protocols, whose template can serve multiple purposes and increases the interest in considering their early integration into development roadmaps of quantum machines.

A strong converse bound for the classical identification capacity of a quantum channel is an upper bound on the asymptotic identification rate of classical messages sent through the channel, such that, above this rate, the probability of an identification error necessarily converges to one. Converse bounds for identification are notoriously difficult to obtain for fully quantum channels. The only previously known converse bound, due to Atif, Pradhan and Winter [Int.~J.~Quantum Inf.~22(5):2440013, 2024], has the unsatisfactory feature of remaining strictly positive even for a completely noisy channel, for which identification is clearly impossible. We derive strong (and hence also weak) converse bounds, for the qubit depolarizing channel with noise parameter $p$, that vanish as $p\to 1$, thereby yielding the correct behavior in the completely noisy limit. Moreover, in the setting of simultaneous classical identification under the constraint of complete product measurements, our converse bound matches the corresponding achievability bound, and establishes that in this case the identification capacity equals the classical capacity of the channel.

Entangled photon pairs are a ubiquitous resource in quantum technologies, used in quantum key distribution and quantum networking as well as fundamental tests of non-locality. For scalable quantum networks, pairs that are indistinguishable in all unentangled degrees of freedom are essential, as they enable high-fidelity entanglement swapping across network nodes. To date the most-studied sources of "swappable" entangled photon pairs have been based on spontaneous parametric down-conversion (SPDC) in non-linear crystals. However, the probabilistic nature and unavoidable trade-off between brightness and unwanted multi-photon emission limits their performance in lossy channels. Here, we demonstrate a high-fidelity source of "swappable" entangled photon pairs using a semiconductor quantum dot (QD) coupled to a tunable microcavity. By actively modulating the QD emission between orthogonal polarisation states, delaying one path in a low-loss Herriott cell, and recombining the two on a balanced beam splitter, we generate entangled photon pairs with a fidelity of $96.1\pm0.5$ %. We identify and mitigate fidelity-limiting factors, achieving a maximum fidelity of $98.1\pm0.5$ % through time-resolved post-selection. The scheme suppresses residual multi-photon events concentrated near the excitation pulse and has only a modest impact on the rate. Furthermore, the photons are mutually indistinguishable, enabling efficient entanglement swapping. Our results establish semiconductor QDs as a viable platform for quantum network-compatible swappable entangled photon pair generation, with feasible entanglement generation rates exceeding 0.5 Gpairs/s.

Quantum sensing technologies offer transformative potential for ultra-sensitive biomedical sensing, yet their clinical translation remains constrained by classical noise limits and a reliance on macroscopic ensembles. We propose a unifying generational framework to organize the evolving landscape of quantum biosensors based on their utilization of quantum resources. First-generation devices utilize discrete energy levels for signal transduction but follow classical scaling laws. Second-generation sensors exploit quantum coherence to reach the standard quantum limit, while third-generation architectures leverage entanglement and spin squeezing to approach Heisenberg-limited precision. We further define an emerging fourth generation characterized by the end-to-end integration of quantum sensing with quantum learning and variational circuits, enabling adaptive inference directly within the quantum domain. By analyzing critical parameters such as bandwidth matching and sensor-tissue proximity, we identify key technological bottlenecks and propose a roadmap for transitioning from measuring physical observables to extracting structured biological information with quantum-enhanced intelligence.

The $1+1$ dimensional $Z_2$ gauge theory is the simplest model that allows for quantum computation or quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from the underlying non-Hermitian evolution and to model the effects of quantum measurements. This work focuses on monitoring ultra-local physical observables for a $\mathbb Z_2$ gauge theory. Tensor network calculations are performed to dynamically probe entanglement entropy at larger lattice sizes. In this work, we report that continuously monitoring local and diagonal observables (electric and mass energy densities) in the computational basis demonstrates the absence of any measurement-induced phase transition, as indicated by the system-size independence of the late-time saturation value of the bipartite entanglement entropy.

We present a systematic derivation of the Heisenberg evolution of a trilinear bosonic Hamiltonian system in presence of a strong drive beyond the standard approximation of a classical, undepleted driving field. We employ a perturbative expansion of the Hamiltonian propagator in orders of the input field amplitudes, as opposed to the standard Baker-Campbell-Hausdorff (BCH) expansion of the propagator in orders of time. Our method automatically provides time-closed expressions; and converges considerably faster than BCH, especially in the regime of high parametric gain because the small parameter it uses is natural to the problem. We obtain the well-known quantum solution for optical parametric amplification of down-conversion simply as the first order of the expansion, and present the rigorous procedure to derive higher order corrections one by one. To demonstrate the utility of higher corrections, we discuss the 2nd order correction to the pump field as an ideal detector of time-energy entanglement in parametric down-conversion. We also use the 3rd order correction to calculate the limits on the fidelity of quantum state-transfer from one optical mode to another using sum/difference frequency generation, due to the quantum properties of the strong driving field.

Recent studies have shown that Trotter errors are highly initial-state dependent and that standard upper bounds often substantially overestimate them. However, the mechanism underlying anomalously small Trotter errors and a systematic route to identifying error-resilient states remain unclear. Using interaction-picture perturbation theory, we derive an analytical expression for the leading-order Trotter error in the eigenbasis of the Hamiltonian. Our analysis shows that initial states supported on spectrally commensurate energy ladders exhibit strongly suppressed error growth together with persistent Loschmidt revivals. We refer to such states as Trotter scars. To identify such states in practice, we further introduce a general variational framework for finding error-minimizing initial states for a given Hamiltonian. Applying this framework to several spin models, we find optimized states whose spectral support and dynamical behavior agree with the perturbative prediction. Our results reveal the spectral origin of Trotter-error resilience and provide a practical strategy for discovering error-resilient states in digital quantum simulation.

This study investigates the spatial confinement of topological $π$-modes in one-dimensional chiral-symmetric systems. In conventional periodic and quasiperiodic structures, edge-mode wave functions inevitably penetrate the bulk. To suppress this, inverse design of a potential sequence is performed using a generative model under a global topological constraint. The generated sequence reveals a characteristic structure consisting of a topological boundary layer and a macroscopic S-dense domain, leading to enhanced confinement ($ξ=0.85$) while preserving topology. Based on the physical principle extracted from this result, a minimal heterostructure composed of only two S-blocks is manually constructed, which further reduces the localization length to $ξ=0.75$. These results provide a compact design principle for strongly localized topological states.

In this work, we study the problems of certifying and learning quantum $k$-local Hamiltonians, for a constant $k$. Our main contributions are as follows: - Certification of Hamiltonians. We show that certifying a local Hamiltonian in normalized Frobenius norm via access to its time-evolution operator can be achieved with only $O(1/\varepsilon)$ evolution time. This is optimal, as it matches the Heisenberg-scaling lower bound of $Ω(1/\varepsilon)$. To our knowledge, this is the first optimal algorithm for testing a Hamiltonian property. A key ingredient in our analysis is the Bonami Hypercontractivity Lemma from Fourier analysis. - Learning Gibbs states. We design an algorithm for learning Gibbs states of local Hamiltonians in trace norm that is sample-efficient in all relevant parameters. In contrast, previous approaches learned the underlying Hamiltonian (which implies learning the Gibbs state), and thus inevitably suffered from exponential sample complexity scaling in the inverse temperature. - Certification of Gibbs states. We give an algorithm for certifying Gibbs states of local Hamiltonians in trace norm that is both sample and time-efficient in all relevant parameters, thereby solving a question posed by Anshu (Harvard Data Science Review, 2022).

We establish a topological sum rule, $ν_U = \frac{1}{2π}\sum_nγ_n = 2mν_H$, connecting the geometric phases accumulated by a two-qubit system over a complete basis of initial states to the winding number $ν_H$ classifying its Hamiltonian. Implementations of the same gate from different topological classes must distribute these phases differently, making their distinction measurable through the Wootters concurrence. As a corollary, nontrivial topology is a necessary condition for entanglement: only Hamiltonians with access to $ν_H \neq 0$ can generate it.

Slow light is a regime of reduced group velocity, resulting in increased photon density in optical pulses and enhanced nonlinear effects. Here, we propose the realization of slow light in the regime of strong light-matter interaction between waveguide photons and semiconductor excitons. We design a dielectric superlattice structure with a nearly-flat band characterized by low group velocity and group velocity dispersion, both required for enhancing nonlinear effects with ultrashort pulses. Furthermore, by applying this general framework to a perovskite-based structure, we demonstrate an enhancement of the single-particle phase shift by a factor of more than 20, representing a significant step toward the few-photon quantum regime. Our results provide a blueprint for accessible strong interactions in solid-state integrated optics.

High-order perfect absorption of coherent input has recently attracted significant attention due to its broadband absorption capacity. However, the realization of a high-order perfect absorber relies on the exceptional point (EP) to coalesce the scattering zeros. Here, we present a general scattering framework and achieve the high-order perfect absorber in the absence of EP. We consider the asynchronous coherent input, where a spatial delay introduces a momentum-dependent phase factor beyond the amplitude and phase control in synchronous coherent input. This new degree of freedom enables active control of the momentum dependent output, effectively reshaping the absorption line shape necessary for the high-order perfect absorber. Remarkably, despite the absence of EP, the proposed high-order perfect absorber exhibits significant response to the perturbations in the delay length. Our findings provide insights for the delay induced momentum-sensitive interference phenomenon and offer a new route for wave control.

Nonequilibrium energy transport serves as one of fundamental problems in quantum thermodynamics and quantum technologies. Driven quantum master equation in the dressed picture provides an efficient way of investigating nonequilibrium energy flow in general driven-dissipative quantum systems, where the systems are simultaneously driven by the finite thermodynamic bias and coherent driving field. The validity and general applicability of driven quantum master equation is confirmed by comparing with Floquet master equation, by analyzing energy currents in generic spin and boson models. The additional driving phase reserved in system-reservoir interactions, will apparently modify microscopic energy exchange processes. The steady-state energy currents are dramatically enhanced, in particular near the resonant regimes. In contrast, the traditional dressed master equation yields distinct behaviors of the energy currents. We hope that the driven quantum master equation may provide an efficient utility for the control of quantum transport and thermodynamic performances in driven-dissipative nanodevices.

We consider a Hamiltonian $\hat H$ with a (partially) continuous spectrum and examine the zero-overlap condition which involves the projection onto exact continuum eigenstates of a set of pseudostates obtained from the diagonalization of $\hat H$ in a finite basis of square-integrable functions. For each projected pseudostate the condition implies the occurrence of zeros at all energies that correspond to the pseudo-continuum matrix eigenvalues, except for the eigenenergy associated with that pseudostate. This feature was observed for the Coulomb continuum represented in a Laguerre basis [M. McGovern et al., Phys. Rev. A 79, 042707 (2009)] and later explained using special properties of the Laguerre functions [I. B. Abdurakhmanov et al., J. Phys. B 44, 075204 (2011)]. We establish that a sufficient condition for the zero-overlap condition to occur is that the image space of the operator $\hat Q \hat H \hat P$, where $\hat P$ is the projection operator onto the subspace spanned by the basis and $\hat Q = \hat 1 - \hat P$ its complement, has dimension one. We show that the condition is met for the one-dimensional free-particle problem by a basis of harmonic oscillator eigenstates and for the Coulomb problem by a Laguerre basis, thus offering an alternative proof for the latter case. The zero-overlap condition ensures that in, e.g., an ionizing collision or laser-atom interaction process, transition probabilities obtained from the projection of a time-propagated pseudostate-expanded system wave function onto eigenstates of $ \hat H $ are asymptotically stable.

We investigate the rotational phase diagram of a quasi-two-dimensional, weakly-interacting Bose-Einstein condensate confined in power-law and in hard-wall trapping potentials. For weak interactions, the system undergoes discontinuous transitions between multiply-quantized vortex states as the rotation frequency of the trap increases. In contrast, stronger interactions induce continuous phase transitions toward mixed states involving both singly and multiply-quantized vortex states. A central result is the qualitative (and experimentally observable) difference between power-law and hard-wall confinement: In hard-wall traps, the leading instability always involves states with nonzero density at the trap center, whereas in power-law traps the density vanishes as the rotation frequency increases. The two different types of confinement give rise to scaling properties in the derived phase diagrams.

Spin squeezing serves as both a fundamental witness of quantum entanglement and a critical resource for quantum-enhanced metrology. While generating substantial spin squeezing in finite-range interacting systems remains challenging, such capability is important for advancing quantum technologies. In this work, we develop an optimal control strategy for achieving enhanced spin squeezing in a two-dimensional XX model with dipolar interactions. Leveraging rotor-spin-wave theory for periodic boundary conditions, we circumvent computational bottlenecks to explore control strategies at unprecedented scales. Remarkably, optimizing a single collective transverse field is sufficient to achieve substantial squeezing enhancement, exceeding the two-axis-twisting benchmark. The optimized control field achieves this breakthrough by dynamically suppressing inter-subspace mixing induced by the finite-range interactions, thereby confining the system evolution predominantly within the maximal spin subspace. We further extend rotor-spin-wave theory to open boundary conditions and incorporate dephasing noise, providing a scalable framework for realistic systems. Under these conditions, the optimized protocol remains effective, highlighting its robustness and suitability for experimental implementation.

Chaotic behavior of quantum systems can be characterized by the adherence of the expectation values of given probes to moments of the Haar distribution. In this work, we analyze the behavior of several probes of chaos using a technique known as Isospectral Twirling [1]. This consists in fixing the spectrum of the Hamiltonian and picking its eigenvectors at random. Here, we study the transition from stabilizer bases to random bases according to the Haar measure by T-doped random quantum circuits. We then compute the average value of the probes over ensembles of random spectra from Random Matrix Theory, the Gaussian Diagonal Ensemble and the Gaussian Unitary Ensemble, associated with non-chaotic and chaotic behavior respectively. We also study the behavior of such probes over the Toric Code Hamiltonian.

Quantum key distribution is often regarded as an unconditionally secure method to exchange a secret key by harnessing fundamental aspects of quantum mechanics. Despite the robustness of key exchange, classical post-processing reveals vulnerabilities that an eavesdropper could target. In particular, many reconciliation protocols correct errors by comparing the parities of subsets between both parties. These communications occur over insecure channels, leaking information that an eavesdropper could exploit. Currently there is no holistic threat model that addresses how parity-leakage during reconciliation might be actively manipulated. In this paper we introduce a new form of attack, namely the Manipulate-and-Observe attack in which the adversary (1) partially intercepts a fraction $ρ$ of the qubits during key exchange, injecting the maximally tolerated amount of errors up to the 11 percent error threshold whilst remaining undetected and (2) probes the maximum amount of parity-leakage during reconciliation, and exploits it using a vectorised, parallel brute force filter to shrink the search space from 2n down to as few as a single candidate, for an n-bit reconciled key. We perform simulations of the attack, deploying it on the most widely used protocol, BB84, andthe benchmark reconciliation protocol, Cascade. Our simulation results demonstrate that the attack can significantly reduce the security below the theoretical bound and, in the worst case, fully recover the reconciled key material. The principles of the attack could threaten other parity-based reconciliation schemes, like Low Density Parity Check, which underscores the need for urgent consideration of the combined security of key exchange and post-processing.

It is a universal empirical observation that socks become unpaired in the laundry. We propose a quasiparticle theory of sock dynamics in which individual socks are modelled as bosonic excitations of the agitated laundry condensate. The sock dispersion relation is material-dependent: nondispersive materials retain their shape, while dispersive materials give rise to the well-documented phenomenon of sock shrinkage. In the convex regions of the dispersive spectrum, socks undergo Beliaev decay and spontaneously split into two lower-momentum socks, while in the concave regions the dominant process is Landau-Khalatnikov scattering, which degrades socks into lint and loose threads. In addition, the rotating drum creates sock-antisock pairs from the laundry vacuum via the dynamical Casimir effect. The coexistence of these creation and destruction channels gives rise to a fundamental ambiguity: an unpaired sock at the end of a wash cycle is equally consistent with the destruction of its partner or the spontaneous creation of an entirely new sock.

The most elementary prepare-and-measure scenarios have no independent measurement inputs. No inputs mean that quantum advantages require two indispensable ingredients: shared entanglement and measurements that can be adapted to the communicated messages. Understanding these scenarios is therefore conceptually natural, but also practically relevant, since they act as testbeds for black-box certification of adaptive one-way LOCC. Here, we study them systematically and reveal several of their basic features. For classical messages, we first identify the minimal scenario with a quantum advantage and show that it is maximised by high-dimensional entanglement. Then, we identify the next-to-minimal scenario, and show that quantum advantages can be propelled by nonlocality of the Clauser-Horne-Shimony-Holt type, which makes this an appropriate setting for certification experiments. Proceeding further, we replace classical messages with quantum messages, but require the receiver to read the message before measuring the entangled particle. We show that this leads to amplified quantum advantages, that are made possible only thanks to non-projective message read-out. This in dispensable role of non-projective measurements challenges the common wisdom that they play a secondary role in revealing the power of quantum correlations in black-box experiments.

The practical utility of a quantum network depends on its ability to establish entanglement between arbitrary node pairs with quality sufficient to execute entanglement enabled tasks. This capability can be assessed globally, through aggregate performance over all node pairs, as well as locally, at the level of individual nodes. Since entanglement-based connections form a layer above the underlying physical topology, quantum connectivity is not adequately captured by classical topological connectivity metrics. To enable characterisation of the quantum connectivity at the level of the network (or its subnetworks), we introduce the quantum connectivity measure (QCM), which quantifies the average connection quality between pairs of network nodes. Further, we describe two quantities, the quantum-connected fraction (QCF) and the quantum clustering coefficient (QCC), naturally derived from the QCM, which capture important features of the functional connectivity of the quantum network at the level of the network and an individual node, respectively. These metrics of quantum connectivity depend crucially on the entanglement distribution protocol and the quantum network parameters in addition to its physical topology. We demonstrate the crucial distinction between topological and quantum connectivity, showing that even a fully connected graph can be functionally disconnected for quantum tasks if average network edge-concurrence falls below a critical threshold. These quantum connectivity metrics thus provide important tools for the design, optimization, and benchmarking of future quantum networks.

We study the dynamics of a lattice hard-core boson gas released from a domain wall initial state in the presence of two weak links (defects). When the two defects are separated by a finite distance, the resulting density profile exhibits clear deviations from the standard Euler-scale hydrodynamic description of the gas, due to genuine quantum interference effects between the two defects. By analyzing the exact fermionic propagators, we show that repeated reflections at the defects give rise to interference fringes and coherent patterns that are beyond the reach of the (generalized) hydrodynamic description. We derive a closed analytic expression for the density profile during the expansion, explicitly highlighting the role played by these interference processes.

We propose an adiabatic Ramsey interferometry technique for detecting weak nonlinearities with trapped ions. The method relies on using the quantum Rabi model as a probe, which is sensitive to nonlinear symmetry-breaking perturbations. We show that the couplings which arise either from anharmonic terms of the trapping potential or due to higher order terms in the Coulomb interaction expansion can be efficiently estimated by measuring the spin state probabilities alone. We show that the spin signal is amplified by the mean-phonon excitations, which results in the estimation precision reaching the super-Heisenberg limit. Notably, achieving such high-precision estimation does not require specific entangled state preparation and can be reached even for initial thermal motion state. Furthermore, we show that the super-Heisenberg scaling can be observed even in the presence of weak spin-dephasing.

Quantum gas microscopes offer unprecedented insights into quantum many-body states of cold atomic gases. Here we introduce concrete protocols for extending quantum gas microscopes to measure in phase space, by mapping momentum onto auxiliary degrees of freedom and using positive operator-valued measures. We distinguish between two distinct operational modes. In the Husimi-Q phase space microscope, position and momentum are jointly measured; in this mode the fundamental quantum noise appears in the position measurement. Conversely, the averaged-mode phase space microscope extracts the spatial dependence of averages of the momentum density (and its moments); these averages can be retrieved with arbitrary spatial resolution. We illustrate the utility of these techniques in diverse physical settings.

Efficiently planning container loads onto trains is a computationally challenging combinatorial optimization problem, central to logistics and supply chain management. A primary source of this complexity arises from the need to model and reduce rehandle operations-unproductive crane moves required to access blocked containers. Conventional mathematical formulations address this by introducing explicit binary variables and a web of logical constraints for each potential rehandle, resulting in large-scale models that are difficult to solve. This paper presents a fundamental departure from this paradigm. We introduce an innovative and compact mathematical formulation for the Train Load Optimization (TLO) problem where the rehandle cost is calculated implicitly within the objective function. This novel approach helps prevent the need for dedicated rehandle variables and their associated constraints, leading to a dramatic reduction in model size. We provide a formal comparison against a conventional model to analytically demonstrate the significant reduction in the number of variables and constraints. The efficacy of our compact formulation is assessed through a simulated annealing metaheuristic, which finds high-quality loading plans for various problem instances. The results confirm that our model is not only more parsimonious but also practically effective, offering a scalable and powerful tool for modern rail logistics.

Decoherence in superconducting qubits emerges from the interplay of multilevel dynamics and structured environmental noise, yet perturbative models cannot capture all resulting signatures. Here, EmuPlat couples instruction-set-architecture-level waveform generation to the hierarchical equations of motion (HEOM) under $1/f$ non-Markovian pure dephasing. In the resulting non-perturbative regime -- where filter-function predictions become quantitatively uninformative -- CPMG scaling of a three-level superconducting transmon yields one calibration result, two physical findings, and one structural null. Y-CPMG exhibits axis-dependent scaling-law breakdown -- non-monotonic decoherence, partial coherence revival, and pronounced X--Y population asymmetry ($0.204$ vs ${<}\,0.01$) -- driven by third-level anharmonicity amplified by bath memory; X-CPMG maintains well-behaved power-law scaling with a finite-$n$ transient excess consistent with non-Markovian bath-memory effects. The structural null is equally informative: waveform-level differences -- Standard versus VPPU realizations -- remain undetectable across all coupling strengths, establishing that rotating-frame pure-dephasing coupling renders control-layer detail invisible to scaling observables. These findings define testable predictions, the most experimentally accessible requiring only qualitative verification.

Molecular quantum sensors represent a promising frontier for the detection of nuclear magnetic resonance signals and alternating current magnetic fields at the nanoscale, potentially reaching single-proton sensitivity. Although the triplet states of molecular pentacene provide a viable sensing architecture, the triplet pair states produced by singlet fission of pentacene dimers could enable more flexible quantum manipulations through entanglement. In this work, we model the quantum sensing efficacy of a spin-polarized quintet manifold in a photoexcited pentacene dimer generated via intramolecular singlet fission. Using a Lindblad master equation approach, we simulate the evolution of the triplet pair state under standard dynamical decoupling sequences, including spin echo, XY4, and XY8 and provide a direct performance comparison to the traditional pentacene monomer benchmark. While both architectures exhibit comparable sensitivity for isolated single-spin detection, our findings indicate that the dimer architecture provides a superior interaction cross-section for detecting small ensembles of nuclear spins. Analytical expressions derived for fluorescence modulation demonstrate that sensitivity is optimized in the low-magnetic field regime and scales with the number of pulses in the sensing protocol. This study establishes a theoretical baseline for utilizing high-spin multi-excitonic states as chemically tunable, high-sensitivity quantum probes.

Superconducting transmon qubits based on hybrid superconductor-semiconductor Josephson junctions (gatemons) offer gate tunability, but their relaxation times remain well below those of state-of-the-art transmons, and the origin of this discrepancy is not fully understood. Here, we co-fabricate gatemons and SIS-junction transmons with nominally identical circuit layouts, gate dielectrics, and control lines, so that the Josephson element is the only intentional distinction. Across multiple chips, transmons in this architecture reach relaxation times in the tens of microseconds, whereas gatemons saturate in the few-microsecond range. Using the transmons as on-chip references, we construct a loss budget including Purcell decay, spontaneous emission through the control line, and internal dielectric loss, and find that the corresponding T1 limits exceed all measured gatemon values by more than an order of magnitude. Temperature-dependent T1 measurements follow a common quasiparticle-activation model and yield similar superconducting gaps for S-Sm-S and SIS junctions, indicating that the reduced gatemon coherence is dominated by additional temperature-independent, junction-intrinsic dissipation.

Open quantum systems are traditionally described by decomposing the total Hilbert space into a system and an external environment, linked by an explicit interaction Hamiltonian. We propose an alternative framework in which the environment is not introduced as an independent sector a priori, but instead emerges from the dynamical activation of constraints in an initially constrained quantum system. Within Dirac quantization, the physical degrees of freedom define the system, whereas the constraint sector, once promoted to carry its own dynamics, functions as an environment. In this picture, the system-environment coupling is not added through a separate interaction term, but is encoded directly in the constraint structure. As an example, we study a quantum particle coupled to a Brownian-oscillator environment and show how the resulting environmental influence can be formulated in this constraint-based setting. Our results provide a new perspective on the origin of quantum environments and point toward a general framework for open quantum systems rooted in constrained quantization.

The quantum Hall effect realizes a quantized Hall resistance $R_{xy} = h/(νe^2)$ whereas the longitudinal resistance vanishes. The quantized value consists of the fundamental physical quantities, the elementary charge $e$ and the Planck constant $h$, along with an integer or fractional constant $ν$. High precision measurements of $R_{xy}$ allude to a linear relation between the applied current $I$ and the Hall voltage $V_\mathrm{H}$. Here, we argue that a nonlinear relation between $I$ and $V_\mathrm{H}$ could arise when the electric field is spatially inhomogeneous. We first discuss that the linear $I$-$V_\mathrm{H}$ relation holds with Galilean invariance. Then we consider a hydrodynamic description of a quantum Hall liquid to deal with an axially symmetric electric field. It reveals a nonlinear electronic response arising from the centrifugal force exerted on a curved flow and the density gradient invoked by vorticity.

We propose high-fidelity controlled-NOT (CNOT) gates in a hybrid system of polar molecules and Rydberg atoms based on the unconventional Rydberg pumping mechanism. By combining the rich internal structure of polar molecules with the strong dipole-dipole interactions of Rydberg atoms, we realize both two-to-one and one-to-two gate configurations. Numerical simulations show that the gate performance is robust against spontaneous emission from Rydberg states. The approach naturally extends to larger systems, as demonstrated by four-qubit implementations achieving three-to-one and one-to-three CNOT gates with fidelities exceeding 99\%. These results highlight hybrid molecule-Rydberg atom architectures as a promising platform for scalable quantum information processing.

We investigate the distribution of entanglement entropy in hybrid quantum circuits consisting of random unitary gates and local measurements applied at a finite rate. We demonstrate that higher moments of the entanglement entropy distribution, such as a ratio between the variance and the mean and skewness, capture nontrivial features of the measurement-induced dynamics that are invisible to the mean entropy alone. We demonstrate that these quantities exhibit distinct and robust behaviors across the volume-law and area-law phases, and can serve as effective diagnostics of measurement-induced entanglement transitions. We propose a phenomenological model describing the effect of measurements in the area-law regime, which, when combined with the directed polymer in a random environment description of the volume-law phase, well matches numerical simulations across the entire phase diagram.

We experimentally investigate how interactions between Kerr parametric oscillators (KPOs) degrade their bit-flip times, where a bit flip is defined as a transition between the two degenerate ground states of a KPO. Interactions between KPOs cause quantum states of KPOs to leak outside the computational subspace, leading to bit flips. Bit flips degrade fidelity and pose a significant problem for KPO-based quantum information processing. We performed an experiment in which a weak microwave signal is injected into one KPO to emulate photon injection from another KPO, and find that the bit-flip time decreases by an order of magnitude due to induced excitations, depending on the frequency and power of the injected signal. Methods to mitigate the decrease in bit-flip times caused by interactions between KPOs are discussed, including adjusting the pump frequencies, coherent-state amplitudes, and couplings between KPOs. These findings provide valuable insights for scaling up KPO-based quantum computers.

We present a theoretical proposal for a hybrid solid-state quantum node based on a single nitrogen-vacancy (NV) center coupled to a topological single-walled carbon nanotube (SWCNT) plasmonic microtoroid. The SWCNT ring supports deeply sub-wavelength whispering-gallery-like plasmonic modes that are naturally described within a Tomonaga-Luttinger liquid framework. Owing to the closed-ring topology, the cavity spectrum contains a zero-mode sector that is tunable by an external magnetic flux through an Aharonov-Bohm shift. We show that the strongly confined CNT near field can exhibit chiral spin-momentum locking, enabling the two circularly polarized NV transitions to couple selectively to clockwise and counter-clockwise cavity modes, while the parasitic linearly polarized $π$-transition is strongly suppressed by the pronounced anisotropy of the local Purcell enhancement. Based on a tripod stimulated Raman adiabatic passage (STIRAP) scheme, the system can in principle map the NV spin onto a spin-photon entangled state in a deterministic manner, which is then emitted into a side-coupled tapered optical fiber as a tunable flying qubit. We derive the cavity spectrum, the chiral selection rules, the effective tripod Hamiltonian, and the open-system master equation. Quantitative estimates indicate that, under cryogenic conditions and in the overcoupled regime, high-fidelity spin-photon entanglement and in situ magnetic tuning of the emitted photon frequency are in principle achievable. We also discuss a realistic fabrication route for the CNT resonator and deterministic positioning strategies for a single NV center in the CNT near field.

We compute the entanglement entropy and the entanglement spectrum of the vacuum state in the massive Schwinger model at a finite $θ$ angle. The $θ$ term is implemented through a chirally rotated lattice Hamiltonian that preserves the periodicity in $θ$ already at the operator level and maintains the correct massless limit without $θ$-dependent lattice artifacts. We clarify the physical origin of entanglement entropy enhancement at $θ=π$ by relating it to the competition between distinct electric-flux vacuum branches. We show that the peak near $θ=π$ persists across the range of masses studied and corresponds to the point of maximal competition between distinct vacuum branches with opposite electric-field orientation, where quantum fluctuations due to fermion pair creation are maximized. While this entropy enhancement is generic, a pronounced narrowing of the entanglement gap occurs only near the critical mass ratio $m/g\simeq0.33$. Using the Bisognano--Wichmann (BW) theorem, we construct a lattice BW entanglement Hamiltonian and compare it with the exact modular Hamiltonian obtained from the reduced density matrix. We observe agreement between these Hamiltonians in the infrared sector, indicating that the entanglement Hamiltonian is well approximated by a spatially weighted microscopic Hamiltonian. These results establish entanglement observables as sensitive probes of the $θ$-dependent vacuum structure and highlight the chirally rotated formulation as a natural framework for open boundary conditions. Additionally, we discuss possible applications to entanglement in topological insulators and quantum wires.

We uncover an inconsistency in the uniform WKB quantization of deformed quantum mechanics.

We study when partial Boolean functions can (and cannot) exhibit superpolynomial quantum query speedups, and develop a general framework for ruling out such speedups via two complementary lenses: promise-aware complexity measures and function completions. First, we introduce promise versions of standard combinatorial measures (including block sensitivity and related variants) and prove that if the relevant promise and completion measures collapse, then deterministic and quantum query complexities are necessarily polynomially related, i.e., $D(f)=poly(Q(f))$. We then analyze structured families of promises, including symmetric partial functions and promises supported on Hamming slices, obtaining sharp (up to polynomial factors) characterizations in terms of a single gap parameter for the symmetric case and refined slice-dependent bounds for $k$-slice domains. Next, we formalize completion complexity as the minimum of a measure over total completions of a partial function, and show that completability of a measure captures the possibility of superpolynomial quantum speedups. Finally, we apply this viewpoint to derive broad non-speedup criteria for some classes of functions admitting well-behaved completions, such as functions with low maximum influence on both the standard and $p$-biased hypercubes and functions with efficiently identifiable domains, and then show some hardness results for general completion techniques.

A novel semiclassical gravity model proposed by Oppenheim et al., that consistently describes interactions between quantum systems and a classical gravitational field, has recently attracted considerable attention. However, the limitations and phenomenological viability of this model have not yet been thoroughly investigated. In this work, based on the model, we study quantum fluctuations of geodesic deviation coupled with a classical gravitational field. We analytically derive the strain spectrum expected from the fluctuations and show that the original Oppenheim et al. model can be tested with the current observational sensitivity of gravitational-wave experiments. Furthermore, motivated by the novel semiclassical model, we construct two additional models: a modified Oppenheim et al. model that is manifestly consistent with Einstein equation, and a classical-quantum model with environment-induced noise. We analyze the strain spectra predicted by these two models through comparison with those of the original Oppenheim et al. model and perturbative quantum gravity.

The mapping between gate voltages applied to a double quantum dot, and the parameters of a Hubbard-like Hamiltonian, is of utmost importance for understanding and operating spin qubits. State-of-the-art techniques for measuring Hamiltonian parameters (e.g., detuning axis pulsed spectroscopy, DAPS) provide details about energy levels; however, tunnel coupling estimates typically reveal only a small portion of the full Hamiltonian. Here, we demonstrate a Hamiltonian-agnostic technique for measuring the double dot energy spectrum over a wide energy range, at every value of the detuning, called delta-axis spectroscopy (DAXS). We apply the DAXS method to obtain the energy spectrum of a Si/SiGe double quantum dot and use this data to extract the diagonal and off-diagonal couplings of a 15-level Hubbard-like Hamiltonian, demonstrating very good agreement with the experimental measurements.

This paper is concerned with finite-level quantum memory systems for retaining initial dynamic variables in the presence of external quantum noise. The system variables have an algebraic structure, similar to that of the Pauli matrices, and their Heisenberg picture evolution is governed by a quasilinear quantum stochastic differential equation. The latter involves a Hamiltonian whose parameters depend affinely on a classical control signal in the form of a deterministic function of time. The memory performance is quantified by a mean-square deviation of quantum system variables of interest from their initial conditions. We relate this functional to a matrix-valued state of an auxiliary classical control-affine dynamical system. This leads to a pointwise control design where the control signal minimises the time-derivative of the mean-square deviation with an additional quadratic penalty on the control. In an alternative finite-horizon setting with a terminal-integral cost functional, we apply dynamic programming and obtain a quadratically nonlinear Hamilton-Jacobi-Bellman equation, for which a solution is outlined in the form of a recursively computed asymptotic expansion.

We propose a dynamical protocol to generate supersolids in dipolar quantum gases by sweeping a repulsive Gaussian barrier through an incoherent quasi-one-dimensional droplet array. Supersolidity is inferred by monitoring the ensuing dynamics of the density, momentum distribution, center-of-mass motion, and superfluid fraction within the framework of the extended Gross-Pitaevskii equation with quantum corrections. A persistent superfluid background arises, atop which the crystals oscillate in unison, indicating the establishment of phase coherence. This process is accompanied by energy redistribution and the gradual transfer of higher-lying momenta toward the zero momentum mode. The dependence of the superfluid fraction on the barrier velocity and height is also elucidated evincing the parametric regions which facilitate the rise of a superfluid background. Our results pave the way for engineering supersolid generation using experimentally accessible protocols.

In this article we consider two classical problems in Quantum Mechanics, namely the 'particle on a ring' and the 'particle in a box' from the viewpoint of symplectic topology. Interpreting the solutions of the corresponding time independent Schrödinger equation as orbits in a suitably chosen time dependent Hamiltonian system allows us to investigate them using Floer theory. More precisely we extend the definition of Rabinowitz Floer homology to non-autonomous Hamiltonians on $\mathbb{R}^{2n}$ with its standard symplectic structure and show that compactness of the moduli space of J-holomorphic curves still holds. With this homology we are then able to prove existence results for energy $E$ eigenstates on the 'ring' or in the 'box' for a big range of exterior potentials.

In this work, we propose new methods of parameter estimation using stochastic sampling quantum phase-space simulations. We show that it is possible to compute the quantum Fisher information (QFI) from semiclassical stochastic samples using the Truncated Wigner Approximation (TWA). This method extends the class of quantum systems whose fundamental sensitivity limit can be computed efficiently to any system that can be modelled using the TWA, allowing the analysis of more meteorologically useful quantum states. We illustrate this approach with examples, including a system that evolves outside the spin-squeezing regime, where the method of moments fails.

We report on a universal topological dichroism of chiral three-dimensional systems in response to the chirality of light. We show that chiral topological invariants result in integer-quantized dichroic excitation rate differences. Moreover, we demonstrate that such topological effects arise more generally from coupling optical chirality to higher tensor Berry curvatures and Dixmier-Douady invariants of quantum states, including Hopf indices. We finally propose an experimental setup that leverages superchiral light as a smoking-gun probe of chiral band topologies in three-dimensional materials. Our findings establish an optical route for probing to date unobserved chiral electronic band topologies.

Quantum coherence, as a direct manifestation of the quantum superposition principle, is a crucial resource in quantum information processing. Block coherence resource theory generalizes the traditional coherence framework by defining coherence via a set of orthogonal projectors. Within this framework, we investigates the construction and comparison of block coherence measures. First, we propose two universal methods for constructing coherence measures and introduce a two-parameter family of measures based on the $α$-$z$ Rényi relative entropy and a family of measures based on the Tsallis relative operator entropy. Second, through theoretical proofs and numerical counterexamples, we compares the ordering relations and numerical magnitudes among different block coherence measures and establishes a series of universal numerical inequalities to constrain their values. Besides, we also use $C_{α,1}$ to show the role of coherence in complex dynamic evolution of the Kominis master equation that includes recombination reactions.

Quantum optomechanical STIRAP (Stimulated Raman Adiabatic Passage) is investigated for a system of two mechanical modes coupled to an optical mode. We show analytically that in a system without loss, fractional STIRAP can generate a mechanical Bell state from a single phonon Fock state of one of the mechanical modes with the other mechanical mode in the vacuum state, and a product state from a coherent state. Relative phases between Fock basis components in the final state of STIRAP are determined by the phonon-number parity of the initial state. Furthermore, the system is numerically studied to determine the effects of dissipation, and it is concluded that high-fidelity entanglement can be achieved via fractional STIRAP using state-of-the-art cryogenic cooling and mechanical devices. Finally, an interferometric protocol using time-reversed fractional STIRAP is proposed to quantify entanglement between two mechanical modes.

Quantum metric learning enhances machine learning by mapping classical data to a quantum Hilbert space with maximal separation between classes. However, on current NISQ hardware, this mapping process itself is prone to errors and could be fundamentally incorrect. Verifying that a quantum embedding model successfully achieves its promised separation is essential to ensure the correctness and reliability. In this paper, we propose a practical black-box verification protocol to audit the performance of quantum metric learning models. We define a setting with two parties: a powerful but untrusted prover, who claims to have a parameterized unitary circuit that embeds classical data from different groups with a guaranteed angular separation, and a limited verifier, whose quantum capabilities are restricted to performing only basic measurements. The verifier has no knowledge of the implementation of the prover, including the structure of the model, its parameters, or the details of the prover measurement setup. To verify the separation between different data groups, the proposed algorithm must overcome two key challenges. First, the verifier is ignorant of the prover's implementation details, such as the optimization cost function and measurement setup. Consequently, the verifier lacks any prior information about the expected quantum embedding states for each group. Second, the destructive nature of quantum measurements prevents direct estimation of the separation angles. Our algorithm successfully overcomes these challenges, enabling the verifier to accurately estimate the true separation angles between the different groups. We implemented the proposed protocol and deployed it to verify the QAOAEmbedding models. The results from both theoretical analysis and practical implementation show that our proposal effectively assesses embedding quality and remains robust in adversarial settings.

The Sourlas-Lechner-Hauke-Zoller (SLHZ) scheme for quantum annealing uses the parity to encode logical variables and has several advantages, but it has not been implemented for large-scale quantum annealers. If the SLHZ-based approach can be implemented on currently available quantum annealers, we can evaluate its performance. An efficient method to embed the parity-encoded model into the hardware graphs of available quantum annealers is one of the key elements for this approach. We propose a qubit-efficient embedding scheme for parity-encoded Hamiltonians on quantum annealers with the Zephyr connectivity. We give an explicit constructive embedding of the interaction graph of an intermediate Hamiltonian, which contains only one- and two-body interactions, into the Zephyr graph. Our embedding maps each spin to a two-qubit chain using systematic chain-assignment rules. Its validity is verified via the resulting chain-to-chain connectivity. Our embedding also offers practical flexibility. Chains assigned to ancillary spins allow reduction to a single physical qubit, leading to options to avoid inactive qubits. The number of required qubits per spin in the parity Hamiltonian is three, which is fewer than that for a known embedding scheme for the Pegasus graph.

Quantum trajectories are Markov chains modeling quantum systems subjected to repeated indirect measurements. Their stationary regime depends on what observables are measured on the probes used to indirectly measure the system. In this article we explore the properties of quantum trajectories when the choice of probe observable is randomized. The randomization induces some regularization of the quantum trajectories. We show that non-singular randomization ensures that quantum trajectories purify and therefore accept a unique invariant probability measure. We furthermore study the regularity of that invariant measure. In that endeavour, we introduce a new notion of ergodicity for quantum channels, which we call multiplicative primitivity. It is a priory stronger than primitivity but weaker than positivity improving. Finally, we compute some invariant measures for canonical quantum channels and explore the limits of our assumptions with several examples.

In light of major developments over the past decades in both quantum computing and simulations on classical hardware, it is a serious challenge to identify a real-world problem where quantum advantage is expected to appear. In quantum chemistry, electronic structure calculations of strongly correlated, i.e. multi-reference problems, are often argued to fall into such category because of their intractability with standard methods based on mean-field theory. Therefore, providing state-of-the-art benchmark data by classical algorithms is necessary to make a decisive conclusion when such competing development directions are compared. We report cutting-edge performance results together with high accuracy ground state energy for the Fe$_4$S$_4$ molecular cluster on a CAS(54,36) model space, a problem that has been included quite recently among the list of systems in the {\it Quantum Advantage Tracker} webpage maintained by IBM and RIKEN. Pushing the limits even further, we also present CAS-SCF based orbital optimizations for unprecedented CAS sizes of up to 89 electrons in 102 orbitals [CAS(89,102)] for the Fe$_5$S$_{12}$H$_4^{5-}$ molecular system comprising twenty five open shell orbitals in its sextet ground state and an active spaces size of 331 electrons in 451 orbitals. We have achieved our results via mixed-precision spin-adapted \textit{ab initio} Density Matrix Renormalization Group (DMRG) electronic structure calculations interfaced with the ORCA program package and utilizing the NVIDIA Blackwell graphics processing unit (GPU) platform. We argue that DMRG benchmark data should be taken as a classical reference when quantum advantage is reported. In addition, full exploitation of classical hardware should also be considered since even the most advanced DMRG implementations are still in a premature stage regarding utilization of all the benefits of GPU technology.

As neural networks are known to efficiently represent classes of tensor-network states as well as volume-law-entangled states, identifying which properties determine the representational capabilities of neural quantum states (NQS) remains an open question. We construct NQS representations of ground states of medium-mass atomic nuclei, which typically exhibit significant entanglement and non-stabilizerness, to study their performance in relation to the quantum complexity of the target state. Leveraging a second-quantized formulation of NQS tailored for nuclear-physics applications, we perform calculations in active orbital spaces using a restricted Boltzmann machine (RBM), a prototypical NQS ansatz. For a fixed number of configurations, we find that states with larger non-stabilizerness are systematically harder to learn, as evidenced by reduced accuracy. This finding suggests that non-stabilizerness is a primary factor governing the compression and representational efficiency of RBMs in entangled regimes, and motivates extending these studies to more sophisticated network architectures.

We propose Quantum Riemannian Hamiltonian Descent (QRHD), a quantum algorithm for continuous optimization on Riemannian manifolds that extends Quantum Hamiltonian Descent (QHD) by incorporating geometric structure of the parameter space via a position-dependent metric in the kinetic term. We formulate QRHD at both operator and path integral formalisms and derive the corresponding quantum equations of motion, showing that quantum corrections appear in the action integral but they are suppressed at late times by the time-dependent dissipation factor. This implies that convergence near optimal points is controlled by the classical potential while quantum effects influence early-time dynamics. By analyzing the semiclassical equation, we estimate a lower bound on the convergence time and numerically demonstrate whether QRHD work as a quantum optimization algorithm in some examples. A quantum circuit implementation based on time-dependent Hamiltonian simulation is also discussed and the query complexity is estimated.

There are two distinct perspectives on the quantum time-of-arrival: one can ask for the probability that a particle is found at the detector at a given time, regardless of whether it was previously detected, or for the probability that the particle is detected there for the first time. In this work, we analyze the latter by constructing the time-of-arrival distribution conditioned on the particle not having been detected at earlier times -- the first-click distribution. We work within the Page and Wootters formalism, where time is treated as a quantum observable, and introduce a memory mechanism that records the outcomes of successive detection attempts separated by the detector's finite time resolution. We apply this framework to a single Gaussian wave packet and to a superposition of two overlapping wave packets. We find that conditioning on non-detection redistributes probability toward earlier arrival times, producing narrower and sharper distributions compared with the standard unconditioned case. This effect persists in the presence of quantum interference, though coarser time resolutions broaden the distribution and shift it toward later times.

Trotter decomposition provides a simple approach to simulating open quantum systems by decomposing the Lindbladian into a sum of individual terms. While it is established that Trotter errors in Hamiltonian simulation depend on nested commutators of the summands, such a relationship remains poorly understood for Lindbladian dynamics. In this Letter, we derive commutator-based Trotter error bounds for Lindbladian simulation, yielding an $O(\sqrt{N})$ scaling in the number of Trotter steps for locally interacting systems on $N$ sites. When estimating observable averages, we apply Richardson extrapolation to achieve polylogarithmic precision while maintaining the commutator scaling. To bound the extrapolation remainder, we develop a general truncation bound for the Baker-Campbell-Hausdorff expansion that bypasses common convergence issues in physically relevant systems. For local Lindbladians, our results demonstrate that the Trotter-based methods outperform prior simulation techniques in system-size scaling while requiring only $O(1)$ ancillas. Numerical simulations further validate the predicted system-size and precision scaling.

Understanding equilibration times in closed quantum systems is essential for characterising their approach to equilibrium. Chaotic many-body systems are paradigmatic in this context: they are expected to thermalise according to the eigenstate thermalisation hypothesis and exhibit spectral properties well described by random matrix theory (RMT). While RMT successfully captures spectral correlations, its ability to provide quantitative predictions for equilibration timescales has remained largely unexplored. Here, we study equilibration within RMT using the framework of equilibration as dephasing, focusing on closed systems whose Hamiltonians are drawn from the Gaussian unitary ensemble (GUE). We derive an analytical expression that approximates the average equilibration time of the GUE and show that it is independent of both the initial state and the choice of observable, a consequence of the rotational invariance of the GUE. Numerical simulations confirm our analytical expression and demonstrate that our approximation is in close agreement with the true average equilibration time of the GUE. We find that the equilibration time decreases with system size and vanishes in the thermodynamic limit. This unphysical result indicates that the true equilibration timescale of realistic chaotic many-body systems must be dominated by physical features not captured by random matrix ensembles -- the GUE in particular.

We study binary discrimination of idempotent quantum channels. When the two channels share a common full-rank invariant state, we show that a simple image inclusion condition completely determines the asymptotic behavior: when it holds, a broad family of channel divergences collapse to a closed-form, single-letter expression, regularization is unnecessary, and all error exponents (Stein/Chernoff/strong-converse) are explicitly computable with no adaptive advantage. Crucially, this yields the strong converse property for this channel family, which is an important open problem for general channels. When the inclusion fails, asymmetric exponents become infinite, implying perfect asymptotic discrimination. We apply the results to GNS-symmetric channels, showing discrimination rates for large number of self iterations converge exponentially fast to those of the corresponding idempotent peripheral projections. If the two channels do not share a common invariant state, we provide a single-letter converse bound on the regularized sandwiched Rényi cb-divergence, which suffices to establish a strong converse upper bound on the Stein exponents.

Between 1933 and 1937, the treatment of relativistic spin-1/2 particles, initially rooted in Hole theory, evolved into the modern framework of quantum field theory. This paper reconstructs the crucial stages of that transition by examining the formal and physical progress of the numerous authors who shaped the field's modern formalism. This historical study traces the development of fermionic field theory in full, beginning with the foundational work of the 1920s, focussing on the results of the 1930s, and concluding with the influential synthesis of Wolfgang Pauli in 1941, the content of which has shaped the subsequent tradition. Within this framework, particular emphasis is given to Ettore Majorana's 1937 quantisation procedure and argument for anti-commuting fermionic quantum fields. This study demonstrates that Majorana's work was not merely a technical variant, but the definitive rejection of the concept of negative energy solutions, whose conceptual clarity and educational value remain vital today.

We introduce Exchange Quantum Polynomial Time (XQP) circuits, which comprise quantum computation using only computational basis SPAM and the isotropic Heisenberg exchange interaction. Structurally, this sub-universal model captures decoherence-free subspace computation without access to singlet states. We show that XQP occupies an intermediate position between BPP and BQP, as its efficient multiplicative-error simulation would collapse the polynomial hierarchy to its third level. We further provide evidence that additive-error simulation of XQP would enable efficient additive-error simulation of arbitrary BQP computations. Remarkably, the restricted family of XQP circuits consisting solely of $\sqrt{\mathrm{SWAP}}$ gates remains hard to simulate to multiplicative error. We additionally prove that circuits generated by $\sqrt{\mathrm{SWAP}}$ gates are semi-universal, generate $t$-designs for the uniform distribution over $SU(2)$-invariant unitaries, and maximise the entangling power within XQP. Finally, we derive structural results linking computational basis states in XQP to the Gelfand-Tsetlin basis of the symmetric group, and expressing XQP output probabilities as partition functions of the six-vertex and Potts models. Our findings indicate that XQP circuits are naturally suited to near-term hardware and provide a promising platform for experimental demonstrations of quantum computational advantage.

We construct an exactly solvable relativistic model that embeds the anomalous inverse-square interaction into a non-Hermitian Klein-Gordon field theory through a purely imaginary, scale-invariant scalar potential. The stationary field equation reduces to an inverse-square Schrodinger-type problem with a quadratic spectral parameter. Imposing a strictly outgoing boundary condition at the singularity-interpreted as irreversible absorption-selects a unique physical realization and converts the fall-to-the-center instability into a discrete, log-periodic spectrum of complex energies. The resulting decay rates exhibit universal geometric spacing, determined solely by the anomalous scaling exponent and insensitive to microscopic short-distance regularization. This structure defines an emergent kinematic energy scale that controls dissipative dynamics and provides a minimal analytic framework for studying scale anomaly, boundary-condition-induced non-Hermiticity, and quantized dissipation in relativistic open quantum systems.

An accurate and efficient numerical electromagnetic model for superconducting qubits is essential for characterizing and minimizing design-dependent dielectric losses. The energy participation ratio (EPR) is the commonly adopted metric used to evaluate these losses, but its calculation presents a severe multiscale computational challenge. Conventional finite element method (FEM) requires 3D volumetric meshing, leading to prohibitive computational costs and memory requirements when attempting to capture singular electric fields at nanometer-thin material interfaces. To address this bottleneck, we propose SesQ, a surface integral equation simulator tailored for the precise simulation of the EPR. By applying discretization on 2D surfaces, deriving a semi-analytical multilayer Green's function, and employing a dedicated non-conformal boundary mesh refinement scheme, SesQ accurately resolves singular edge fields without an explosive growth in the number of unknowns. Validations with analytically solvable models demonstrate that SesQ accelerates capacitance extraction by roughly two orders of magnitude compared to commercial FEM tools. While achieving comparable accuracy for capacitance extraction, SesQ delivers superior precision for EPR calculation. Simulations of practical transmon qubits further reveal that FEM approaches tend to significantly underestimate the EPR. Finally, the high efficiency of SesQ enables rapid iteration in the layout optimization, as demonstrated by minimizing the EPR of the qubit pattern, establishing the simulator as a powerful tool for the automated design of low-loss superconducting quantum circuits.

We report implementation and modelling of an efficient photon-triplets generation experiment based on a difference-frequency-mixing of two picosecond beams at 532 nm and 1491 nm in a type II phase-matched KTP crystal. The photon-triplets flux was measured as a function of the energy of the two incident beams using a coincidence protocol. A maximal flux of 11.6 photon-triplets per second was achieved. These experimental data were satisfactorily described by a semiclassical model based on the quantum fluctuations of vacuum and the classical equations of nonlinear optics.

We propose concrete protocols to realize quantum criticality due to excited-state quantum phase transitions (ESQPTs) experimentally in presumably the simplest and most resilient system involving a single trapped ion oscillating in a radio-frequency Paul trap. We identify a specific class of excited states of the Extended Rabi Model (ERM) Hamiltonian, which occur between two critical ESQPT energies of the model in its (anti)Jaynes-Cummings superradiant phase. Properties of these states motivate the definition of several ESQPT witness observables. We study their critical scaling behaviors as well as various distinct state evolutions by driving the system across the quantum criticalities by changing the qubit-phonon coupling strength linearly in time at different finite rates. A mapping of the theoretical control parameters of the ERM to the experimental parameters of a trapped ion setup is provided, and simulations are performed for values referencing existing state-of-the-art setups, addressing both unitary state evolutions as well as relevant open-system corrections.

The performance of the variational quantum eigensolver depends critically on the choice of ansatz. In this work, we experimentally evaluate the emergent-coupling-based ansatz (ECBA), a physically motivated variational ansatz for disordered systems. The ECBA is based on a renormalization (semi-)group approach to determine the dominant effective couplings, resulting in shallow circuits that capture the essential long-range entanglement structure while balancing local correlations. We implement the ECBA on superconducting quantum processors and benchmark it on disordered Heisenberg chain models. Using classically pre-optimized parameters and error mitigation techniques, we study systems of up to 30 qubits and observe an experimental relative energy accuracy of 96.47% for the largest system. Furthermore, we find that the ECBA can be efficiently embedded on hardware with two-dimensional square-lattice connectivity. We compare to commonly used hardware efficient ansätze and observe that the ECBA achieves significantly higher accuracy at a similar gate count.

Quantum metrology exploits quantum resources to enhance measurement precision beyond the classical limit. Conventional protocols normally rely on the preparation of delicate quantum states to acquire these resources, posing a major challenge for scaling and robustness. Here we introduce a paradigm that circumvents this requirement with a collectively enhanced quantum mirror (CEAM), i.e., a mesoscopic array of $N$ atoms coupled to a semi-infinite waveguide. When injecting single photons into the waveguide and estimating the CEAM-boundary distance from the reflection phase, a $1/N^2$ precision scaling can be obtained, which surpasses the Heisenberg limit. In this protocol, the quantum resource stems from the cooperative optical response, requiring no entangled state preparation. Our scheme is robust against positional and coupling disorder, offering a practical route to ultra-sensitive quantum metrology in integrated photonic systems.

The emission of photon from an individual atom encodes the phase of its initialized quantum state. Using single-shot heterodyne detection, we measure the phase distribution of the emission from a superconducting transmon qubit in an open waveguide configuration and track its evolution over time. We demonstrate that the presence of a quantum superposition is encoded in the phase statistics of the emission and remains resolvable despite a high noise level. These phase statistics serve as a quantitative probe of the qubit coherence. The decay of the emission envelope with increasing integration time reveals the energy relaxation rate of the emitted wavepacket, while phase distribution broadening tracks pure dephasing processes. We thereby establish a direct link between the decoherence dynamics of an open quantum system and the statistical properties of its radiated field.

Generating and preserving metrologically useful quantum states is a central challenge in quantum-enhanced atomic magnetometry. In multilevel atoms operated in the low-field regime, the nonlinear Zeeman (NLZ) effect is both a resource and a limitation. It nonlinearly redistributes internal spin fluctuations to generate spin-squeezed states within a single atomic qudit, yet under fixed readout it distorts the measurement-relevant quadrature and limits the accessible metrological gain. This challenge is compounded by the time dependence of both the squeezing axis and the effective nonlinear action. Here we show that physics-informed reinforcement learning can transform NLZ dynamics from a source of readout degradation into a sustained metrological resource. Using only experimentally accessible low-order spin moments, a trained agent identifies, in the $f=21/2$ manifold of $^{161}\mathrm{Dy}$, a unified control policy that rapidly prepares strongly squeezed internal states and stabilizes more than $4\,\mathrm{dB}$ of fixed-axis spin squeezing under always-on NLZ evolution. Including state-preparation overhead, the learned protocol yields a single-atom magnetic sensitivity of $13.9\,\mathrm{pT}/\sqrt{\mathrm{Hz}}$, corresponding to an advantage of approximately $3\,\mathrm{dB}$ beyond the standard quantum limit. Our results establish learning-based control as a practical route for converting unavoidable intrinsic nonlinear dynamics in multilevel quantum sensors into operational metrological advantage.

The quantum approximate optimization algorithm (QAOA) is a leading variational approach to combinatorial optimization, but its practical performance depends strongly on objective design, parameter search, and shot allocation. We present a resource-efficient QAOA framework that uses the cut value of the most probable measured bitstring as the optimization objective, combines it with Bayesian optimization, and adaptively allocates shots using dual criteria based on mode confidence and normalized cut-value variance. Numerical experiments on 3-regular MaxCut show that, for both unweighted and weighted instances, the proposed scheme achieves discrete-solution quality comparable to that of the conventional expectation-based objective while typically requiring fewer total shots to reach the same final mode accuracy. These results indicate that reorganizing QAOA around the maximum-probability bitstring provides an effective route to improving practical performance under limited measurement budgets.

In this letter, we derive the interaction energy and the force between two parallel metal plates, arising from quantum vacuum fluctuations when they are very close to each other. We consider the vacuum to be composed of a meson field. In Quantum Hadrodynamics, mesons are the carriers of the nuclear force.

This perspective provides a succinct history of Fermi's golden rule (FGR), overview of its derivation, assumptions, and representative forms. Major applications of FGR, mostly in the field of chemical physics, are reviewed. These illustrate the broad applicability and success of FGR. Ambiguities and open issues encountered in practical applications of FGR are clarified. Recent advances in generalizations of FGR and computational methods for practical applications are addressed.

We study the conditions under which Matrix Product States (MPS) or Matrix Product Operators are exact eigenvectors of an extensive local operator, such as a Hamiltonian. By suitably choosing the local operator, this covers a wide range of settings: Exact eigenstates of Hamiltonians, including scar states, exact MPS trajectories for driven quantum systems, steady states of local Lindbladians, generalized symmetries of either Hamiltonians or density matrices, and many more. Our key result is that that a local, fixed-size equation -- namely, how a single term in the operator acts on a block of tensors -- provides a necessary and sufficient condition for exact solutions. This allows to characterize the full space of solutions in all of the aforementioned problems, and to identify them both analytically and numerically. We elaborate on the concrete application of this characterization to all of the aforementioned settings, and in particular exemplify the power of our local characterization by using it to recover the quantum group symmetries of the XXZ model. We also discuss applications to numerical algorithms with MPS and the generalization of our results to 2D, i.e., projected entangled pair states (PEPS).

Catalytic carbon fixation to formic acid is important for studying the reduction of carbon footprint and the emergence of life. Can discrete quantum exhaustive search merged with other methods help reduce the carbon footprint? We suggest merging quantum, quantum inspired, and classical tools for a better simulation of various relevant processes. Quantum tools are often used for analyzing the electronic structure of molecules, sometimes because this problem is not scalable (in the number of orbitals) on classical computers while it is potentially approximately scalable on (future) quantum computers. It is potentially even solvable in the near future using variational quantum eigensolvers (VQE) yet a major obstacle to such analysis is the appearance of barren plateaus in the Hilbert space describing the problem. Here we make use of the basic (standard) tools while also including a novel one -- the discrete quantum exhaustive search, which relies on mutually unbiased bases, for analyzing the simplest non-catalytic process involving carbon dioxide, hydrogen and formic acid.

Adversarial training is a standard defense against malicious input perturbations in security-critical machine-learning systems. Its main burden is structural: before every parameter update, the current model must first be attacked to find a new adversarial perturbation, making training increasingly expensive and hard to sustain at large-model scale. Here we give an end-to-end quantum procedure for projected-gradient robust training under local stability and sparsity assumptions. The key step is to reformulate the coupled attacker--learner dynamics as a high-dimensional sparse linear system whose terminal block yields the final network-parameter state. In this formulation, the dominant query cost scales linearly with training time steps, up to logarithmic factors, and polylogarithmically with model size, while the full gate complexity records separate input-preparation and sparse-access overheads. This places core computational tasks for AI security on a concrete quantum footing and identifies a regime in which robust-training overhead can be reduced.

We demonstrate the first CV-QKD system featuring a custom-designed monolithic silicon photonic dual-polarisation transceiver. Leveraging PS-64-QAM, we achieved 1.9 Mbit/s secret key rate across 25 km of standard single-mode fibre, highlighting the potential of electronic-photonic integration for practical QKD.

We experimentally demonstrate local robust shadows on a trapped-ion device, a protocol developed to counteract measurement errors. We alternate between a calibration stage and the shadow estimation stage and also introduce Pauli-X-twirling before measurements in both stages to symmetrize error rates. We then demonstrate the protocol on a trapped-ion quantum computer with artificially shortened measurement pulse duration. This yields faster experiments at the cost of increased error rates which are subsequently mitigated by the robust shadow protocol. We benchmark this approach on three exemplary quantum states: a local Haar random state, as well as standard and Pauli-correlation encoded QAOA states. In all three cases, the local robust shadow protocol succeeds at mitigating the increased error rates hailing from shorter measurement pulse durations.

Learning from quantum data using classical machine learning models has emerged as a promising paradigm toward realizing quantum advantages. Despite extensive analyses on their performance, clean and fully labeled quantum data from the target domain are often unavailable in practical scenarios, forcing models to be trained on data collected under conditions that differ from those encountered at deployment. This mismatch highlights the need for new approaches beyond the common assumptions of prior work. In this work, we address this issue by employing an unsupervised domain adaptation framework for learning from imperfect quantum data. Specifically, by leveraging classical representations of quantum states obtained via classical shadows, we perform unsupervised domain adaptation entirely within a classical computational pipeline once measurements on the quantum states are executed. We numerically evaluate the framework on quantum phases of matter and entanglement classification tasks under realistic domain shifts. Across both tasks, our method outperforms source-only non-adaptive baselines and target-only unsupervised learning approaches, demonstrating the practical applicability of domain adaptation to realistic quantum data learning.

We develop a geometric formulation of stochastic dynamics in which noise, diffusion, path probabilities, fluctuation theorems, and entropy production arise from the intrinsic geometry of an evolving manifold rather than from externally imposed randomness. Within the theory of moving manifolds, we establish a curvature-noise correspondence: fluctuations are governed by the inverse curvature tensor, while entropy production is controlled by curvature deformation. The invariant continuity law on a moving hypersurface yields a geometric Fokker-Planck equation, and curvature-velocity coupling generates a quadratic Onsager-Machlup functional determining path weights. The resulting entropy functional satisfies a curvature-driven monotonicity law, providing a geometric derivation of the Second Law. In two dimensions, the curvature invariant reduces to Gaussian curvature and encodes topology, so topological transitions produce discrete entropy jumps. When the ambient space carries a Minkowskian signature, the same curvature-kinetic quadratic form that generates dissipative thermal weights produces oscillatory phase weights, and the Laplace-Beltrami operator governing entropy evolution acquires a Schrödinger-type structure. This provides a geometric resolution of the apparent distinction between classical stochastic behaviour and quantum dynamics. These results show that stochastic behaviour, thermodynamic irreversibility, and quantum transition amplitudes are unified within the moving manifold framework. Geometry does not merely accommodate stochasticity; stochastic behaviour arises as a consequence of deterministic geometric evolution. The theory predicts curvature-controlled anisotropic diffusion, entropy jumps at topology-changing events, and a geometric thermal-quantum crossover in which classical stochastic weights and quantum amplitudes are generated by the same curvature-kinetic action.

In this work, we construct small sets of bipartite orthogonal pure states that cannot be perfectly distinguished by local operations and classical communication (LOCC). We mention that not all the states within the constructed sets are necessarily entangled. However, such a set contains at least one entangled state which cannot be conclusively identified by LOCC (with nonzero probability). Then, we show that the states of any such set can be perfectly distinguished by LOCC using a minimal-dimensional entangled resource state. Clearly, here the entangled resource state provides an advantage irrespective of the dimension of the given set. Using this result, we also prove that any pure entangled state is useful as a resource to distinguish the states of any present set unambiguously with nonzero probability under LOCC. These sets exist in all two-qudit Hilbert spaces. Furthermore, it is possible to decrease the average entanglement content of such a set or to increase the cardinality of the set without changing certain properties of the same.

Understanding whether the features of open quantum dynamics are genuinely quantum remains a central challenge in quantum dynamics. Even though the non-Markovian behavior of quantum dynamics has been widely investigated across different settings, there is still no consensus on which properties of a dynamics reflect genuine quantum features and which arise from classical or non-genuine quantum sources. In this review, we provide detailed information on recent developments in characterizing quantum non-Markovianity based on information backflow and the nature of its origin. We also present a survey on how various approaches separate classical and quantum contributions, as well as how they define operational tasks that reveal genuine quantum non-Markovianity. We analyze several frameworks, including state-distinguishability -based, channel-based (``CP-divisibility''), and process-tensor methods. For each framework, we outline the underlying physical motivation, the criteria proposed to distinguish genuine quantum non-Markovianity from practical or apparent memory effects. We further compare different approaches and their strengths and limitations. The review aims to clarify the conceptual and operational aspects of quantum non-Markovian processes based on their nature and to provide a foundation for future research on quantum non-Markovianity and its role in advancing quantum information science and technology.

Polar molecules represent a promising platform for quantum simulation and computation protocols. Highly controllable arrays of optical tweezers are now accessible in experiments, allowing for unprecedented control of individual molecules. Motional dephasing is typically seen as an obstacle in quantum computing scenarios. Here, we instead consider using the trap structure as a resource for implementing efficient quantum gates. By numerically solving the two-body problem of dipoles trapped in separate tweezers, we identify trap-induced resonances that can serve as the mechanism for achieving state-dependent dynamics and can be further utilized for quantum sensing.

The 2D $\mathbb{Z}_2$ toric code admits a global symmetry exchanging electric and magnetic quasiparticles, known as electromagnetic duality. Known realizations include lattice translation symmetry, an exact $\mathbb{Z}_4$ symmetry generated by a Clifford circuit, and an exact $\mathbb{Z}_2$ symmetry generated by a non-Clifford circuit. We show that a Clifford electromagnetic duality cannot realize an exact internal $\mathbb{Z}_2$ symmetry. This is proved rigorously for symmetries with coarse translation invariance by $l$ lattice units for generic odd $l$. Therefore an exact internal $\mathbb{Z}_2$ electromagnetic duality must be non-Clifford, whereas generic internal Clifford realization necessarily has $\mathbb{Z}_{2^m}$ algebra with $m\ge 2$. Our result suggests an unexpected connection between exact electromagnetic duality and Clifford hierarchy of circuits.

The generation of complex states like multifractal critical states has been an outstanding challenge in both classical and quantum physics. Here we propose a general framework, termed the imaginary gauge phase imprint, allowing to engineer rigorous wavefunctions in any-dimensional non-Hermitian lattices. Using this method, we uncover a novel phase with exact critical wavefunctions in one (and two) dimension, dubbed the skin critical phase (SCP). Unlike conventional critical phases with overall uniform density distributions and non-Hermitian skin effect with eigenstate accumulation at open boundaries, the SCP is marked by a macroscopically multifractal distribution with all critical eigenstates sharing an identical profile and always accumulating at specific bulk interfaces under periodic boundary condition, which become topology-dependent boundary or interface skin modes under open boundary condition. We also show the ballistic dynamics in the SCP, in contrast to the diffusive behaviour in conventional critical phases. Moreover, we validate our method by imprinting configurable wavefunctions in higher dimensions, including complex fractal states with Sierpinski-carpet and Koch-snowflake profiles in non-fractal lattices and Moire states in non-Moire lattices. Our work not only offers fresh insights into fractal phenomena and critical phases, but also provides a rigorous paradigm for wave manipulations in engineered non-Hermitian systems.

Frustrated spin-ice systems support emergent gauge fields and fractionalized quasiparticles that act as magnetic monopoles. Although artificial platforms have enabled their direct visualization, access to their quantum-coherent dynamics has remained limited. Here we realize a programmable dipolar square spin-ice model using a superconducting-qubit quantum annealer, providing access to a previously unexplored quantum-coherent regime of artificial spin ice. By implementing a direct one-to-one mapping between lattice spins and physical qubits, together with engineered extended couplings, we realize effective dipolar interactions on frustrated lattices comprising more than 400 vertices. Tuning transverse-field fluctuations enables us to probe the real-time dynamics of Dirac-string defects and interacting monopole plasmas. We observe super-diffusive monopole transport, with scaling exponents intermediate between classical diffusion and ballistic motion, indicating dynamics beyond classical stochastic relaxation and consistent with coherent propagation within an emergent gauge manifold. These results establish programmable quantum spin ice as a scalable platform for investigating fractionalized excitations and emergent gauge dynamics in engineered quantum matter.

Integrating quantum circuits into deep learning pipelines remains challenging due to heuristic design limitations. We propose Q-DIVER, a hybrid framework combining a large-scale pretrained EEG encoder (DIVER-1) with a differentiable quantum classifier. Unlike fixed-ansatz approaches, we employ Differentiable Quantum Architecture Search to autonomously discover task-optimal circuit topologies during end-to-end fine-tuning. On the PhysioNet Motor Imagery dataset, our quantum classifier achieves predictive performance comparable to classical multi-layer perceptrons (Test F1: 63.49\%) while using approximately \textbf{50$\times$ fewer task-specific head parameters} (2.10M vs. 105.02M). These results validate quantum transfer learning as a parameter-efficient strategy for high-dimensional biological signal processing.

Device-independent quantum key distribution (DIQKD) provides a model of quantum key distribution with minimal assumptions and highly abstract theoretical building blocks. Although DIQKD frees us from detailed discussions of specific device models and associated error parameters, it replaces them with fundamental assumptions about the validity of quantum experiments. In this work, we propose a way to lift a protocol based on DIQKD-style assumptions to a device-dependent QKD protocol by performing local self-tests in the laboratories of the two key-generating parties. In particular, we consider routed Bell-test setups as a means of self-testing the local parties in earnest and develop a rigorous mathematical framework showing that the underlying optimization problems can indeed be transferred to the device-dependent QKD setting. As an application, we illustrate many of the relevant techniques through the case study of a routed BB84 protocol.

We propose an efficient and robust protocol for the generation of entanglement between a superconducting qubit and a squeezed cavity. By applying a parametric drive to the cavity coupled to the qubit, the dynamical evolution of the system is precisely described by an anisotropic Rabi model within a squeezed reference frame. Utilizing high-order time-averaging methods, we analytically derive the resonance conditions and the effective Rabi frequency for the high-order three-photon process. By implementing an adiabatic passage, slowly tuning the cavity frequency across the resonance, the system is steered into a maximally entangled state, e.g., between the three-photon state $\ket{g,3}$ and the qubit excited state $\ket{e,0}$ in the squeezed picture. Numerical simulation results confirm the high fidelity and robustness of the proposed protocol. Our method provides a practical pathway for generating complex non-Gaussian entangled states, which are of significant value for fault-tolerant quantum computation and quantum metrology beyond the standard quantum limit.

Quantum-enhanced Markov chain Monte Carlo, a hybrid quantum-classical algorithm in which configurations are proposed by a quantum proposer and accepted or rejected by a classical algorithm, has been introduced as a possible method for robust quantum speedup. Previous work has identified competing factors that limit the algorithm's performance: the quantum dynamics should delocalize the system across a range of classical states to propose configurations beyond the reach of simple classical updates, whereas excessive delocalization produces configurations unlikely to be accepted, slowing the chain's convergence. Here, we show that controlling the degree of delocalization by adiabatically dressing the quench protocol can significantly enhance the Markov gap in paradigmatic spin-glass models.

We present an analytic flat-spacetime accelerating boundary analog of Hawking-type emission that possesses infinite asymptotic acceleration (and radial acceleration in the black hole analog) but finite total radiated energy (and zero surface gravity in the black hole analog). We perform a unified study of its scattering symmetry, horizon formation, asymptotically extreme acceleration, finite total radiated energy, and the distinction between local energy flux and global particle production within a single closed-form model. The particle spectrum, energy spectrum, and equivalent spacetime metric are derived, revealing an interesting mix of normal and extremal black hole properties.

The model of light-matter interaction in quantum electrodynamics typically relies on the Markovian approximation, which assumes that the system's future evolution depends solely on its current state, effectively treating it as a ``memoryless" process. However, this approximation is not valid in scenarios when retardation effects are significant. These memory and retardation effects have the potential to improve existing quantum technologies (e.g., large-scale quantum networks, quantum information processing) and unlock new phenomena for future applications. In this work, we show theory and experiments of a time-delayed coherent feedback system using a transmon artificial atom (treated as a qubit) embedded in a superconducting circuit waveguide, in both linear and nonlinear excitation regimes. By using a feedback loop with a delay time comparable to the qubit relaxation time, pronounced non-Markovian effects appear in the dynamics of the qubit evolution. We also show how the resonance fluorescence spectrum, including elastic and inelastic scattering (such as the well-known Mollow triplet), can be significantly modified through the interaction between the qubit and feedback loop to show genuine non-Markovian and quantum nonlinear phenomena that cannot be explained with instantaneous coupling parameters. This work presents the first experimental report of Mollow triplets in the non-Markovian regime.

Achieving both broad solar-spectrum absorption and strong redox capability is critical for semiconductor photocatalysts in environmental remediation and energy conversion. Herein, an S-scheme heterojunction photocatalyst is constructed by coupling TiO2(B) nanorods with g-C3N4 nanosheets. Its well-matched band structure extends light absorption from the UV to the visible region and enables efficient charge separation. Under simulated sunlight irradiation, the 40 wt% g-C3N4/TiO2(B) heterojunction delivers a H2 evolution rate of 1.98 mmol g-1 h-1 for water reduction with methanol as the sacrificial agent, which is 1.5 and 2.0 times higher than those of pure g-C3N4 and TiO2(B), respectively. When exposed to amoxicillin wastewater instead of methanol solution, the heterojunction degrades 98.2% of amoxicillin and produces 20.70 umol g-1 of H2 within 90 min. Moreover, the heterojunction shows excellent photodegradation activity toward various organic antibiotics and dyes, owing to the S-scheme charge separation mechanism. This work highlights the promising potential of S-scheme heterojunctions for photocatalytic H2 production coupled with organic wastewater treatment.