Quantum Physics Paper Analysis

Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have recently emerged as a promising route to efficient fault tolerance, current decoding algorithms do not allow one to realize the full potential of these codes in practical settings. Here, we introduce a convolutional neural network decoder that exploits the geometric structure of QEC codes, and use it to probe a novel "waterfall" regime of error suppression, demonstrating that the logical error rates required for large-scale fault-tolerant algorithms are attainable with modest code sizes at current physical error rates, and with latencies within the real-time budgets of several leading hardware platforms. For example, for the $[144, 12, 12]$ Gross code, the decoder achieves logical error rates up to $\sim 17$x below existing decoders - reaching logical error rates $\sim 10^{-10}$ at physical error $p=0.1\%$ - with 3-5 orders of magnitude higher throughput. This decoder also produces well-calibrated confidence estimates that can significantly reduce the time overhead of repeat-until-success protocols. Taken together, these results suggest that the space-time costs associated with fault-tolerant quantum computation may be significantly lower than previously anticipated.

The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic candidate for realizing fault-tolerant quantum computation. Among existing error-correction protocols for GKP code, the Steane-type scheme is a canonical and widely adopted paradigm, yet its intrinsic noise propagation pattern limits further performance improvement. In this work, we propose a preprocessing-based Steane-type (P-Steane) scheme, which introduces a tunable preprocessing stage with squeezing parameters $a$ and $b$ to actively reshape noise propagation, thereby constituting a parameter framework. This framework spans a spectrum of protocols beyond existing methods, reproducing the performance of both the ME-Steane scheme ($a=1$, $b=1$) and the teleportation-based scheme ($a=1/\sqrt{2}$, $b=\sqrt{2}$) as special cases. Crucially, in the small-noise regime and when the data qubit is noisier than the ancilla qubits, P-Steane scheme achieves the minimum product of position- and momentum-quadrature output noise variances when $2a = b$, and consistently outperforms the ME-Steane scheme within a specific squeezing-parameter range under this condition.

Decoding Bivariate Bicycle (BB) quantum error correction codes typically requires Belief Propagation (BP) followed by Ordered Statistics Decoding (OSD) post-processing when BP fails to converge. Whether BP will converge on a given syndrome is currently determined only after running BP to completion. We show that convergence can be predicted in advance by a single modulo operation: if the syndrome defect count is divisible by the code's column weight w, BP converges with high probability (100% at p <= 0.001, degrading to 87% at p = 0.01); otherwise, BP fails with probability >= 90%. The mechanism is structural: each physical data error activates exactly w stabilizers, so a defect count not divisible by w implies the presence of measurement errors outside BP's model space. Validated on five BB codes with column weights w = 2, 3, and 4, mod-w achieves AUC = 0.995 as a convergence classifier at p = 0.001 under phenomenological noise, dominating all other syndrome features (next best: AUC = 0.52). The false positive rate scales empirically as O(p^2.05) (R^2 = 0.98), confirming the analytical bound from Proposition 2. Among BP failures on mod-w = 0 syndromes, 82% contain weight-2 data error clusters, directly confirming the dominant failure mechanism. The prediction is invariant under BP scheduling strategy and decoder variant, including Relay-BP - the strongest known BP enhancement for quantum LDPC codes. These results apply directly to IBM's Gross code [[144, 12, 12]] and Two-Gross code [[288, 12, 18]], targeted for deployment in 2026-2028.

Variational quantum algorithms (VQAs) have established themselves as a central computational paradigm in the Noisy Intermediate-Scale Quantum (NISQ) era. By coupling parameterized quantum circuits (PQCs) with classical optimization, they operate effectively under strict hardware limitations. However, as quantum architectures transition toward early fault-tolerant (EFT) and ultimate fault-tolerant (FT) regimes, the foundational principles and long-term viability of VQAs require systematic reassessment. This review offers an insightful analysis of VQAs and their progression toward the fault-tolerant regime. We deconstruct the core algorithmic framework by examining ansatz design and classical optimization strategies, including cost function formulation, gradient computation, and optimizer selection. Concurrently, we evaluate critical training bottlenecks, notably barren plateaus (BPs), alongside established mitigation strategies. The discussion then explores the EFT phase, detailing how the integration of quantum error mitigation and partial error correction can sustain algorithmic performance. Addressing the FT phase, we analyze the inherent challenges confronting current hybrid VQA models. Furthermore, we synthesize recent VQA applications across diverse domains, including many-body physics, quantum chemistry, machine learning, and mathematical optimization. Ultimately, this review outlines a theoretical roadmap for adapting quantum algorithms to future hardware generations, elucidating how variational principles can be systematically refined to maintain their relevance and efficiency within an error-corrected computational environment.

Programmable neutral-atom arrays offer a promising route toward scalable quantum computing, where coherent qubit transfer enables non-local connectivity and reduces resource overhead. However, transfer speed and motional heating remain key bottlenecks for fast and deep quantum circuits. Here, we employ a fiber array neutral-atom quantum computing architecture with site-resolved control of trap depths to realize smooth amplitude exchange between static and moving traps, thereby enabling fast and coherent qubit transfer with ultralow motional heating. With a 10 $μ$s in situ transfer between static and moving traps, we obtain a per-cycle heating rate of 0.156(9) $μ$K, sustain over 500 cycles with negligible atom loss, and achieve a quantum state fidelity of 0.99992(5) per cycle. For inter-site transfer between two separated static traps, the operation takes 120 $μ$s with 0.783(17) $μ$K heating per transfer, and remains negligible atom loss for up to 100 repeated cycles with a fidelity of 0.9998(1) per transfer. Furthermore, through experimental studies of parallel transfer, we establish a model that elucidates the relationship between array inhomogeneity and the transfer heating rate. This fast, low-heating coherent transfer capability provides a practical route for improving both speed and fidelity in atom-shuttling based quantum computing.

Efficiently simulating many-body quantum systems with Coulomb interactions is a fundamental question in quantum physics, quantum chemistry, and quantum computing, yet it presents unique challenges: the Hamiltonian is an unbounded operator (both kinetic and potential parts are unbounded); its Hilbert space dimension grows exponentially with particle number; and the Coulomb potential is singular, long-ranged, non-smooth, and unbounded, violating the regularity assumptions of many prior state-of-the-art many-body simulation analyses. In this work, we establish rigorous error bounds for Trotter formulas applied to many-body quantum systems with Coulomb interactions. Our first main result shows that for general initial conditions in the domain of the Hamiltonian, second-order Trotter achieves a sharp $1/4$ convergence rate with explicit polynomial dependence of the error prefactor on the particle number. The polynomial dependence on system size suggests that the algorithm remains quantumly efficient, even without introducing any regularization of the Coulomb singularity. Notably, although the result under general conditions constitutes a worst-case bound, this rate has been observed in prior work for the hydrogen ground state, demonstrating its relevance to physically and practically important initial conditions. Our second main result identifies a set of physically meaningful conditions on the initial state under which the convergence rate improves to first and second order. For hydrogenic systems, these conditions are connected to excited states with sufficiently high angular momentum. Our theoretical findings are consistent with prior numerical observations.

We report on a cryogenic platform at 4 K incorporating high numerical aperture optics for the generation of large-scale tweezers arrays, and compatible with Rydberg-state manipulation. We achieve trapping lifetimes of around 5000 s, significantly extending the available experimental time for the preparation of large-scale arrays. By combining two trapping lasers at different wavelengths and by minimizing other atom losses during the rearrangement and imaging processes, we demonstrate the preparation of defect-free arrays with up to 1024 atoms. Our cryogenic design opens exciting prospects for analog and digital quantum computing.

Shor's algorithm outperforms its classical counterpart in efficient prime factorization. We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm, showing that the coherence in each step relies on the dimension of register or the order, and discuss the relations between geometric coherence and geometric entanglement. We investigate how unitary operators induce variations in coherence and entanglement, and analyze the variations of coherence and entanglement within the entire algorithm, demonstrating that the overall effect of Shor's algorithm tends to deplete coherence and produce entanglement. Our research not only deepens the understanding of this algorithm but also provides methodological references for studying resource dynamics in other quantum algorithms.

Magic states play an important role in fault-tolerant quantum computation, and so the quantification of magic for quantum states is of great significance. In this work, we propose two new magic quantifiers by introducing two versions of quantum $(α,β)$ Jensen-Shannon divergence based on the quantum $(α,β)$ entropy and the quantum $(α,β)$-relative entropy, respectively. We derive many desirable properties for our magic quantifiers, and find that they are efficiently computable in low-dimensional Hilbert spaces. We also show that the initial nonstabilizerness in the input state can boost the magic generating power for our magic quantifiers with appropriate parameter ranges for a certain class of quantum gates. Our magic quantifiers may provide new tools for addressing some specific problems in magic resource theory.

Grover's algorithm searches for data satisfying a desired condition in an unstructured database. This algorithm can search a space of size $N$ in $\sqrt{N}$ queries, thereby achieving a quadratic speedup. However, within the Grover oracle circuit that is repeatedly applied, the quantum state preparation circuit -- which embeds database information into quantum states -- suffers from a large gate count and circuit depth. To address this problem, we propose reducing the quantum state preparation circuit by reordering the database. Specifically, we consider a Quantum Read-Only Memory (QROM), where data are assigned to addresses, and assume that the address assignment of data can be freely permuted. By applying Exclusive Sum-of-Products (ESOP) minimization to the resulting truth table, we reduce the quantum circuit. Although the resulting circuit logic differs from the original, the state preparation remains correct in the sense that every desired datum is encoded at some address. Furthermore, we propose a proxy metric that estimates circuit size without compilation, and combine it with simulated annealing to efficiently find a near-optimal data ordering. In our experiments, an exhaustive search over all orderings for databases of size $N=8$ reveals that circuit size varies by up to approximately a factor of two depending on the ordering, demonstrating the utility of reordering. Compared with applying ESOP minimization without reordering, simulated annealing reduces the circuit size by approximately 30\% and yields circuits close to optimal. For $N=64$ and $128$, simulated annealing is shown to discover smaller circuits compared with random search.

Robust continuous-variable (CV) quantum information processing requires correcting realistic errors in bosonic systems, but all existing schemes rely on auxiliary Gottesman-Kitaev-Preskill (GKP) states which the preparation and operation are demanding in many platforms. In this work, we propose a novel CV quantum error correction (QEC) scheme that utilizes a broadly accessible resource: discrete-variable (DV) ancilla. Our scheme extracts information about CV displacement to the DV ancilla, measuring that allows counteracting the unwanted displacement error. We show that a simple single-qubit ancilla can already suppress CV infidelity by more than 20%. By concatenating with DV QEC codes, our scheme is robust against the physical errors in hybrid CV-DV systems, and yields a new class of oscillator-in-oscillator code that does not involve GKP states. Our work facilitates the implementation of CV QEC on realistic platforms.

Is gauge symmetry merely a redundancy in our description, or does it carry a deeper information-theoretic significance? Quantum error-correcting codes (QECCs) show that redundancy can serve as a resource for protecting information against noise. In this work, we ask whether gauge theories can be understood in similar terms, and make this idea concrete in lattice quantum electrodynamics (QED), building on and extending earlier works that established a bridge between gauge systems, stabilizer codes, and quantum reference frames (QRFs). For Abelian gauge groups, we show that explicit recovery operations can be constructed using group-theoretical methods for error sets determined by both ideal and non-ideal QRFs. Applied to lattice QED, this yields two QECC structures: one in the pure-gauge sector and one including fermions. We construct a gauge-field QRF based on spanning trees of the lattice and a fermionic field QRF from the matter field, thereby making explicit how physical information is encoded. While the syndromes of gauge-violating errors associated with constraint measurements are generically degenerate, QRFs resolve this degeneracy and single out families of correctable errors. This establishes lattice QED as a QECC beyond the stabilizer setting and shows concretely how gauge symmetry provides an encoding structure that supports error correction.

We develop a comprehensive framework for constructing quantum error correcting codes (QECCs) from Abelian lattice gauge theories (LGTs) using quantum reference frames (QRFs) as a unifying formalism. We consider LGTs with arbitrary compact Abelian gauge groups supported on lattices in arbitrary numbers of spatial dimensions, and we work with both pure gauge theories and theories with couplings to bosonic and fermionic matter. The codes that we construct fall into two classes: First, Gauss law codes identify the code subspace with the full gauge-invariant sector of the theory. In models with matter coupled to gauge fields, these codes inherit a natural subsystem structure in which gauge-invariant Wilson loops and dressed matter excitations factorize the code space. Second, vacuum codes restrict the code subspace to the matter vacuum sector within the gauge-invariant subspace, yielding codes where errors correspond to gauge-invariant charge excitations rather than to violations of the Gauss law. Despite their distinct setup, we show that when the gauge group is finite, vacuum codes are unitarily equivalent to pure gauge theory Gauss law codes, and that when the group is continuous, this is only true upon a charge coarse-graining of the vacuum code. In all cases, QRFs provide a systematic apparatus for fully characterizing the codes' algebraic structures and correctable error sets. For clarity, we illustrate our general results in $\mathbb{Z}_2$-gauge theory, as well as in scalar and fermionic QED. These findings offer fundamental insights into the parallelism between quantum error correction and gauge theory and point toward practical advantages for simulating LGTs on noisy quantum devices.

Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and impair their error correction capabilities. Although defect adaptive methods for surface codes have been extensively studied, other topological codes such as color codes still lack a systematic framework for handling defects. To address this issue, we propose a universal superstabilizer scheme applicable to data qubit defects in arbitrary stabilizer codes. Based on this scheme, we develop concrete repair methods for isolated defects of both internal data qubits and ancilla qubits in color codes defined on square lattices. Furthermore, for ancilla qubit defects, we present two optimization schemes. One scheme reuses neighboring ancilla qubits, and the other employs iSWAP gates. Unlike conventional approaches that directly disable neighboring data qubits and thus cause resource waste, both of our schemes avoid such waste and consequently achieve a lower logical error rate.Integrating the above techniques, we construct a comprehensive defect adaptive architecture for color codes to handle various defect clusters. We also show that our scheme supports a full transversal Clifford gate set and lattice surgery operations. These results provide a systematic theoretical pathway for deploying robust and low overhead color codes on defective quantum hardware.

Dynamical decoupling is a long-established and effective way to suppress unwanted interactions in qubit systems, enabling advances in fields ranging from quantum metrology to quantum computing. For general qudit systems, however, comparable protocols remain rare, mainly because Hamiltonian engineering in higher dimensions lacks the geometric intuition available for qubits. Here we present a general framework for dynamical decoupling in qudit systems, based on Lie group representation theory. By extending the group theory approach to dynamical decoupling, we show how decoupling groups can be systematically identified among the finite subgroups of SU(d) by analyzing their access to the irreducible components of the operator space. As an application, we construct new pulse sequences for interacting qutrit systems based on finite subgroups of SU(3), and show how subgroup factorizations and group orientations can be exploited to obtain shorter and more experimentally practical protocols for spin-1 systems with large zero-field splitting. We further show that the same symmetry-based framework yields quantum error-correcting codes: whenever a finite subgroup of SU(d) acts as a decoupling group for the relevant error algebra, the associated one-dimensional symmetry sectors define codespaces satisfying the Knill-Laflamme conditions, thereby unifying dynamical decoupling and quantum error correction in multi-level quantum systems.

Consider a rectangular grid of qubits in 2D with single-qubit and nearest-neighbor two-qubit operations subject to local stochastic Pauli noise. At different length scales, this setup describes both a single quantum computing device with geometrically limited connectivity between qubits arranged on a disc, and planar networks composed of quantum repeater stations of constant size. We give a protocol which robustly generates entanglement between distant qubits in this setup. For noise below a constant threshold error strength, it generates a constant-fidelity Bell pair between qubits separated by an arbitrarily large distance $R$. To generate distance-$R$ entanglement, a rectangular grid of qubits of dimensions $Θ(R)\times Θ(\mathsf{poly}(\log R))$ suffices. Our protocol applies quantum operations in one shot, establishing a Bell state in a constant time up to a known Pauli correction. In contrast, existing entanglement generation protocols either require local quantum devices controlling a number of qubits growing with the targeted distance, or are not single-shot, i.e., have a distance-dependent execution time. The protocol leverages many-body entanglement in networks and provides the first example of a short-range entangled state in 2D with long-range localizable entanglement robust to local stochastic Pauli noise. As an immediate corollary, we construct a 2D-local stabilizer Hamiltonian whose Gibbs states possess long-range localizable entanglement at constant positive temperature.

The development of large-scale superconducting quantum computing requires efficient in-situ control methods that allow high-fidelity operations at millikelvin temperatures. Superconducting circuits based on Josephson junctions offer a promising solution due to their high speed, low power dissipation, and cryogenic nature. Here, we report a superconducting quantum controller that enables direct chip-to-chip interconnection with qubits at 10 mK and high-fidelity, all-digital manipulation. Randomized benchmarking reveals a uniformly high average Clifford fidelity of 99.9% with leakage to high energy levels on the order of $10^{-4}$, and an estimated average gate operation energy of 0.121 fJ, demonstrating the potential to resolve the control bottleneck in superconducting quantum computing.

We present a layered and modular network architecture that combines Quantum Key Distribution (QKD) and Post-Quantum Cryptography (PQC) to provide scalable end-to-end security across long distance multi-hop, trusted-node quantum networks. To ensure interoperability and efficient practical deployment, hop-wise tunnels between physically secured nodes are protected by WireGuard with periodically rotated pre-shared keys sourced via the ETSI GS QKD 014 interface. On top, Rosenpass performs a PQC key exchange to establish an end-to-end data channel without modifying deployed QKD devices or network protocols. This dual-layer composition yields post-quantum forward secrecy and authenticity under practical assumptions. We implement the design using open-source components and validate and evaluate it in simulated and lab test-beds. Experiments show uninterrupted operation over multi-hop paths, low resource footprint and fail-safe mechanisms. We further discuss the design's compositional security, wherein the security of each individual component is preserved under their combination and outline migration paths for operators integrating QKD-aware overlays in existing infrastructures.

Quantum phase estimation~(QPE) is central to numerous quantum algorithms, yet its standard implementation demands an $\calO(m^{2})$-gate quantum Fourier transform~(QFT) on $m$ control qubits-a prohibitive overhead on near-term noisy intermediate-scale quantum (NISQ) devices. We introduce the \emph{Phase-Fidelity-Aware Truncated QFT} (PFA-TQFT), a family of approximate QFT circuits parameterised by a truncation depth~$d$ that omits controlled-phase rotations below a hardware-calibrated fidelity threshold~$\eps$. Our central result establishes $\TV(P_{\varphi},P_{\varphi}^{d})\leqπ(m{-}d)/2^{d}$, showing that for $d=\calO(\log m)$ circuit size collapses from $\calO(m^{2})$ to $\calO(m\log m)$ while estimation error grows by at most $\calO(2^{-d})$. We characterise $\dstar=\Floor{\log_{2}(2π/\eps_{2q})}$ directly from native gate fidelities, demonstrating 31.3 -43.7\% at m = 30, gate-count reduction on IBM Eagle/Heron and IonQ~Aria with negligible accuracy loss. Numerical experiments on the transverse-field Ising model confirm all theoretical predictions and reveal a \emph{noise-truncation synergy}: PFA-TQFT outperforms full QFT under NISQ noise $\eps_{2q}\gtrsim 2\times10^{-3}$.

Assembling large-scale, defect-free Rydberg atom arrays is a key technology for neutral-atom quantum computation. Dynamic holographic optical tweezers enable the assembly and reconfiguration of such arrays, but phase mismatches between successive holograms can induce destructive interference and transient trap loss during spatial-light-modulator refresh. In this work, we introduce the weighted-projective Gerchberg--Saxton (WPGS) algorithm, a phase-stable approach to dynamic hologram updates for large-scale Rydberg atom-array reconfiguration. By enforcing inter-frame trap-phase continuity while retaining weighted intensity equalization, WPGS suppresses refresh-induced transient degradation. The phase-difference distribution between consecutive holograms further provides a simple diagnostic of transient robustness. Moreover, enforcing the phase constraint reduces the number of iterations required at each update step, thereby accelerating hologram generation. Numerical simulations of 2D and 3D reconfiguration with more than $10^3$ traps, including multilayer assembly and interlayer transport, show robust transient intensities and significantly faster updates than conventional methods. These results establish inter-frame phase continuity as a practical design principle for dynamic holographic control and scalable neutral-atom array reconfiguration.

Quantum simulation and computing traditionally has been based on two main paradigms, namely, digital and analog. In the digital paradigm, usually single and two-qubit gates (where qubit is an acronym for quantum bit) are employed as building blocks for scalable, universal quantum computing, although errors add up fast and error correction will be ultimately needed for scaling up. In the analog paradigm, large analog blocks are normally employed for a unitary dynamics that carries out the computation, enabling quantum operations on many qubits with reduced errors, but with the drawback of a limited choice of evolutions and lack of universality. In the past decade, a new paradigm has emerged, showing interesting possibilities for quantum simulation and computing in the near and mid term. This is the paradigm of digital-analog quantum technologies, which proposes to combine the best of both paradigms: large analog blocks, provided by native interactions of the employed quantum platform, enabling scalability, combined with digital gates, allowing for more versatility and, ultimately, universality. In this Perspective, I give an overview of the evolution of the field along the past decade, and an outlook for its future possibilities.

We find that reinforcement exponentially reduces computation time of the quantum search problem from $\sqrt{D}$ to $\ln D$ in a $D$-dimensional system. Therefor, a reinforced quantum search is expected to exhibit an exponentially larger noise threshold compared to a standard search algorithm in a noisy environment. We use numerical simulations to characterize the level of noise tolerance via reinforcement in the presence of both coherent and incoherent noise, considering a system of $N$ qubits and a single $D$-level (qudit) system. Our results show that reinforcement significantly enhances the algorithm's success probability and improves the scaling of its computation time with system size. These findings indicate that reinforcement offers a promising strategy for error mitigation, especially when a precise noise model is unavailable.

In superconducting quantum circuits, decoherence improvements are frequently obtained through process interventions that simultaneously modify surface chemistry, microstructural topology, and device geometry, leaving mechanistic attribution structurally underdetermined. Predictive materials engineering requires measurable structural statistics to be separated from geometry-dependent coupling coefficients into independently testable factors. We introduce the concept of classical and quantum microstructure. In that context, we formulate a channel-wise separable framework for decoherence in superconducting transmon qubits in which each loss channel is described by a reduced prescriptor. Here, a channel-specific microstructural state variable is determined independently of device geometry, and a geometry-dependent coupling functional is computable from field solutions without reference to surface chemistry. We derive this product form from a spatially resolved kernel representation and establish a perturbative separability criterion that defines the regime where independent variation of the variables is valid. The framework specifies five prescriptor classes for dominant loss pathways in transmon-class devices. Falsifiability is operationalized through a pre-committed 2x2 experimental protocol in which the variables must satisfy independent ratio checks within propagated uncertainty. A Minimum-Dataset Specification standardizes reporting for cross-laboratory inference. Part I establishes the conceptual and mathematical architecture; coordinated experimental validation is reserved for Part II.

Understanding the mechanisms that limit high-fidelity readout in circuit quantum electrodynamics is essential for its optimization. Multi-photon resonances are understood to be a limiting factor, causing population transfer from the computational states to higher-energy states under drive. This effect, known as measurement-induced state transitions, has been extensively studied for the transmon qubit. While this exploration has begun for the fluxonium qubit, a systematic study of this effect is lacking. Here, we bridge this gap by theoretically studying measurement-induced state transitions in the fluxonium qubit over a wide range of parameters, comprising essentially all experimentally explored ranges. We find that lighter fluxoniums are less susceptible to these state transitions when compared to their heavier counterparts. We attribute this effect to the combination of lower density of multi-photon resonances, a smaller requisite coupling for a given dispersive shift, and a more harmonic-like structure of the charge operator. We confirm the validity of our analysis by performing time-dependent readout simulations. Finally, we consider the impact of the superinductor's array modes on measurement-induced state transitions over a large range of parameters.

Quantum trajectory methods reduce the computational overhead of simulating noisy quantum systems, approximating them with $m$ stochastically sampled $2^n$-entry quantum statevectors rather than exact $2^{2n}$-entry density matrices. Recently, Pre-Trajectory Sampling with Batched Execution (PTSBE) has dramatically increased the data collection rate of these methods. While statevector PTSBE has demonstrated data collection speedups of over $10^6 \times$, tensor network implementations only achieved $\sim 15 \times$ speedup. This comparatively modest tensor network advantage stemmed from 1) contraction path recalculations, 2) sequential tensor network sampling, and 3) inflexible/unoptimized contraction hyperparameters. In this manuscript, we increase PTSBE's tensor network data collection rate to more than $10^8\times$ that of traditional trajectories methods by developing 1) error-independent unified path variation, 2) non-degenerate tensor network sampling, and 3) a flexible/optimized contraction framework. While our methods are particularly powerful for accelerating non-proportional sampling, we also demonstrate a more than $1000\times$ speedup for more general quantum simulations.

Impurity Hamiltonians are systems of $N$ fermionic modes where $O(1)$ of them interact among themselves via quartic (or higher order) fermion terms, while coupling quadratically with $O(N)$ bath modes. Without the quartic interactions, these systems are classically simulable with $O(N^3)$ resources. It was proved that the time-dependent evolution of these systems can perform universal quantum computation. The question of whether or not this remains true for time-independent evolution remains open. Here, we prove that the time evolution of generic time-independent impurity Hamiltonians on $O(N)$ qubits is universal on $N$ qubits if the input state is a product state of fermions in any single particle basis. In our proof we find that for a computation of depth $S$, the size of the impurity scales as $O(S\log S)$.

Quantum reservoir computing is a promising paradigm for processing temporal data. So far, the primary focus has been on univariate time series. However, the most relevant and complex real-world data is multidimensional. In this paper, we establish an extensive framework for multivariate data processing in quantum reservoir computing. We propose and evaluate three multivariate encoding schemes and introduce the mixing capacity as a novel metric to evaluate the effectiveness with which a reservoir combines independent data streams. The computational performance of these proposed schemes is systematically assessed using this metric, as well as on the chaotic Lorenz-63 system prediction task, for two quantum reservoirs based on discrete and continuous-variable quantum systems. Furthermore, we relate the computational performance on these tasks to the underlying quantum properties of the reservoir. Our findings reveal that the optimal encoding method is highly dependent on the reservoir system and the specific task, underlining the importance of a task-specific input design. Moreover, we observe that peak computational performance coincides with the presence of non-classical effects, which indicates that quantum resources play a role in processing multivariate data.

Gibbs states are a natural model of quantum matter at thermal equilibrium. We investigate the role of external fields in shaping the entanglement structure and computational complexity of high-temperature Gibbs states. External fields can induce entanglement in states that are otherwise provably separable, and the crossover scale is $h\asymp β^{-1} \log(1/β)$, where $h$ is an upper bound on any on-site potential and $β$ is the inverse temperature. We introduce a quasi-local Lindbladian that satisfies detailed balance and rapidly mixes to the Gibbs state in $\mathcal{O}(\log(n/ε))$ time, even in the presence of an arbitrary on-site external field. Additionally, we prove that for any $β<1$, there exist local Hamiltonians for which sampling from the computational-basis distribution of the corresponding Gibbs state with a sufficiently large external field is classically hard, under standard complexity-theoretic assumptions. Therefore, high-temperature Gibbs states with external fields are natural physical models that can exhibit entanglement and classical hardness while also admitting efficient quantum Gibbs samplers, making them suitable candidates for quantum advantage via state preparation.

We study the interconversion of families of quantum states ("statistical experiments") via positive, trace-preserving (PTP) maps and clarify its mathematical structure in terms of minimal sufficient Jordan algebras, which can be seen to generalize the Koashi-Imoto decomposition to the PTP setting. In particular, we show that Neyman-Pearson tests generate the minimal sufficient Jordan algebra, and hence also the minimal sufficient *-algebra corresponding to the Koashi-Imoto decomposition. As applications, we show that a) equality in the data-processing inequality for the relative entropy or the $α$-$z$ quantum Rényi divergence implies the existence of a recovery map also in the PTP case and b) that two dichotomies can be interconverted by PTP maps if and only if they can be interconverted by decomposable, trace-preserving maps. We thoroughly review the necessary mathematical background on Jordan algebras. As a step beyond the finite-dimensional case, we also prove Frenkel's formula for approximately finite-dimensional von Neumann algebras.

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for addressing combinatorial optimization problems on near-term quantum hardware. In this work, we conduct an empirical evaluation of QAOA on the Max-Cut problem, using the Goemans-Williamson (GW) algorithm as a classical baseline for comparison. Unlike many prior studies, our methodology treats QAOA implementations as black-box optimizers, relying solely on default parameter settings without manual fine-tuning. We evaluate specific off-the-shelf QAOA implementations under default settings, not the algorithmic potential of QAOA with optimized parameters. This reflects a more realistic use case for end users who may lack the resources or expertise for instance-specific optimization. To facilitate fair and informative evaluation, we construct benchmark instances using well-known graph generation models that emulate practical graph structures, avoiding synthetic constructions tailored to either quantum or classical algorithms. A central component of our analysis is a per-shot statistical framework, which tracks the quality of QAOA outputs as a function of the number of circuit executions. This enables probabilistic comparisons with the GW algorithm by examining when and how frequently QAOA surpasses classical performance baselines such as the GW expectation and lower bound. Our results provide insight into the practical applicability of QAOA for Max-Cut and highlight its current limitations, offering a framework that can guide the assessment and development of future QAOA implementations.

We investigate when temporal ordering becomes operationally meaningful in relativistic quantum field theory using localized detector models. A time parameter alone does not ensure that different sequences of operations are physically distinguishable. We show that distinguishability arises when the state satisfies the Kubo--Martin--Schwinger (KMS) condition and the detector couples through non-commuting observables. We consider uniformly accelerated two-level detectors interacting with a quantum field in the Minkowski vacuum. The restriction of the vacuum to the detector trajectory induces a thermal response characterized by the Unruh temperature and the Tolman profile. For sequential couplings through distinct observables, the reduced detector state depends on the ordering of interactions already at second order, with a dependence controlled by the KMS parameter. This asymmetry is quantified using quantum relative entropy. In a minimal model, the relevant states form a family of non-commuting Gibbs states with identical spectra and different generators, yielding a closed-form expression depending only on the dimensionless combination of temperature and detector energy scale.

We develop a comprehensive analysis of the Kirkwood-Dirac distributions in classical optics, revealing their deep connection with optical coherence as fundamental concept in optics. From their very definition, the Kirkwood-Dirac distributions emerge as generalized mutual coherence functions involving two different bases instead of just one. This perspective provides a unified interpretation of the so-called anomalous values, that are complex and negative values, as direct manifestations of coherence. We show that this interpretation consistently applies across all field variables considered in this work, including polarization, interference and wave propagation. Furthermore, we propose diverse methods of experimental determination of these distributions based on interference, in full agreement with their coherence-based interpretation.

The integration of large language models (LLMs) into scientific research is accelerating the realization of autonomous ``AI Scientists.'' While recent advancements have empowered AI to formulate hypotheses and design experiments, a critical gap remains in the execution of these tasks, particularly in the domain of quantum computing (QC). Executing quantum algorithms requires not only generating code but also managing complex computational resources such as QPUs and high-performance computing (HPC) clusters. In this paper, we propose an AI-driven framework specifically designed to bridge this execution gap through the implementation of a Model Context Protocol (MCP) server. Our system enables an LLM agent to process natural language prompts submitted as part of a job, autonomously executing quantum computing workflows by invoking our tools via the MCP. We demonstrate the framework's capability by performing essential quantum algorithmic primitives, including sampling and computation of expectation values. Key technical contributions include the development of an MCP server for quantum execution, a pipeline for interpreting OpenQASM code, an automated workflow with CUDA-Q for the ABCI-Q hybrid platform, and an asynchronous execution pipeline for remote quantum hardware using the Quantinuum emulator via CUDA-Q. This work validates that AI agents can effectively abstract the complexities of hardware interaction through an MCP-based architecture, thereby facilitating the automation of practical quantum research.

We initiate the study of asynchronous quantum distributed systems, focusing on the case of implementing atomic quantum global operations that can be decomposed into a collection of local operations on the components of the system. A simple example of such an operation is a quantum snapshot in which the whole system is instantaneously measured. Based on the classical snapshot algorithm of Chandy and Lamport, we design a quantum distributed algorithm to implement such decomposable global operations, which we call the QGO Algorithm. The analysis of our algorithm shows that arguments based on Lamport's computational causality remain valid in the quantum world, even though, due to entanglement, causality is not manifest from the standard description of the system in terms of a (global) quantum state. Our other contributions include a formal model of quantum distributed computing, and a formal specification for the desired behavior of a global operation, which may be of interest even in classical settings (such as in the setting of randomized algorithms).

We present a quantum-inspired ARIMA methodology that integrates quantum-assisted lag discovery with \emph{fixed-configuration} variational quantum circuits (VQCs) for parameter estimation and weak-lag refinement. Differencing and candidate lags are identified via swap-test-driven quantum autocorrelation (QACF) and quantum partial autocorrelation (QPACF), with a delayed-matrix construction that aligns quantum projections to time-domain regressors, followed by standard information-criterion parsimony. Given the screened orders $(p,d,q)$, we retain a fixed VQC ansatz, optimizer, and training budget, preventing hyperparameter leakage, and deploy the circuit in two estimation roles: VQC-AR for autoregressive coefficients and VQC-MA for moving-average coefficients. Between screening and estimation, a lightweight VQC weak-lag refinement re-weights or prunes screened AR lags without altering $(p,d,q)$. Across environmental and industrial datasets, we perform rolling-origin evaluations against automated classical ARIMA, reporting out-of-sample mean squared error (MSE), mean absolute percentage error (MAPE), and Diebold--Mariano tests on MSE and MAE. Empirically, the seven quantum contributions -- (1) differencing selection, (2) QACF, (3) QPACF, (4) swap-test primitives with delayed-matrix construction, (5) VQC-AR, (6) VQC weak-lag refinement, and (7) VQC-MA -- collectively reduce meta-optimization overhead and make explicit where quantum effects enter order discovery, lag refinement, and AR/MA parameter estimation.

Quantum communication protocols require efficient detection schemes to maximize the information transfer rate between the sender and the receiver. To this aim, we have demonstrated that weak-field receivers, merging wave-like and particle-like features, can be considered as a valid alternative to already existing receivers, such as optical homodyne detection. To better emphasize the potential of our receiver, in this work we consider a proof of concept for quaternary communication based on coherent states with the same amplitude and different phase values. The encoding in phase requires a fine control of phase noise obtained through a feedback system. The results achieved in terms of mutual information and secret key generation rate encourage further increase of the alphabet towards an approximately continuous phase modulation.

We investigate work extraction in open quantum batteries composed of interacting spin chains weakly coupled to engineered environments. Focusing on two- and four-qubit XX models initially prepared in thermal Gibbs states, we analyze how dissipation and dephasing, acting either locally or collectively, can generate and shape ergotropy during both transient and steady-state dynamics. By introducing a continuous interpolation between parallel and collective noise channels, we systematically characterize the impact of environmental structure on work extractability. We show that purely dissipative dynamics can activate finite ergotropy from completely passive thermal states, giving rise to temperature-dependent transient regimes where hotter initial states temporarily outperform colder ones in an ergotropic Mpemba-like fashion. In contrast, collective dissipation leads to steady states whose passivity crucially depends on the initial temperature and system size, a behavior we trace back to the emergence of non-trivial dark subspaces. Finally, we demonstrate that dephasing channels suppress both transient advantages and steady-state work extraction, highlighting the qualitative difference between dissipative and dephasing environments.

We develop a theoretical description of quantum wave mixing (QWM) in a cascaded waveguide-QED system of two superconducting qubits, where the probe is driven by an external coherent tone and by the resonance fluorescence of a strongly driven source qubit. Starting from the field correlation functions of the source emission, we derive an effective master-equation treatment for the probe and identify the regime in which the incident fluorescence is characterized by anomalous correlations. When the coherent Rayleigh component of the source spectrum is suppressed, the probe equations of motion become equivalent to those for a qubit driven by a coherent tone and broadband squeezed light. This equivalence implies a selection rule for the peaks of the QWM spectrum, with a strong suppression of sidebands associated with processes involving an odd number of photons taken from the source field. Numerical simulations of the full cascaded two-qubit model for different ratios of radiative decay rates unambiguously confirm the participation of correlated photon pairs in QWM processes. The current research illustrates that the analysis of peak amplitudes can be used to probe photon statistics in the incident nonclassical field.

We investigate how to combine a collection of quantum binary models into a multinomial classifier. We employ a hybrid approach, adopting strategies like one-vs-one, one-vs-rest and a binary decision tree. We benchmark each method, by emphasizing their computational overhead and their impact on the quantum advantage. By comparison against a classical binary model (generalized using the same approach), we show that the decision tree represents a cost-effective solution, achieving similar accuracies to other methods with an overhead at most logarithmic in the total number of classes.

We introduce the concept of self-guided imaging (SGI) as a linear analogue of self-guided quantum tomography (SGQT). We show that SGI is mathematically equivalent to single-pixel imaging (SPI). Taking inspiration from orthogonalised ghost imaging, a recent advance in SPI, we introduce orthogonalised SGQT. This requires no additional experimental overhead and leads to faster and more accurate final convergence, as we demonstrate numerically (fidelity $95.2\% \rightarrow 99.17\%$) and experimentally (fidelity $92.1\% \rightarrow 95.3\%$). This work suggests that further routines from SPI and SGQT can be interchanged to optimise measurements and convergence.

We investigate the task of local marking for locally implementable unitary operations. In this setting, multipartite quantum unitary channels, chosen randomly from a known set, are distributed among spatially separated parties without revealing their identities. The objective is to correctly identify (mark) the applied process using only local operations supplemented with classical communication (LOCC). While local distinguishability implies local marking, local marking does not guarantee either local or even global distinguishability of a set of unitaries. Thus the task of marking is not equivalent to the task of discrimination. We demonstrate a stronger manifestation of nonlocality without entanglement by constructing a set of globally distinguishable tripartite product unitaries that cannot be locally marked. In contrast to state marking, we find that marking a subset of product unitaries does not imply the ability to mark a larger subset. Finally, we explore the hierarchy of probes-entangled and product-in the context of local marking with respect to the standard discrimination scenario.

Semi-classical approaches approximate fully quantum descriptions with partially classical ones. Here we use a toy model to highlight the failings of the standard mean-field semi-classical approach, and show how including environmental decoherence can lead to improved semi-classical theories that are exact descriptions of the original quantum dynamics. In doing so, we show how consistent models of classical-quantum dynamics can arise as effective descriptions of open quantum systems.

The dark-state effect, caused by destructive interference, not only is an important fundamental research topic in atomic physics and quantum optics, but also has wide potential application in quantum physics and quantum information science. Using the arrowhead-matrix method, here we study the dark-state effect in a coupled cavity-Rydberg-atom system, in which $N$ Rydberg atoms with the dipole-dipole interactions are coupled to a single-mode cavity field. We obtain the numbers and form of the dark states in certain excitation-number subspaces for the two-, three-, and four-atom cases, as well as in the single-excitation subspace for a general $N$-atom case. We also suggest to characterize the dark states by inspecting the populations of some specific quantum states, which can be detected in experiments. Furthermore, we analyze the dark-state effect in a realistic case, where both the atomic dipole-dipole interaction strengths and the atom-cavity-field coupling strengths depend on the position of the atoms. Our findings pave the way for studying dark-state physics and applications in the cavity-Rydberg-atom platform.

In this note, we show that the well-known leading low-temperature correction to the Heisenberg-Euler Lagrangian in a constant electromagnetic field arising at two loops can be efficiently extracted from its one-loop zero-temperature analogue. Resorting to the real-time formalism of equilibrium quantum field theory that explicitly separates out the zero-temperature contribution from the finite-temperature corrections the determination becomes essentially trivial. In essence, it only requires taking derivatives of the Heisenberg-Euler Lagrangian at one loop and zero temperature for the field strength. As a bonus, we then effectively dress the low-temperature contribution at two loops by one-particle reducible tadpole structures. This generates a subset of higher-loop contributions to the Heisenberg-Euler Lagrangian in the limit of low temperatures. We extract their leading strong-field behavior at a given loop order, and finally resum these to all loop orders.

Ground-state cooling is a prerequisite for exploring macroscopic quantum effects in mechanical motion of massive objects. Here we construct a polarization-angle-controllable coupled cavity-levitated-nanoparticle system in which two nanoparticles trapped by individual tweezers are coupled to a single-mode field in a cavity. We also study the simultaneous ground-state cooling of six mechanical displacement modes of the two levitated nanoparticles through the coherent scattering mechanism. By deriving the Hamiltonian of the system and performing the linearization, we obtain a linearized seven-mode Hamiltonian, which can exhibit the coupling structure and cooling mechanism. We confirm the physical condition for the appearance of dark modes, which will suppress the simultaneous ground-state cooling of these mechanical modes. We also find that, by properly tuning the polarization angle $θ$ between the cavity field and the optical tweezer fields, the coupling channels can be controlled on demand and simultaneous ground-state cooling of these six motional modes of the two nanoparticles can be realized. Our work paves the way for generation and manipulation of collective macroscopic quantum effects in multiple levitated nanoparticles.

We study quantum property testing for directed graphs with maximum in-degree and out-degree bounded by some universal constant $d$. For a proximity parameter $\varepsilon$, we show that any property that can be tested with $O_{\varepsilon,d}(1)$ queries in the classical bidirectional model, where both incoming and outgoing edges are accessible, can also be tested in the quantum unidirectional model, where only outgoing edges are accessible, using $n^{1/2 - Ω_{\varepsilon,d}(1)}$ queries. This yields an almost quadratic quantum speedup over the best known classical algorithms in the unidirectional model. Moreover, we prove that our transformation is almost tight by giving an explicit property $P_\varepsilon$ that is $\varepsilon$-testable within $O_\varepsilon(1)$ classical queries in the bidirectional model, but requires $\widetildeΩ(n^{1/2-f'(\varepsilon)})$ quantum queries in the unidirectional model, where $f'(\varepsilon)$ is a function that approaches $0$ as $\varepsilon$ approaches $0$. As a byproduct, we show that in the unidirectional model, the number of occurrences of any constant-size subgraph $H$ can be approximated up to additive error $δn$ using $o(\sqrt{n})$ quantum queries.

Efficient ground state search is fundamental to advancing combinatorial optimization problems and quantum chemistry. While the Variational Imaginary Time Evolution (VITE) method offers a useful alternative to Variational Quantum Eigensolver (VQE), and Quantum Approximate Optimization Algorithm (QAOA), its implementation on Noisy Intermediate-Scale Quantum (NISQ) devices is severely limited by the gate counts and depth of manually designed ansatz. Here, we present an automated framework for VITE circuit design using Double Deep-Q Networks (DDQN). Our approach treats circuit construction as a multi-objective optimization problem, simultaneously minimizing energy expectation values and optimizing circuit complexity. By introducing adoptive thresholds, we demonstrate significant hardware overhead reductions. In Max-Cut problems, our agent autonomously discovered circuits with approximately 37\% fewer gates and 43\% less depth than standard hardware-efficient ansatz on average. For molecular hydrogen ($H_2$), the DDQN also achieved the Full-CI limit, with maintaining a significantly shallower circuit. These results suggest that deep reinforcement learning can be helpful to find non-intuitive, optimal circuit structures, providing a pathway toward efficient, hardware-aware quantum algorithm design.

Quantum systems are inherently fragile to environmental fluctuations or decoherence, limiting their advantages in applications of quantum information and quantum computation. State purification offers a route to recover the purity of system under noisy conditions. Here, we demonstrate a rapid purification of initially mixed states by harnessing collective reservoir engineering in driven non-Hermitian qubit systems, together with multipartite entanglement generation in larger systems. We show that the onset of efficient purification-assisted entanglement generation is dictated by the degeneracy of collective subradiant modes, rather than by exceptional points. Moreover, the system dynamics manifests an informational Mpemba effect, i.e., a more mixed initial state reaches its steady state with unit purity at a faster rate, resembling the conventional Mpemba effect where a hotter system cools more rapidly. These results reveal a unique advantage of driven non-Hermitian quantum systems with engineered collective dissipation, enabling enhanced purification efficiency and offering new opportunities for quantum engineering.

Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren plateaus, non-variational QKMs employ fixed quantum feature maps, with model selection performed classically via convex optimisation and cross-validation. This separation of quantum feature embedding from classical training ensures stable optimisation while leveraging quantum circuits to encode data in high-dimensional Hilbert spaces. In this review, we provide a thorough analysis of non-variational supervised QKMs, covering their foundations in classical kernel theory, constructions of fidelity and projected quantum kernels, and methods for their estimation in practice. We examine frameworks for assessing quantum advantage, including generalisation bounds and necessary conditions for separation from classical models, and analyse key challenges such as exponential concentration, dequantisation via tensor-network methods, and the spectral properties of kernel integral operators. We further discuss structured problem classes that may enable advantage, and synthesise insights from comparative and hardware studies. Overall, this review aims to clarify the regimes in which QKMs may offer genuine advantages, and to delineate the conceptual, methodological, and technical obstacles that must be overcome for practical quantum-enhanced learning.

We propose and analyse a quantum thermal field-effect transistor (qtFET) composed of left-qubit, middle-qutrit, and right-qubit subsystems. In this architecture, the left qubit is coupled to the middle qutrit, which in turn interacts with the right qubit. Each subsystem interacts independently with its respective baths. The middle subsystem serves as a modulator. We have shown that the qtFET exhibits functionality analogous to that of a conventional electronic field-effect transistor (eFET). The left, right, and middle subsystems of the qtFET correspond to the drain, source, and gate of an eFET in a common gate configuration, respectively. Our results show that the qtFET can precisely modulate thermal currents, highlighting its potential as a fundamental building block for quantum thermal devices and amplifiers in emerging quantum technologies.

Clustering is one of the most fundamental tasks in machine learning, and the k-means clustering algorithm is perhaps one of the most widely used clustering algorithms. However, it suffers from several limitations, such as sensitivity to centroid initialization, difficulty capturing non-linear structure, and poor performance in high-dimensional spaces. Recent work has proposed improved initialization strategies and quantum-assisted distance computation, but the similarity metric itself has largely remained classical. In this study, we propose a quantum-enhanced variant of k-means that replaces the Euclidean distance with a quantum kernel derived from the inner product between feature-mapped quantum states. Using the Iris dataset, we use multiple quantum feature maps, including entangled SU2 and ZZ circuits, to embed classical data into a higher-dimensional Hilbert space where cluster structures become more separable. We will also be testing using another dataset, namely the breast cancer dataset. Similarity between data points is computed through the inner product between two states. Our results show that this approach achieves improved clustering stability and competitive accuracy compared to the classical algorithm, with the SU2 feature map yielding an accuracy of 88.6 % on the Iris dataset and 91.0 % on the breast cancer dataset, despite operating on NISQ-feasible shallow circuits. These findings suggest that quantum kernels provide a richer similarity landscape than traditional distance metrics, offering a promising path toward more robust unsupervised learning in the NISQ era.

Deploying quantum machine learning algorithms on near-term quantum hardware requires circuits that respect device-specific gate sets, connectivity constraints, and noise characteristics. We present a hardware-aware Neural Architecture Search (NAS) approach for designing quantum feature maps that are natively executable on IBM quantum processors without transpilation overhead. Using genetic algorithms to evolve circuit architectures constrained to IBM Torino native gates (ECR, RZ, SX, X), we demonstrate that automated architecture search can discover quantum Support Vector Machine (QSVM) feature maps achieving competitive performance while guaranteeing hardware compatibility. Evaluated on the UCI Breast Cancer Wisconsin dataset, our hardware-aware NAS discovers a 12-gate circuit using exclusively IBM native gates (6 ECR, 3 SX, 3 RZ) that achieves 91.23 % accuracy on 10 qubits-matching unconstrained gate search while requiring zero transpilation. This represents a 27 percentage point improvement over hand-crafted quantum feature maps (64 % accuracy) and approaches the classical RBF SVM baseline (93 %). We show that removing architectural constraints (fixed RZ placement) within hardware-aware search yields 3.5 percentage point gains, and that 100 % native gate usage eliminates decomposition errors that plague universal gate compilations. Our work demonstrates that hardware-aware NAS makes quantum kernel methods practically deployable on current noisy intermediate-scale quantum (NISQ) devices, with circuit architectures ready for immediate execution without modification.

Noise is a major challenge in quantum computing, affecting the reliability of quantum protocols. In this work, we analytically study the impact of various noise processes, such as depolarization, bit flip, and phase flip, on the quantum state teleportation protocol. Each noise process is modeled as a quantum channel and is applied individually to all qubits after the corresponding unitary operations to simulate realistic conditions. We evaluate the fidelity between the ideal and noisy teleported states to quantify the effect of noise. Our analysis shows that the fidelity decreases polynomially, in general, as the noise strength increases for all noise types, highlighting the sensitivity of state teleportation to different noise mechanisms. However, in the low noise regime, the fidelity decreases only linearly, indicating the robustness of the teleportation protocol. These results provide insight into error characterization and can inform strategies for noise mitigation in practical quantum computing applications.

We revisit the longstanding issue of why no well defined probability measure exists corresponding to a classical (Kolmogorov) path integral representation of the Dirac equation in Minkowski space. Two complementary perspectives are compared: (i) Zastawniak's observation that the distributional character of the Dirac propagator (presence of derivatives of the delta distribution) obstructs the construction of a nonnegative transition kernel, and (ii) the indefinite signature of the Minkowski metric which prevents positivity of the action and yields oscillatory integrals. We show how these viewpoints can be unified as different manifestations of a single mathematical obstruction from measure theoretical point of view, and we discuss consequences for stochastic representations of relativistic first-order equations.

Phase estimation in quantum interferometry is a major scenario where the quantum advantage is significantly revealed. Recently, the optimal finite-dimensional probe states (OFPSs) for phase estimation in two-mode quantum interferometry have been provided with the absence of noise [J.-F. Qin et al., Phys. Rev. A 112, 052428 (2025)]. However, the noise is inevitable in practice and the previously obtained OFPSs may cease to be optimal anymore. Hence, the forms of the true OFPSs in the existence of various noises are still open questions. Hereby, the noise of particle loss is studied and the true OFPSs under this noise have been investigated with the numerical algorithm named constrained optimization by linear approximation. Furthermore, a two-step measurement strategy is proposed to realize the ultimate precision limit in practice. The validity of this strategy is confirmed by the numerical simulation of practical experiments.

Continuous-variable (CV) cluster states offer a promising platform for large-scale measurement-based quantum computations (MBQC). However, finite squeezing inevitably introduces Gaussian noise during MBQC. While fault-tolerant MBQC schemes exist in principle, they require the scalable incorporation of non-Gaussian resources, such as GKP states, which remain experimentally challenging. Consequently, a central question at this stage is how finite squeezing fundamentally constrains the intrinsic computational power of CV cluster states themselves. In this work, we address this question by analyzing the classical complexity of measurement-based linear optics (MBLO) implemented with such states, motivated by its near-term feasibility and recent experimental progress. We develop an explicit MBLO framework and examine how the squeezing level governs the complexity of the classical simulation of the resulting output states. Specifically, we identify squeezing-level thresholds that delineate classically tractable and intractable regimes, thereby revealing a squeezing-driven complexity phase transition. These findings advance our understanding of the squeezing resources necessary for meaningful quantum computation in current experimental regimes. Furthermore, they underscore the critical need to either scale the squeezing level or integrate error-correction schemes to achieve reliable, large-scale quantum computation with CV cluster states.

Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum chromodynamics, in which the optic theorem and the renormalization group equation can be solved by a unique contour integral written in two different "dual" ways related between themselves by a complex map in the complex plane of Mellin variable. The inverse integral transformation should be modified to be applied for these contour integral solutions. These modified inverse transformations may be used in security protocols for quantum computers. Here we do a brief review of the basic integral transforms and propose their modification for the extended domains.

Ghost imaging was first demonstrated with entangled photon pairs and well-known for its peculiar properties. The signal beam that illuminates the object possesses no spatial resolution, whereas the reference beam, which never interacts with the object, is spatially resolved. Either beam alone cannot retrieve the image, which can only be obtained when the signal and reference beams are correlated. Here we will report a ghost imaging experiment with even more peculiar properties, in which the image can be reconstructed when no photon interacts with the object or even no photon in neither signal nor reference beam. All the photons interacted with the object are discarded. Only the time bins with zero photon are employed to retrieve the image, a process referred to as "ghost imaging with zero photons" hereafter. The reason why ghost image can be retrieved with zero photons is jointly determined by photon-number projection measurement and photon statistics of thermal light. The results are helpful to resolve the debate on the physics of ghost imaging and understand the relation between quantum and classical correlations.

We investigate the critical behavior of momentum-space entanglement entropy at dynamical quantum phase transitions (DQPTs) in translationally invariant two-band insulators and superconductors. By analyzing the Su-Schrieffer-Heeger model, the quantum XY chain, and the Haldane model, we establish that the geometric DQPT condition $\hat{\textbf{d}}_{\textbf{k}}^{i} \cdot \hat{\textbf{d}}_{\textbf{k}}^{f} = 0$ manifests as exact degeneracy $p_{\textbf{k}^{*}}=1/2$ in the entanglement spectrum defined with respect to the post-quench eigenbasis, yielding a maximal momentum-space entropy of $\ln 2$. In one dimension, critical momenta appear as isolated points, whereas in two dimensions they form continuous one-dimensional manifolds, reflecting the dimensional dependence of the underlying critical structure. Importantly, alternative bipartitions such as the sublattice basis produce qualitatively different behavior: the entropy becomes explicitly time-dependent and attains a minimum at DQPT critical times, underscoring the essential role of basis selection. Our results establish that momentum-space entanglement entropy, when evaluated in the appropriate eigenbasis, provides a robust, time-independent diagnostic of DQPTs and offers a unified geometric perspective linking entanglement, topology, and non-equilibrium criticality.

Precise environmental-noise characterisation in open quantum systems is a key step toward high-fidelity quantum control and targeted decoherence suppression in computing and sensing applications. Non-parametric quantum noise spectroscopy (QNS) provides a general-purpose, model-agnostic framework for estimating the spectral properties of an environment. The ability to perform such protocols under realistic constraints is key to their practical applicability. Notably, it is important to account for control constraints and understand how they limit the ability to learn about noise correlations as experiment-agnostic objects. We show how adopting a control-centric point of view allows one to recast the noise spectroscopy problem in such a way that (i) the central objects are now the time-ordered polyspectra, (ii) control filter functions are no longer encumbered by time-ordering. In particular, we show that this approach enables the seamless generalisation of frequency-comb QNS protocols to arbitrary control scenarios without introducing additional control symmetries that effectively remove time-ordering from filter functions, improving estimation in typically pathological scenarios. We demonstrate the targeted reconstruction of the time-ordered polyspectra across classical Gaussian and quantum non-Gaussian environments via simulations.

Entanglement criteria based on variances or Fisher information are well developed for compact collective spin algebras, but their extension to non-compact dynamical sectors is less straightforward. In particular, double-quantum (DQ) observables associated with effective SU(1,1) structures can lead to formally unbounded classical fluctuation estimates unless additional physical constraints are imposed. In this note, we develop a thermodynamic witness framework in which the classically accessible fluctuation sector is strictly bounded by finite-temperature detailed-balance conditions and motionally narrowed sequence-transfer limits. By analyzing the quantum dynamical semigroup of the spin-bath interaction, we demonstrate that spontaneous transient pair correlations generated by a stationary incoherent bath are contractively capped near an amplitude of \(10^{-9}\). Furthermore, classical coherent sequence amplification is empirically bounded to \(\mathcal{O}(10^{-2})\) in motionally narrowed tissue. The resulting functional provides a concrete, theoretically derived bounding framework against which macroscopic DQ anomalies (e.g., fractional amplitudes on the order of \(10\%\) to \(15\%\)) can be rigorously classified as classically inexplicable, provided macro-scale structural stability (constant \(T_2^*\)) is empirically verified.

Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale classification and dimension reduction on massive classical data by processing samples on the fly, whereas any classical machine achieving the same prediction performance requires exponentially larger size. Furthermore, classical machines that are exponentially larger yet below the required size need superpolynomially more samples and time. We validate these quantum advantages in real-world applications, including single-cell RNA sequencing and movie review sentiment analysis, demonstrating four to six orders of magnitude reduction in size with fewer than 60 logical qubits. These quantum advantages are enabled by quantum oracle sketching, an algorithm for accessing the classical world in quantum superposition using only random classical data samples. Combined with classical shadows, our algorithm circumvents the data loading and readout bottleneck to construct succinct classical models from massive classical data, a task provably impossible for any classical machine that is not exponentially larger than the quantum machine. These quantum advantages persist even when classical machines are granted unlimited time or if BPP=BQP, and rely only on the correctness of quantum mechanics. Together, our results establish machine learning on classical data as a broad and natural domain of quantum advantage and a fundamental test of quantum mechanics at the complexity frontier.

We analyze fermionic entanglement and correlation measures in the ground and the low temperature thermal state of the water molecule as a function of the internuclear distance in the context of the full configuration interaction approach. The aim is to obtain a general entanglement based characterization of the electronic eigenstates. We consider first the spin-up - spin-down partition and the associated Schmidt decomposition, examining the total up-down entanglement of the electronic wave function. We then consider the one- and two-body entanglement derived from the one- and two-body reduced density matrices (DMs), which measure both the deviation of the state from a Slater Determinant (SD) as well as the up-down correlation at the two-body level. All blocks of these DMs are examined. We also introduce and analyze new measures like the up-down two-body mutual information and two types of two-body negativities, the latter measuring the "inner" entanglement of the reduced two-body DMs, i.e., their deviation from a convex mixture of SDs. Finally, the dissociation limit is also analyzed, considering both the exact ground state (GS) as well as the thermal state in the zero temperature limit, representing the projector onto the "GS band" of almost degenerate lowest lying eigenstates.

Dynamic control of visible light is crucial for technologies such as holographic displays and adaptive optics. Passive metasurfaces can shape wavefronts at the subwavelength scale and active metasurfaces promise to extend this functionality into the temporal domain. However, existing metasurfaces for dynamic phase manipulation typically cannot deliver phase modulation across a broad range without causing variations in the scattering amplitude. Here, we use an inverse-design pipeline to numerically demonstrate a hybrid-2D excitonic metasurface platform offering independent amplitude and phase control in the visible regime. Harnessing the gate-tunable excitonic response of monolayer WS2 retrieved from experiments, we design a pi-phase modulator with a uniform amplitude profile. Adding a second tunable monolayer, we achieve independent control of the amplitude and phase over the full 0-2pi phase range, which we leverage for a reconfigurable beam-steering metadevice. Our results demonstrate how hybrid-2D excitonic metasurfaces enable electrically tunable wavefront shaping in the visible regime.

A foundational result in relativistic quantum information theory due to Peres, Scudo, and Terno, is that von Neumann entropy is not Lorentz invariant. Motivated by the "It from Qubit" paradigm, here we show that Lorentzian symmetries of quantum information emerge naturally in a pre-spacetime setting, without any reference to external variables such as position or momentum. In particular, we derive the natural action of the restricted Lorentz group $\text{SO}^+(1,3)$ on the internal degrees of freedom of a single qubit from a simple, information-theoretic principle we refer to as preservation of linear entropy. It is then shown that the Lorentz invariance of the linear entropy of a relativistic qubit is a special case of a much more general phenomenon, namely, that any spectral invariant of an operator we term the '$W$-matrix' is an $\text{SL}(2,\mathbb C)^{\otimes n}$ invariant scalar. Consequently, the linear $n$-partite quantum mutual information is shown to be an $\text{SL}(2,\mathbb C)^{\otimes n}$ invariant for all $n$-qubit states. Finally, we show that the correlation function associated with a pair of qubits in the singlet state yields the Minkowski metric on the space of qubit observables, whose symmetry group is the full Lorentz group $\text{SO}(1,3)$. In accordance with the "It from Qubit" paradigm, our results thus establish the natural emergence of relativistic spacetime structure from intrinsic properties of quantum information.

In this work, we consider the fundamental task of quantum state certification: given copies of an unknown quantum state $ρ$, test whether it matches some target state $σ$ or is $ε$-far from it. For certifying $d$-dimensional states, $Θ(d/ε^2)$ copies of $ρ$ are known to be necessary and sufficient. However, the algorithm achieving this complexity makes fully entangled measurements over all $O(d/ε^2)$ copies of $ρ$. Often, one is interested in certifying states to a high precision; this makes such joint measurements intractable even for low-dimensional states. Thus, we study whether one can obtain optimal rates for quantum state certification and related testing problems while only performing measurements on $t$ copies at once, for some $1 < t \ll d/ε^2$. While it is well-understood how to use intermediate entanglement to achieve optimal quantum state learning, the only protocol known to achieve optimal testing is the one using fully entangled measurements. Our main result is a smooth copy complexity upper bound for state certification as a function of $t$, which achieves a near-optimal rate at $t = d^2$. In the high-precision regime, i.e., for $ε< \frac{1}{\sqrt{d}}$, this is a strict improvement over the entanglement used by the aforementioned optimal protocol. We also extend our techniques to develop new algorithms for the related tasks of mixedness testing and purity estimation, and show tradeoffs achieving the optimal rates for these problems at $t = d^2$ as well. Our algorithms are based on novel reductions from testing to learning and leverage recent advances in quantum state tomography in a non-black-box fashion. We complement our upper bounds with smooth lower bounds that imply joint measurements on $t \geq d^{Ω(1)}$ copies are necessary to achieve optimal rates for certification in the high-precision regime.

In dense neutrino gases, which exist for instance in supernovae, the flavour states of different neutrinos may become entangled with one another. The theoretical description of such systems may therefore call for simulations on a quantum computer. Existing quantum simulations of simple toy systems are not optimal in the sense that they do not fully exploit the symmetries of the system. Here, we propose a new class of qubit-efficient algorithms based on Dicke states and the $su(2)$ spin algebra. We demonstrate the excellent performance of these algorithms both on classical and on quantum hardware.

Reservoir engineering has emerged as a powerful paradigm to realize non-reciprocal dynamics in open quantum many-body systems. Here, we show that density-density interactions can transfer bath-induced non-reciprocity between different degrees of freedom. Specifically, we investigate a one-dimensional lattice of spin-$\frac{1}{2}$ fermions with all-to-all Hatsugai-Kohmoto interactions in the presence of an engineered reservoir. We establish the exact solvability of the Lindbladian dynamics and show that the interplay between non-reciprocity and interactions qualitatively reshapes the dynamics of excitations. Remarkably, interactions induce directional drift even in spin sectors that are not directly coupled to the reservoir. By analyzing a driven-dissipative Fermi-Hubbard chain, we show that the same mechanism persists for local interactions. The Hatsugai-Kohmoto model thus emerges as a minimal, exactly solvable platform for interaction-mediated non-reciprocal many-body dynamics.

The design of polarization-encoded quantum interfaces relies on the assumption that solid-state emitters possess static transition dipoles defined by the host lattice symmetry. Here, we demonstrate the vibronic breakdown of this static dipole approximation in hexagonal boron nitride quantum emitters. Through high-resolution energy-resolved spectroscopy, we reveal a continuous, spectral rotation of the emission dipole orientation reaching up to 40$^{\circ}$, driven by coupling to the phonon bath. This spectral gradient is significantly suppressed at cryogenic temperatures (6 K), identifying thermally activated lattice vibrations as the primary driver of the dipole reorientation. First-principles calculations on two representative defect types indicate the microscopic origin of this phenomenon as a coordinate-dependent transition dipole, where phonon-induced atomic displacements fundamentally perturb the electronic wavefunctions. By comparing the distinct defect environments, we demonstrate that the magnitude of the polarization rotation scales with the strength of the vibronic coupling. Our results not only identify a fundamental limit for polarization fidelity in solid-state quantum networks but also suggest a new class of strain-tunable quantum photonic devices based on vibronic dipole reorientation.

We take the first steps to address via integrability the spectral problem of AdS/CFT dual pairs deformed by Groenewold-Moyal twists. In particular, we start by considering a twisted spin-chain that couples, through a Groenewold-Moyal twist deformation, two $\mathfrak{sl}(2)$-invariant spin-chains. We interpret this deformed spin-chain as a deformation of a subsector of the $AdS_3/CFT_2$ spin-chain, but the construction shares qualitative features also with the corresponding deformation of the $AdS_5/CFT_4$ spin-chain, for example. As in similar types of deformations, we show that there exists a certain basis in which the spin-chain Hamiltonian takes a Jordan-block form. At the same time, by working in the basis of eigenstates of the generators used to construct the Groenewold-Moyal twist, the Hamiltonian appears to be diagonalisable and with a deformed spectrum. Employing the method of the Baxter equation, we write down the energy of the ground state and of excited states in a perturbation of the deformation parameter. We then consider the string-theory side of the duality, where the twist is realised as a deformation of AdS of the type of Maldacena-Russo-Hashimoto-Itzhaki. We construct a deformation of the usual BMN classical solution, and in the large-$J$ limit we match the leading $\mathcal O(J^{-3})$ term of the energy of the spin-chain groundstate with a conserved charge of the string classical solution. Differently from the undeformed setup as well as similar kinds of deformations, we find that the general expression of this charge of the string sigma-model is non-local, and that it does not correspond to a standard isometry. Nevertheless, it can be computed from the monodromy matrix and it is part of the tower of conserved charges provided by integrability.

We extend the SeQUeNCe discrete-event simulator with physics-based models for polarization-encoded photonic quantum networks. Our framework integrates Jones-calculus optical components, including an SPDC Bell-state source, wave plates, and polarizing beam splitters, together with a multi-section fiber model capturing polarization mode dispersion, chromatic dispersion, and Raman noise from coexisting classical traffic. We validate the simulator by reproducing experimentally reported spectra, polarization correlations, quantum state tomography, and dispersion- and Raman-induced noise. The resulting platform enables hardware-parameterized prediction of entanglement distribution performance under realistic deployment conditions.

The open inner-shell electronic structure of lanthanides with large magnetic moments gives rise to a rich spectrum of transitions available for laser cooling, trapping, and coherent control. Despite this, the large number of ultraviolet (UV) transitions below 400nm have so far been rarely utilized in dipolar atom experiments. Here, we investigate multiple UV ground state transitions in dysprosium. Several of these UV excited states have the largest decay strengths to the ultralong-lived, low-lying first excited state which are comparable to the most commonly used strongest transitions found in dipolar atoms. Using two-dimensional shelving spectroscopy which improves detection sensitivity and provides a straightforward way to determine the hyperfine-isotope structure and excited state total angular momentum $J$, we measure isotope shifts, hyperfine coefficients, and create King plots to determine their electronic nature. Such knowledge of these UV transitions which analogously exist in other magnetic atoms is important for optically populating the first excited state and can be used towards creating an optical clock, high resolution imaging in quantum gas microscopy, and probing lanthanide nuclei with enhanced Schiff moments in search of physics beyond the standard model.

Quantum-state texture is a recently proposed quantum resource that characterizes the inhomogeneity of a quantum state's matrix element distribution in the computational basis, enriching our understanding of quantum state structure. To expand its quantification toolkit and establish detection methods, in this article, we investigate the resource theory of texture from both quantitative and detection perspectives. First, we construct a texture measure $\mathcal{T}^{\text{GR}}_{α,z}(ρ)$ based on the $α$-$z$ Rényi relative entropy and present some of its inherent properties. Second, we analyze the mathematical relationships between several existing texture measures, revealing connections among different quantifiers. Finally, drawing on the witness concept from other resource theories, we systematically introduce texture witnesses into the texture theory and provide examples of texture witnesses with special properties.

The deterministic generation and SWAP of Fock states in isolated high-Q modes form a core foundation for architectures in bosonic quantum computing. Conventionally, these operations necessitate strong coupling to a qubit, which inherently compromises the required cavity isolation. To address this trade-off, we introduce a tunable mechanism wherein a weakly coupled qubit, which preserves mode isolation, is driven to induce a strong interaction on demand. By leveraging a Rabi-driven, qubit-mediated sideband interaction, we realize on-demand Jaynes-Cummings coupling between a transmon and a long-lived cavity mode. Using a superconducting flute cavity with two high-Q modes, we deterministically demonstrate Fock state preparation up to n=5 at operation times of less than 2 microseconds per photon. We also demonstrate and characterize single-photon SWAP in approximately 2 microseconds. Finally, we adapt our SWAP method to generate a dual-rail Bell state. While current performance is constrained by baseline coherence rather than fundamental methodological limits, the protocol scales inherently to accommodate higher photon numbers and faster operational regimes. By enabling complex operations on modes that remain strictly weakly coupled to qubits, this approach establishes a robust pathway for advancing scalable bosonic quantum computing.

The Quantum Approximate Optimization Algorithm (QAOA) is a leading framework for quantum combinatorial optimization. The Vehicle Routing Problem (VRP), a core problem in logistics and transportation, is a natural application target, but it poses a major feasibility challenge for standard QAOA because feasible solutions occupy only a tiny fraction of the search space, and the conventional Pauli-$X$ mixer can disrupt partial solution structures that satisfy key local constraints. To address this issue, we propose a constraint-aware QAOA framework with two complementary components. First, we design a lightweight initialization strategy that encodes a selected subset of simple yet informative local one-hot constraints into the initial state, thereby reducing the initial superposition space and increasing the probability mass on states with important local structure. Second, we introduce a hybrid XY-$X$ mixer that preserves the constraint structure imposed at initialization while retaining exploratory flexibility over the remaining unconstrained degrees of freedom during QAOA evolution. We evaluate the proposed framework against standard QAOA under three progressively more realistic regimes: ideal statevector simulation, finite-shot sampling, and noisy finite-shot sampling. Across all regimes, the proposed method consistently achieves lower average energy and higher feasible-solution ratios than standard QAOA, indicating more effective guidance toward structurally valid, lower-cost VRP solutions. However, the performance gap narrows in the noisy regime. Because this setting adopts a hardware-inspired error model based on near-best-reported laboratory-level qubit gate and readout fidelities, the observed attenuation suggests that the practical advantage of the more structured mixer is likely to grow as quantum hardware improves and error rates decline.

Gibbs state preparation is an important subroutine in quantum computing. In this work we use the detectability lemma to improve Gibbs state preparation. Specifically, we design new Gibbs state preparation methods that do not rely on simulating Lindbladian evolution, thus avoiding the overhead from it. For local Lindbladians consisting of $M$ terms, this approach reduces the cost by a factor of $O(M)$. We also combine the detectability lemma operator and quantum singular value transformation to implement ground state projection operators of frustration-free Hamiltonians, resulting in a quadratic speedup in the spectral gap dependence. Applying this method to Lindbladians for the Gibbs state of local commuting Hamiltonians, we achieve quadratically better dependence on the Lindbladian spectral gap.

The computational complexity of $\mathsf{QAC}^0$, which are constant-depth, polynomial-size quantum circuit families consisting of arbitrary single-qubit unitaries and $n$-qubit generalized Toffoli gates, has gained tremendous focus recently. In this work, we initiate the study of the computational complexity of geometrically local $\mathsf{QAC}^0$ circuits, where all the generalized Toffoli gates act on nearest neighbor qubits. We show that any $\mathsf{QAC}^0$ circuit can be exactly simulated by a two-dimensional geometrically local $\mathsf{QAC}^0$ circuit, i.e., a $\mathsf{2D\text{-}QAC}^{0}$ circuit, with a quadratic size blow-up. This implies that $\mathsf{QAC}^0 = \mathsf{2D\text{-}QAC}^{0}$. We further show that if there existed a $\mathsf{QAC}^0$ circuit that computes Parity with a bounded constant error, then for any $\varepsilon > 0$, there would exist a $\mathsf{2D\text{-}QAC}^{0}$ circuit that exactly computes Parity, with a very "thin" width $n^\varepsilon$. We further study the computational power of $\mathsf{1D\text{-}QAC}^{0} $ circuits, i.e., one-dimensional $\mathsf{QAC}^0$ circuits, which are the "thinnest" $\mathsf{2D\text{-}QAC}^{0}$ circuits. We prove a nearly logarithmic depth lower bound on $\mathsf{1D\text{-}QAC}^{0} $ circuits to compute the Parity function, even if allowing an unlimited number of ancilla. Furthermore, if the inputs are encoded in contiguous qubits, we prove that it requires a nearly linear depth $\mathsf{1D\text{-}QAC}^{0} $ circuit to compute the Parity function. This lower bound is almost tight. The results are proved via the combination of the restriction argument and the light-cone argument. These results may provide a new angle for studying the computational power of $\mathsf{QAC}^0$ circuits and for resolving the long-standing open problem of whether Parity is in $\mathsf{QAC}^0$.

Implementing high-fidelity controlled two-qubit gates in dipole-dipole interacting systems, such as rare-earth-ion crystals, in hindered by spectral inhomogeneity and weak coupling. Existing method often rely on detuned pulses, making them susceptible to frequency errors and AC Stark shifts. We propose a robust resonant scheme for arbitrary controlled two-qubit gates that utilizes asymmetric excitation and pulse engineering to achieve decoupled, parallel qubit control. Simulations on rare-earth-ion ensemble qubits demonstrate gate fidelities exceeding 99% within a 170 kHz detuning range with off-resonant excitation below 0.2%. This approach offers a robust, scalable route for quantum computing in spectrally crowded systems.

Grouping-based measurement strategies are widely used to reduce measurement complexity in near-term quantum algorithms. While these schemes have typically produced disjoint groups, recently this has been relaxed in what is known as overlapped grouping or coefficient splitting where operators may appear in more than one compatible group. In recent work, it has been numerically shown that this strategy can reduce the variance of energy estimates on small benchmark problems, motivating both the application and further analysis of the method. Here we prove that overlapped grouping for energy estimation can lead to a maximal variance reduction that is linear in the number of Hamiltonian terms. We introduce a new algorithm which we call repacking to transform existing groups into overlapped groups, and we show this repacking procedure iteratively reduces variance under mild assumptions. We also perform numerical simulations with Hamiltonians up to $44$ qubits and $575 \cdot 10^{3}$ terms, assessing overlapped grouping at scale on problems of practical importance. Our numerics show that the variance reduction relative to state-of-the-art (disjoint) grouping increases linearly with the problem size, suggesting that overlapped grouping methods can be a powerful strategy for quantum energy estimation at the scale of Megaquop computers and beyond.

We demonstrate the experimental realization of two-dimensional, continuous variable (CV) cluster states between 191 microwave frequency modes. This result is obtained by exposing vacuum fluctuations to the input of a Josephson Parametric Amplifier, parametrically pumped by a sum of coherent tones around twice its resonant frequency. By carefully tuning pump frequencies, amplitudes, and phases we engineer the interference between mixing products and realize honeycomb and square lattice CV cluster states with three and four pump tones respectively. We prove the presence of the cluster states with a suitable nullifier test, reaching up to $-1.2$ dB of squeezing of the cluster state's nullifiers. We study hidden entanglement (HE) and show no hidden entanglement up to $\sim -1$ dB of squeezing and negligible HE at optimal squeezing.

The Holevo limit bounds the channel capacity of a communication channel in which information is encoded in quantum states in a Hilbert space at the transmitter and decoded using quantum measurements at the receiver. Saturating the Holevo limit requires quantum-limited transceivers that either generate quantum states of light or employ quantum-limited measurements. Here, we demonstrate an integrated photonic-electronic quantum-limited coherent receiver (QRX) achieving 14.0 dB shot noise clearance (SNC), 520 $μ$W knee power, 2.57 GHz 3-dB bandwidth, 3.50 GHz shot-noise-limited bandwidth, and 90.2 dB common-mode rejection ratio ($\mathrm{CMRR}$). We scale this design to a 32-channel QRX array with median 26.6 dB $\mathrm{SNC}$, and automatic $\mathrm{CMRR}$ correction yielding a median 76.8 dB $\mathrm{CMRR}$ at minimum. Using the integrated QRX and fiber-optic transmitter, we measure $0.15\pm0.01$ dB of squeezing below the shot noise limit, limited by off-chip losses. We propose a squeezed light communication scheme that can surpass the Shannon limit, with a path toward the Holevo limit.

The study of stronger-than-quantum phenomena (i.e., postquantum) has enabled a deeper understanding of the scope of quantum theory. Much is known about the case of correlations in Bell scenarios, where the device-independent framework allowed us to explore its possibilities independently of the formalism of quantum theory. However, less is known about the phenomenon of Einstein-Podolsky-Rosen steering. Here, the `characterised parties' are assumed to describe their systems locally through the quantum formalism, which inconveniences a theory-independent description. In addition, a theorem by Gisin and Hughston, Josza and Wootters further hindered the discovery of the phenomenon. The study of postquantum steering, initiated about a decade ago, has been quite fruitful, including: the development of mathematical formalisms that frame the effect, resource theories that quantify it as a resource, and activation protocols that relate it to Bell correlations. However, all these results have a limitation in common: they apply to scenarios with only one quantum party. Here we articulate the concept of postquantum steering for scenarios with multiple quantum parties, bringing in the missing piece to the puzzle. We provide an algorithm to certify postquantumness, which in some cases also certifies quantumness. We also define a hierarchy of semidefinite programs that bounds the set of quantum assemblages from the outside. Moreover, we show that the study of postquantum steering is fundamentally relevant since it is not just a mere mathematical curiosity allowed by the no-signalling principle, but it may arise within compositional theories beyond quantum theory. Our work further discovers a peculiarity of steering: its theory-independent description fundamentally prevents a direct connection with Bell nonlocality -- e.g., nonclassical Bell correlations do not imply nonclassical steering.

We demonstrate complete coherent control of a single spin qubit confined in a self-assembled InAs negatively charged quantum dot subjected to an Oblique magnetic field, and directly compare this regime with the conventional Voigt geometry. In the Oblique-field configuration, the groundstate spin eigenstates are found to be unequal superpositions of the bare electron spin, with their composition tunable via the orientation of the applied field. This tunable spin mixing provides an additional degree of freedom to engineer the spin basis and associated optical couplings in the charged quantum dot system. Although this geometry has a distinct structure with important implications, it provides a regime in which we can fully and coherently control the tailored spin qubit. We observe Rabi oscillations and Ramsey fringes, and demonstrate arbitrary single-qubit rotations, enabling a direct comparison with the Voigt case. Our results establish that spin-qubit control does not necessarily require a pure Voigt geometry and can instead be achieved under Oblique magnetic fields. This relaxes constraints on device and field alignment and offers a versatile route to design and optimize quantum information processing architectures in semiconductor quantum dots.

Designing quantum neural networks (QNNs) that are both accurate and deployable on NISQ hardware is challenging. Handcrafted ansatze must balance expressivity, trainability, and resource use, while limited qubits often necessitate circuit cutting. Existing quantum architecture search methods primarily optimize accuracy while only heuristically controlling quantum and mostly ignore the exponential overhead of circuit cutting. We introduce QNAS, a neural architecture search framework that unifies hardware aware evaluation, multi objective optimization, and cutting overhead awareness for hybrid quantum classical neural networks (HQNNs). QNAS trains a shared parameter SuperCircuit and uses NSGA-II to optimize three objectives jointly: (i) validation error, (ii) a runtime cost proxy measuring wall clock evaluation time, and (iii) the estimated number of subcircuits under a target qubit budget. QNAS evaluates candidate HQNNs under a few epochs of training and discovers clear Pareto fronts that reveal tradeoffs between accuracy, efficiency, and cutting overhead. Across MNIST, Fashion-MNIST, and Iris benchmarks, we observe that embedding type and CNOT mode selection significantly impact both accuracy and efficiency, with angle-y embedding and sparse entangling patterns outperforming other configurations on image datasets, and amplitude embedding excelling on tabular data (Iris). On MNIST, the best architecture achieves 97.16% test accuracy with a compact 8 qubit, 2 layer circuit; on the more challenging Fashion-MNIST, 87.38% with a 5 qubit, 2 layer circuit; and on Iris, 100% validation accuracy with a 4 qubit, 2 layer circuit. QNAS surfaces these design insights automatically during search, guiding practitioners toward architectures that balance accuracy, resource efficiency, and practical deployability on current hardware.

We design and experimentally characterize a balanced homodyne detector optimized for high-repetition-rate (100 MHz) pulsed optical sources. Unlike conventional transimpedance-amplifier architectures, which suffer from nonlinearities and dynamic instabilities with ultrashort pulses, our approach allows to directly amplify the photocurrent extracted at the common photodiode node without feedback loops. A theoretical model describing the detector response, noise, and pulse-to-pulse correlations is developed, providing quantitative predictions for the signal variance, signal-to-noise ratio (SNR), and inter-pulse correlations. Implemented with two matched InGaAs photodiodes illuminated by a 1030 nm mode-locked laser at 100 MHz, the detector exhibits excellent linearity and shot-noise-limited scaling of the signal variance with optical power. Optimizing the temporal integration window yields a maximum SNR of about 14 dB, while correlation measurements confirm negligible inter-pulse correlations. These results demonstrate that the proposed architecture offers a robust and simple solution for high-speed pulsed homodyne detection, suitable for quantum optics and continuous-variable quantum information applications.

Chip integration of quantum emitters is a crucial milestone for scalable quantum photonic information processing. Among optically active defect centers for quantum photonics, diamond color centers are promising because of their long spin coherence times and high photon emission rates. However, for a coherent-photon emission, they typically require a cryogenic environment to protect optical coherence from thermal phonons, which makes chip integration challenging. In this paper, we develop a chip-integrated diamond photonic crystal cavity embedding an ensemble of nitrogen-vacancy (NV) centers. We confirm cryogenic operation by observing Purcell enhancement of NV-center emission via an edge-coupled optical fiber. This result demonstrates successful integration of diamond color centers, a photonic crystal cavity, and an optical waveguide-fiber package, representing a key step toward scalable diamond-based quantum communication platforms.

Transport through correlated nanoscale systems underpins the operation of quantum-dot and molecular-scale devices, yet accurate simulations of large open quantum systems remain computationally challenging as system size increases. Tensor-network methods offer a promising route past this scaling barrier by efficiently compressing quantum states. Here we extend a tensor-based solver with a jump-counting estimator that enables direct computation of steady-state electron currents from lead-induced tunneling events. We benchmark the resulting currents against the state-of-the-art master-equation solver QmeQ across a range of lead-dot and inter-dot coupling parameters and find quantitative agreement in the tractable regime. Compared with classical approaches, TJM reduces memory requirements and wall-clock time by orders of magnitude, enabling simulations of interacting quantum-dot arrays far beyond the range accessible to density-matrix-based transport solvers and systematic studies of size-dependent nonequilibrium transport in larger arrays. Our approach allow us to model quantum transport in an array of up to fifty (50) quantum dots.

Free-space optical (FSO) links supporting spatial multiplexing provide a natural physical realization of Quantum MIMO channels. We develop a first-principles model for Quantum MIMO channels derived directly from wave-optical propagation through three-dimensional atmospheric turbulence. The framework explicitly accounts for intermodal crosstalk, finite detection apertures, and the system-bath separation induced by spatial-mode projection. We distinguish between distinguishable and indistinguishable photon regimes, showing that indistinguishability leads to intrinsically many-body interference effects described by matrix permanents. To obtain a completely positive and trace-preserving logical description, we introduce an erasure-extended encoding in which turbulence-induced leakage and photon loss are mapped to flagged erasure states. The resulting Quantum MIMO channel naturally reduces to a correlated n-qubit erasure channel, with correlations arising from the shared turbulent medium. Limiting regimes in which correlated Pauli channels emerge as effective approximations are also identified.

We present TNRKit.jl, an open-source Julia package for Tensor Network Renormalization (TNR) of two- and three-dimensional classical statistical models and Euclidean lattice field theories. Built on top of TensorKit.jl\cite{tensorkit}, it provides a symmetry-aware framework for constructing tensor-network representations of partition functions and coarse-graining them using methods such as TRG, HOTRG, and LoopTNR. Beyond thermodynamic quantities, the package enables the extraction of universal conformal data -- including scaling dimensions and the central charge -- directly from fixed-point tensors. TNRKit.jl is designed with both usability and extensibility in mind, offering a practical platform for applying, benchmarking, and developing modern tensor renormalization algorithms. This paper also serves as a self-contained introduction to the TNR framework.

Most quantum divergences derive their structure from classical f-divergences or Renyi-type constructions, a dependence that obscures several quantum geometric effects. We introduce a quantum relative-alpha-entropy that extends Umegaki's relative entropy while falling outside the f-divergence class. The proposed divergence exhibits a nonlinear convexity property, which yields a generalized convexity result for the Petz-Renyi divergence for alpha greater than one, complementing the known convexity for alpha less than one. It is additive under tensor products, invariant under unitary transformations, and depends only on the relative geometry of quantum states rather than their absolute magnitudes. Using Nussbaum-Szkola-type distributions, we also establish an exact correspondence of this divergence with classical relative-alpha-entropy. This reveals relative-alpha-entropy as a fundamentally geometric notion of quantum distinguishability not captured by existing divergence frameworks.

The quantum nature of gravity remains experimentally unverified, despite recent proposals to probe it using tabletop experiments such as gravity-mediated entanglement schemes. In parallel, consistent formulations of classical--quantum dynamics have been developed as alternative descriptions of gravity, in which quantum matter interacts with a classical mediator assumed to be fundamentally classical. In this work, we show that classical--quantum dynamics arise generically as an effective description of fully quantum systems under decoherence, providing a bridge between fully quantum and classical--quantum dynamics. We derive the reduced dynamics, which are generically non-Markovian, using an explicit hidden model in which the mediator is coupled to unobserved environmental degrees of freedom. We identify a concrete criterion for when a classical--quantum interpretation is valid: the semi-Wigner operator associated with the mediator sector must remain positive semidefinite, which can be expressed as a positivity condition on nonlocal kernels governing the evolution. In the short-memory limit, the reduced evolution reproduces Markovian classical--quantum dynamics of Oppenheim and collaborators. Our results imply that a classical mediator can arise effectively from decohered quantum dynamics, so that experimental agreement with classical-quantum models does not uniquely determine whether the mediator is fundamentally classical.

The unique combination of outstanding optical quality and attractive spin properties opens new avenues for optical spin control in hybrid organic-inorganic perovskite semiconductors. Using the optically detected magnetic resonance technique, we study the spins of electrons and holes in mixed-cation MA$_x$FA$_{1-x}$PbI$_3$ single crystals with $x = 0.4$ and 0.8. Multiple distinct spin subensembles with $g$-factors spanning from 2.9 to 3.6 for electrons and from 0.5 to 1.2 for holes are resolved, revealing diverse localization environments. We measure the longitudinal spin relaxation times, $T_1$, reaching 2 ms and remaining in the $μ$s range even for weakly localized carriers at the cryogenic temperature of 1.6 K. The magnetic-field dependence of $T_1$ is dominated by the random nuclear (Overhauser) fields with strengths of $\sim 0.4-0.8$ mT for electrons and $\sim 4-12$ mT for holes, corresponding to $μ$s-long correlation times of the hyperfine field determined by carrier hopping between shallow localization sites. The temperature dependence of $T_1$ reveals a weak localization potential of the charge carriers and shows a correlation between $T_1$ and the inhomogeneity of the spin ensemble. These results establish mixed-A-site perovskite single crystals as a promising solid-state platform with long-lived spin states for quantum information applications.

Secure communications with quantum key distribution over fiber-optic links is one of the few recognized applications of quantum physics at the level of individual quanta -- single C-band photons. Currently, the widely used sources of such photons are highly attenuated laser pulses, featured by a low probability of single photon occurrence. Here, we present an efficient source with an InAs/GaAs quantum dot on a metamorphic buffer layer inside a micropillar-shaped microcavity. The key innovation is the use of different semiconductor and dielectric materials to form the lower (GaAs/AlGaAs) and upper (Si/SiO$_2$) Bragg reflectors. Compatibility of these materials in a monolithic source is achieved by depositing a small amount of Si/SiO$_2$ pairs on an incomplete micropillar made from a coherent heterostructure grown by molecular beam epitaxy. This design enables resonant excitation with $π$-pulses and generation of polarized photons with a record-breaking end-to-end efficiency of 11%.

We propose a hardware efficient quantum residual neural network which implements residual connections through a deterministic linear combination of identity and variational unitaries, enabling fully differentiable training. In contrast to the previous implementation of residual connections, our architecture avoids post-selection while preserving residual learning. Furthermore, we establish trainability of our model, mitigating barren plateaus which are considered as a major limitation of variational quantum learning models. In order to show the working of our model, we report its application to image classification tasks by training it for MNIST, CIFAR, and SARFish datasets, achieving accuracies of 99% and 80% for binary and multi-class classifications, respectively. These accuracies are comparable to previously achieved from the standard variational models, however our model requires 10x fewer gates making it better suited for resource constraint near-term quantum processors. In addition to high accuracies, the proposed architecture also demonstrates adversarial robustness which is another desirable parameter for quantum machine learning models. Overall our architecture offers a new pathway for developing accurate, robust, trainable and hardware efficient quantum machine learning models.

It is shown that algebraic techniques based on the Lie algebra so(4,2) provide efficient tools for evaluating Lamb shifts and radiative decay rates for hydrogenic energy eigenstates as they systematically exploit the intrinsic symmetry of the hydrogenic Hamiltonian. As a main result in lowest order perturbation theory with respect to the fine-structure constant integral representations are derived for the complex-valued energy shifts of hydrogen-like ions from which Lamb shifts and radiative decay rates can be evaluated in a unified way, thus generalizing a recently discussed algebraic approach of Maclay. In order to exemplify the usefulness of this algebraic approach numerical results are presented for Lamb shifts and radiative decay rates which transcend the dipole approximation and contain the dipole approximation as a limiting case.

The European Union is developing the European Quantum Communication Infrastructure (EuroQCI) as a pan-European network to provide secure communication capabilities across Member States, including governmental and critical-infrastructure domains. While the strategic objective is defined at EU level, the required scale and structure of national quantum key distribution (QKD) networks remain largely unspecified. This work addresses the question of how to plan and size national terrestrial QKD networks to support critical infrastructure and public authorities. We propose a reproducible planning methodology that estimates network size, total fiber length, and the number of required QKD components based on a small set of explicit assumptions. The approach is demonstrated for Austria, where a synthetic but structured network model is constructed and evaluated using Monte Carlo simulation. The model focuses on terrestrial QKD infrastructure and explicitly excludes space-based segments. It estimates endpoint counts, trusted repeater node requirements, and hop-length distributions under realistic operational constraints. The Austrian case is then used as a baseline to derive scaling rules for other EU Member States based on population and geographic extent. The results provide first-order planning estimates for national QKD backbone sizes across Europe. These estimates are not intended as deployment designs but as planning-level references that support early-stage cost assessment and infrastructure dimensioning under the EuroQCI framework.

We present a first real-time study of hadronic scattering in a $(1+1)$-dimensional SU(2) lattice gauge theory with fundamental fermions using tensor-network techniques. Working in the gaugeless Hamiltonian formulation, we investigate scattering processes across sectors of fixed global baryon number $B = 0, 1, 2$, corresponding respectively to meson--meson, meson--baryon, and baryon--baryon collisions. At strong coupling, the $B = 0$ and $B = 2$ channels exhibit predominantly elastic dynamics closely resembling the U(1) Schwinger model. The mixed $B = 1$ sector displays qualitatively new behavior: meson and baryon wavepackets become entangled during the collision, with the slower state becoming spatially delocalized while the faster one propagates ballistically. We characterize these processes through local observables, entanglement entropy, and the information lattice.

Quantum computing simulators form the classical software foundation on which virtually all quantum algorithm research depends. We present Broken Quantum, the first comprehensive formal security audit of the open-source quantum computing simulator ecosystem. Applying COBALT QAI -- a four-module static analysis engine backed by the Z3 SMT solver -- we analyze 45 open-source quantum simulation frameworks from 22 organizations spanning 12 countries. We identify 547 security findings (40 CRITICAL, 492 HIGH, 15 MEDIUM) across four vulnerability classes: CWE-125/190 (C++ memory corruption), CWE-400 (Python resource exhaustion), CWE-502/94 (unsafe deserialization and code injection), and CWE-77/22 (QASM injection -- a novel, quantum-specific attack vector with no classical analog). All 13 vulnerability patterns are formally verified via Z3 satisfiability proofs (13/13 SAT). The 32-qubit boundary emerges as a consistent formal threshold in both C++ and Python vulnerability chains. Supply chain analysis identifies the first documented case of vulnerability transfer from a commercial quantum framework into US national laboratory infrastructure (IBM Qiskit Aer to XACC/Oak Ridge National Laboratory). Nine frameworks score 100/100 under all four scanners; Qiskit Aer,Cirq, tequila, PennyLane, and 5 others score 0/100.

Bright squeezed light from parametric down-conversion in the infrared (IR) frequency range has triggered the emergence of attosecond quantum optics -- a new research field at the interface of quantum optics, strong-field physics, and attosecond technology. Two challenges arise at this interface: transferring quantum features of the IR light sources to the ultraviolet (UV) and extreme ultraviolet (XUV) frequency range via strong-field nonlinearities, and exploiting quantum optical properties of the nonlinear optical response as a new probe in ultrafast dynamics. Here, we address both by driving high-harmonic generation (HHG) in solids with entangled photon pairs either in degenerate or non-degenerate frequency modes. In the degenerate mode, single-shot measurements of harmonics up to the 10th order reveal strong photon bunching whose $g^{(2)}$ first grows and then decreases with the harmonic order. We show that this behavior tracks different microscopic mechanisms responsible for harmonic emission, demonstrating the potential of attosecond quantum optical spectroscopy. In the non-degenerate case, the harmonics retain quantum-induced correlations, verified by wavelength-resolved second-order cross-correlation maps. Our findings demonstrate transfer of quantum photon correlations into the XUV domain and open a pathway toward quantum-enhanced attosecond spectroscopy and control of ultrafast dynamics in solids.

Strong-field ionization is the cornerstone of attosecond physics, which has been extensively studied under coherent-state driving. Recently, the interface between attosecond physics and quantum optics has emerged as a new frontier. Yet, owing to experimental limitations, the role of the quantum nature of light in atomic strong-field ionization has remained unexplored. Here, we demonstrate strong-field ionization of xenon atoms driven by bright squeezed vacuum (BSV) with average pulse energy up to 10 \textmu J. We show that, as a nonclassical state with zero mean field and strong intensity fluctuations, BSV selectively enhances the spider-like holographic structures in the photoelectron momentum distributions. Using a quantum-light-corrected quantum-trajectory Monte Carlo (q-QTMC) model, we attribute this effect to the intrinsic coherence of trajectory pairs emitted within the same subcycle field fluctuation. These dynamically correlated paths exhibit enhanced phase stability and remain robust against dephasing, whereas asynchronous paths are filtered out by field noise. Our results reveal a quantum-fluctuation-induced mechanism for coherence protection in strong-field processes, positioning BSV as an effective coherence filter and establishing a new regime of quantum-enabled noise-resilient ultrafast dynamics.

In recent years, techniques of intense THz laser have enabled us to experimentally observe nonlinear spin dynamics in antiferromagnets since the elementary excitations such as magnons reside on a THz to GHz range in antiferromagnets and THz laser thus can directly excite them. We numerically and theoretically investigate THz-laser or GHz-wave driven harmonic generations in typical ordered phases of antiferromagnets: Néel, canted and weak ferromagnetic phases. The radiation waves (harmonic generations) are created by the incident-wave driven magnon dynamics. We point out that magnetic orders and phase transitions can change the spectra of harmonic generations, differently from those of metallic, semiconductor, or atomic-gas systems without (spontaneous) symmetry breakings. We consider both the magnon harmonic generation driven by standard single-color laser and that by two-color laser in the antiferromagnets, and find several dynamical symmetries and the corresponding selection rules of the harmonic generations. These results indicate that the magnon harmonic generation spectra provide new information about symmetry or symmetry breaking of antiferromagnets.

Optical loss is a common bottleneck in photonic quantum information processing, undermining the quantum advantage over classical approaches. Although several countermeasures, such as quantum distillation and error correction, have been proposed, they typically require experimentally demanding non-Gaussian operations. Here, we demonstrate a Gaussian-only scheme that suppresses loss-induced decoherence for general, unknown optical quantum states. By injecting a squeezed vacuum state into an environment of the loss channel and performing feedforward based on environmental monitoring, the scheme effectively suppresses loss-induced noise. Our programmable loop-based optical circuit allows us to implement the scheme for several types of loss-sensitive non-Gaussian states under various loss conditions for up to five steps, and directly compare the results with the unsuppressed case. Our results show that the scheme consistently mitigates state degradation, preserving higher fidelity and Wigner negativity than without suppression. This approach can be applied to mitigating a broad class of errors in optical systems and extending quantum memory lifetimes. Moreover, it is compatible with other loss-suppression techniques and extendable to physical platforms beyond optics, offering a promising route toward reducing the overhead required for fault-tolerant quantum information processing.

Laser frequency stabilization is conventionally analyzed using continuous-time control theory, which accurately models analog feedback but is insufficient for digital implementations where quantization, sampling, and stochastic noise shape the dynamics. In modern digital laser systems, such as Photonic Integrated Circuit (PIC)-based lasers, finite discriminator and actuator resolution, sampling delays, and measurement noise introduce stochastic behavior that deterministic models do not capture. We present a discrete-time Markov-state framework that models the evolution of the quantized actuator in a digital laser frequency lock, with state-transition probabilities determined by the frequency discriminator response, noise statistics, and implemented digital control logic. The steady-state actuator and locked-laser frequency distributions are obtained directly from the unit-eigenvalue solution of the transition matrix, providing immediate access to key stability metrics without long time-domain simulations. For white frequency noise, we show that the Markov formulation is exact under decorrelated sampling and update schemes, while correlated discriminator sampling introduces a predictable inflation of actuator variance without shifting the operating point. In the presence of colored noise, long-range temporal correlations induce sampling-dependent deviations in both actuator mean and variance, defining the regime of validity of the memoryless Markov description. This framework provides a compact and physically transparent tool for analyzing and optimizing digitally stabilized lasers in integrated photonic systems.

Quantum target ranging, which estimates a target position using entangled photon pairs, is known to offer an error-probability advantage over classical ranging strategies. Yet, realizing this advantage in practice remains challenging, as an existing receiver design relies on collective measurements and requires an impractically large number of quantum memories and linear passive components. In this work, we propose the hetero-homodyne receiver, a practically implementable architecture that achieves quantum advantage in target ranging using only local measurements. The receiver requires only one heterodyne setup, a single homodyne setup, and a delay line, making the implementation scalable and experimentally feasible. Our results establish a realistic framework for demonstrating quantum advantage in target ranging and contribute toward practical quantum radar systems.

We present an enhanced entangled quantum clock protocol that incorporates a quantum phase estimation algorithm to directly estimate proper-time differences as an unknown phase. By employing highly entangled multi-clock states, the achievable uncertainty scales inversely with the total number of quantum clocks, surpassing the standard projection-noise limit. This approach extends the original EQC framework and provides a systematic method for high-precision relativistic time comparison.

A particular type of linear optical multiport, the Grover four-port, has previously been shown to couple the spatial symmetry of a photon to its direction of travel. It is shown here that use of a nonstandard choice of qubit, based on symmetry, allows Grover four ports to act as compact, low-resource deterministic linear optical controlledNOTgates, with no post-selection or ancilla measurements required. This approach allows programmable devices, made from Grover multiports in combination with other standard optical components, that can implement multiple different one-, two-, and three-qubit gates, including the Fredkin and Toffoli gates.

The purpose of this paper is to investigate the coherent feedback $H^\infty$ control problem for linear quantum systems. A key contribution is a simplified design methodology that guarantees closed-loop stability and a prescribed level of disturbance attenuation. It is shown that for general linear quantum systems, a physically realizable quantum controller can be obtained by solving at most four Lyapunov equations. In the passive case, a necessary and sufficient condition is provided in terms of two uncoupled pairs of Lyapunov equations. These results represent a significant simplification over the standard approach, which requires solving two coupled algebraic Riccati equations. The effectiveness of the proposed method is demonstrated through two typical quantum optical devices: an empty optical cavity and a degenerate parametric amplifier. These results provide a computationally efficient procedure for the robust and optimal control of quantum optical and optomechanical systems.

We investigate whether a multiscale tensor-network architecture can provide a useful inductive bias for reconstruction-based anomaly detection in collider jets. Jets are produced by a branching cascade, so their internal structure is naturally organised across angular and momentum scales. This motivates an autoencoder that compresses information hierarchically and can reorganise short-range correlations before coarse-graining. Guided by this picture, we formulate a MERA-inspired autoencoder acting directly on ordered jet constituents. To the best of our knowledge, a MERA-inspired autoencoder has not previously been proposed, and this architecture has not been explored in collider anomaly detection. We compare this architecture to a dense autoencoder, the corresponding tree-tensor-network limit, and standard classical baselines within a common background-only reconstruction framework. The paper is organised around two main questions: whether locality-aware hierarchical compression is genuinely supported by the data, and whether the disentangling layers of MERA contribute beyond a simpler tree hierarchy. To address these questions, we combine benchmark comparisons with a training-free local-compressibility diagnostic and a direct identity-disentangler ablation. The resulting picture is that the locality-preserving multiscale structure is well matched to jet data, and that the MERA disentanglers become beneficial precisely when the compression bottleneck is strongest. Overall, the study supports locality-aware hierarchical compression as a useful inductive bias for jet anomaly detection.

The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.

Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters via gradient descent. The high cost of training and low fidelity of current quantum devices, however, restricts much of quantum machine learning to classical simulation. For few-qubit problems with large datasets, training the matrix elements directly, as is done with weight matrices in classical neural networks, can be faster than decomposing data and parameters into gates. We propose a method that trains matrices directly while maintaining unitarity through a single regularization term added to the loss function. A second training step, circuit alignment, then recovers a gate-based architecture from the resulting soft-unitary. On a five-qubit supervised classification task with 1000 datapoints, this two-step process produces a trained variational circuit in under four minutes, compared to over two hours for direct circuit training, while achieving lower binary cross-entropy loss. In a second experiment, soft-unitaries are embedded in a hybrid quantum-classical network for a reinforcement learning cartpole task, where the hybrid agent outperforms a purely classical baseline of comparable size.

We unite two of the most widely used approaches for strongly damped, non-Markovian open quantum dynamics, the Hierarchical Equations of Motion (HEOM) and the pseudomode method by proving two statements: First, every physical bath correlation function (BCF) that can be written as a sum of $N$ exponential terms can be obtained from a physical model with $N$ interacting pseudomodes which are damped in Lindblad form. Second, for every such BCF there exists a non-unitary, linear transformation which mirrors the evolution of the system-pseudomode state onto the HEOM hierarchy, and vice versa. Our proofs are constructive and we give explicit expressions for the mirror transformation as well as for the pseudomode Lindbladian corresponding to a given exponential BCF. This approach also gives insight and provides elegant derivations of the corresponding Hierarchy of stochastic Pure States (HOPS) method and its nearly-unitary version, nuHOPS. Our result opens several avenues for further optimization of non-Markovian open quantum system dynamics methods.

We introduce a systematic protocol for constructing quantum Hilbert-space-fragmented Hamiltonians, whose Krylov-sector structure, unlike in classically fragmented models, can be fully resolved only in an entangled basis. The protocol takes as input a classically fragmented model and uses a Rokhsar-Kivelson type construction to promote it to a quantum fragmented model. Notably, the procedure also works with non-fragmented inputs (such as Ising models). We explain how the Krylov sectors of the resulting quantum fragmented model may be labeled and counted in one dimension, and outline experimentally accessible verification of quantum fragmentation, assuming the ability to prepare specific initial states and perform tomography on reduced density matrices. We further analyze the entanglement structure of the entangled basis underlying quantum fragmentation, which sharply distinguishes it from both classical fragmentation and the trivial "fragmentation" of generic Hamiltonians in their eigenbasis. We also extend the construction to higher dimensions, with an explicit proof of principle example in two dimensions. We expect these results to open a new route to the systematic exploration of quantum fragmentation.

We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and cumulants, quantities which characterize the fluctuations of an underlying probability distribution. In all of the cases we review, the fluctuations are those of a quantum system. We show that the original formalism for geometric phases, in which a quantum system is taken around an adiabatic cycle, can be extended to the case when degeneracy points are encountered along the cycle (quasiadiabatic cycles). The essential tool for this extension is a generalized Bargmann invariant which plays the role of a generating function. From the cumulants generated this way one can form ratios according to the Binder cumulant scheme in statistical mechanics. Such geometric Binder cumulants are sensitive to gap closure, as such, they are useful in identifying metal-insulator transitions, localization, and quantum phase transitions. We present example calculations on simple model systems, whose localization properties are well known, to validate to approach. We also complement our geometric Binder cumulant calculations with results for the fidelity susceptibility, a quantity directly related to the quantum geometry of the parameter space.

In an optical cavity, strong light--matter coupling between excitons and photons has been widely reported as a way to enhance energy delocalization through spatially extended polaritonic states. In contrast, leveraging cavity-mediated light--matter effects to promote the reciprocal phenomenon, namely \textit{energy localization}, remains largely underexplored. In the present work, we address this question by focusing on a special form of energy localization arising from nonlinear matter interactions: \textit{Quantum Self-Trapping} (QST). We employ a generalized Tavis--Cummings model to investigate the transport of vibrational excitons -- \textit{i.e., vibrons} -- between two anharmonic vibrational modes and examine their interplay with cavity photons. In the absence of a cavity, the arising of true and complete QST -- \textit{i.e.}, an infinite-lifetime localization -- is not possible due to the symmetry of the system. The energy transfer between the two modes still occurs, slowed down by the many-body interactions. Coupling the system to a single-mode cavity strongly alters this behavior, with two emerging regimes. First, at weak light--matter coupling, destructive interference between newly opened transition pathways suppresses energy exchange, leading to cavity-enhanced self-trapping. As the coupling strength increases, these interference effects evolve leading to cavity-assisted energy transfer, where we observe an acceleration of the vibrational energy flow. Most notably, we identify critical coupling strengths that separate both regimes in which the dynamics almost totally freeze, suggesting the arising of a ``stabilized'' light-induced~QST of many-vibron bound states. These results suggest that optical cavities can not only enhance transport but could also stabilize energy localization phenomena, providing a new route to control energy flow in quantum systems.

Efficient data loading remains a bottleneck for near-term quantum machine-learning. Existing schemes (angle, amplitude, and basis encoding) either underuse the exponential Hilbert-space capacity or require circuit depths that exceed the coherence budgets of noisy intermediate-scale quantum hardware. We introduce Shot-Based Quantum Encoding (SBQE), a data embedding strategy that distributes the hardware's native resource, shots, according to a data-dependent classical distribution over multiple initial quantum states. By treating the shot counts as a learnable degree of freedom, SBQE produces a mixed-state representation whose expectation values are linear in the classical probabilities and can therefore be composed with non-linear activation functions. We show that SBQE is structurally equivalent to a multilayer perceptron whose weights are realised by quantum circuits, and we describe a hardware-compatible implementation protocol. Benchmarks on Fashion MNIST and Semeion handwritten digits, with ten independent initialisations per model, show that SBQE achieves 89.1% +/- 0.9% test accuracy on Semeion (reducing error by 5.3% relative to amplitude encoding and matching a width-matched classical network) and 80.95% +/- 0.10% on Fashion MNIST (exceeding amplitude encoding by +2.0% and a linear multilayer perceptron by +1.3%), all without any data-encoding gates.

The computational cost of concurrent multiscale finite element methods is dominated by the repeated solution of microscopic representative volume element (RVE) problems at macroscopic quadrature points. In this work, we introduce a quantum-classical framework for multiscale finite element analysis (QAFE$^2$) that leverages quantum parallelism to fundamentally alter the scaling of RVE-based homogenisation. At the single-RVE level, the proposed quantum solver attains polylogarithmic complexity with respect to the microscopic discretisation size, yielding an exponential asymptotic speedup over the best available classical solvers. More importantly, QAFE$^2$ exploits quantum superposition and entanglement to evaluate, in a single quantum execution, the entire ensemble of RVE problems associated with all macroscopic quadrature points. This capability is a form of intrinsic quantum concurrency with no classical analogue. Numerical experiments on one- and two-dimensional model problems with known analytical solutions confirm the accuracy of the proposed formulation and verify the theoretical computational scaling and parallel performance.

We establish necessary and sufficient conditions for the N-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the true energy in one-electron reduced density matrix functional theory, regardless of the strength of the interparticle repulsion. Conversely, any functional violating these conditions will necessarily underestimate the true energy for certain systems. These exact constraints impose a stringent restriction on density matrix functional approximations, as many existing functionals-including the Hartree-Fock functional-appear to violate them. This mathematical formalism, therefore, can guide the development of new approximate functionals and numerical algorithms.

Assembling genomes from short-read sequencing data remains difficult in repetitive regions, where reference bias and combinatorial complexity limit existing methods. Pangenome-guided sequence assembly (PGSA) mitigates reference bias by reconstructing an individual genome as a walk through a population-level graph. The associated problem, identifying a walk whose node visits match read-derived copy numbers, is NP-hard and already challenges classical solvers at a moderate scale. We develop near-term quantum optimisation approaches for this computational bottleneck. We consider two problem encodings: an established quadratic unconstrained binary optimisation and a new higher-order binary optimisation (HUBO) formulation. The latter reduces the number of variables from $O(N^2)$ to $O(N\log N)$ and places moderate-sized instances within the qubit budget of current devices. We solve both using the Iterative-QAOA framework, which combines a fixed linear-ramp QAOA schedule with iterative warm-start bias updates, avoiding the overhead of full variational parameter optimisation. A custom circuit compilation strategy reduces hardware gate overhead by up to 67\% compared with standard tools. In noiseless simulations of QUBO problems, Iterative-QAOA reliably identifies optimal assemblies from as few as $10^{-17}\%$ of all candidate solutions, and \textit{IBM} quantum hardware closely reproduces relevant results with sufficient sampling via CVaR-style post-selection. For HUBO, the variable reduction comes at the cost of deeper compiled circuits and greater noise sensitivity: an expected qubit--depth trade-off. Our findings establish pangenome assembly as a concrete, biologically motivated problem class at the scale where quantum optimisation may first provide practical value.

Convolutional neural networks owe much of their success to hard-coding translation equivariance. Quantum convolutional neural networks (QCNNs) have been proposed as near-term quantum analogues, but the relevant notion of translation depends on the data encoding. For address/amplitude encodings such as FRQI, a pixel shift acts as modular addition on an index register, whereas many MERA-inspired QCNNs are equivariant only under cyclic permutations of physical qubits. We formalize this mismatch and construct QCNN layers that commute exactly with the pixel cyclic shift (PCS) symmetry induced by the encoding. Our main technical result is a constructive characterization of all PCS-equivariant unitaries: conjugation by the quantum Fourier transform (QFT) diagonalizes translations, so any PCS-equivariant layer is a Fourier-mode multiplexer followed by an inverse QFT (IQFT). Building on this characterization, we introduce a deep PCS-QCNN with measurement-induced pooling, deferred conditioning, and inter-layer QFT cancellation. We also analyze trainability at random initialization and prove a lower bound on the expected squared gradient norm that remains constant in a depth-scaling regime, ruling out a depth-induced barren plateau in that sense.

While recent advances have established efficient quantum algorithms for preparing Gibbs states of finite-dimensional systems, comparable complexity results for bosonic and other infinite-dimensional models remain unexplored. We introduce the first general rigorous Gibbs sampling framework for bosonic many-body systems, showing that physically relevant bosonic models admit gapped dissipative generators, enabling efficient preparation of thermal states. Although our results hold for broad classes of models, we illustrate them using Bose-Hubbard Hamiltonians, both within and beyond the mean-field regime. In both cases, we show that the associated dissipative generators maintain a positive spectral gap, thereby implying exponential convergence to the thermal state. Our argument in the multi-mode case is based on a finite-rank reduction of the dissipative dynamics, which allows us to control the generator via compact perturbations and deduce the discreteness of the spectrum and the stability of the gap. We apply our results to provide efficient preparation of the corresponding Gibbs state on qubit hardware, and by that a quantum algorithm to compute thermal properties of the associated model. This provides the first mathematically controlled route to Gibbs sampling in infinite-dimensional systems, with implications for quantum simulation, thermalization, and many-body complexity, where quantum advantages may arise.

Due to rising electricity demand, accurate short-term load forecasting is increasingly important for grid stability and efficient energy management, particularly in resource-constrained edge settings. We present a hardware-efficient Quantum Reservoir Computing (QRC) framework based on a fixed, untrained quantum circuit with Chebyshev feature encoding, brickwork entanglement, and single- and two-qubit Pauli measurements, avoiding quantum backpropagation entirely. Using the Tetouan City Power Consumption dataset, we examine the effect of post-training fixed-point quantization on the classical readout layer, with the reservoir architecture selected through a genetic search over 18 candidate configurations. Under finite-shot evaluation, 8-bit and 6-bit quantization maintain forecasting accuracy within 1% of the FP32 baseline while reducing readout memory by 75% and 81%, respectively. These results suggest that quantized readout can improve the hardware efficiency and deployment practicality of QRC for memory-constrained energy forecasting.

We introduce a new approach to confusability in a quantum channel, namely quantum confusability multigraph, which incorporates the output information into the graphical structure. By``counting" the edges between two vertices of this confusability multigraph, one recovers the traditional confusability ``single-edged" graph of the channel. With this physical motivation, we therefore develop a theory of quantum multigraphs from Weaver's quantum relations point of view and explore its quantum graph theoretic properties. Finally, we provide a necessary and sufficient condition characterizing those quantum multigraphs that arise as quantum confusability multigraphs.

Bound states are dissipation-resilient states that may emerge when quantum systems are strongly coupled to reservoirs with band gaps. We analyze an exactly solvable bosonic model for bound state existence and reproduce these results by a weak-coupling treatment of a supersystem composed of the original system and multiple reaction coordinates, which are individually representing small energy intervals of the reservoir spectral function. Within the perturbative supersystem treatment, the bound state stability results from its energy being inside the band gap. We discuss cases of multiple band gaps and also show that already in presence of weak interactions the bound state's lifetime is finite -- but can be increased by raising the system-reservoir coupling strength.

Hybrid quantum neural networks are increasingly explored for classification, yet it remains unclear how their performance and quantum behavior scale with circuit depth and qubit count. We present a controlled scaling study of hybrid quantum-classical classifiers along two axes: (1) increasing the number of quantum layers L at fixed qubits Q, and (2) increasing the number of qubits Q at fixed depth L. Across multiple datasets, we evaluate predictive performance using Accuracy, PR-AUC, Precision, Recall, and F1, and track quantum-specific metrics (QCE, EEE, QGN) to characterize how quantum properties evolve under scaling. Our results summarize scaling trends, saturation regimes, and dataset-dependent sensitivity, and further analyze how quantum metrics relate to predictive performance. This study provides practical guidance for selecting (Q,L) in hybrid QNN classifiers and establishes a consistent evaluation protocol for scaling analysis.

Entanglement is a key quantity for characterizing quantum correlations in particle scattering processes, but its direct evaluation is computationally demanding on quantum hardware. In this work, we investigate whether fermion density profiles, which are easier to access, can serve as proxies for entanglement by framing the problem as a classification task across multiple entanglement thresholds. Using the fermion scattering in the Thirring model as a test bed, we compare Quantum Convolutional Neural Networks (QCNNs) with classical CNNs of comparable parameter counts, and find that QCNNs achieve consistently competitive or superior accuracy with faster convergence and lower variance. Notably, we observe that increasing the model size does not improve the performance within the architectures studied here, and larger models appear to be more sensitive to the choice of encoding. Instead, a compact 4-qubits QCNN provides the best results, suggesting the importance of trainability and encoding choices over model scaling. These findings demonstrate the potential of quantum and quantum-inspired machine learning models for extracting nontrivial quantum information from accessible observables, with implications for high-energy physics and quantum many-body systems.

Expectation values of measurement operators, interpreted as measurement probabilities, arise frequently throughout quantum algorithms. When quantum states are randomly distributed, their expectation values are also randomly distributed. In this work, with the goal of understanding non-unitary dynamics, we generalize previous derivations for distributions of expectation values (Campos Venuti and Zanardi, Physics Letters A (377), 2013) to the case of sets of measurement operators and random mixed quantum states within variable sized environments. Using combinatorics approaches, we derive expressions for their moments. We proceed to construct empirical distributions of simulated Haar random brickwork quantum circuits with local depolarizing noise, and compare their form to a proposed effective global-depolarizing-like model with variable effective noise scales and environment dimensions. The fitted effective distributions reproduce peak behaviour across circuit depths, noise scales, and system sizes, while deviations in the distribution tails arise from local noise effects. The fit effective model parameters are also shown to vary smoothly and consistently with circuit depth and noise scale. Finally, sets of non-symmetric measurement operators are shown to exhibit distinct multi-modal distributions relative to uni-modal distributions for symmetric measurement operators, opening up questions about their simulability.

We introduce a framework for distributed quantum inference under communication constraints. In our model, $m$ distributed nodes each receive one copy of an unknown $d$-dimensional quantum state $ρ$, before communicating via a constrained one-way communication channel with a central node, which aims to infer some property of $ρ$. This framework generalizes the classical distributed inference framework introduced by Acharya, Canonne, and Tyagi [COLT2019], by allowing quantum resources such as quantum communication and shared entanglement. Within this setting, we focus on the fundamental problem of quantum state certification: Given a complete description of some state $σ$, decide whether $ρ=σ$ or $\|ρ-σ\|_1\geq ε$. Additionally, we focus on the case of limited quantum communication between distributed nodes and the central node. We show that when each communication channel is limited to only $n_q\leq \log d$ qubits, then the sample complexity of distributed state certification is $\mathcal{O}(\frac{d^2}{2^{n_q}ε^2})$ when public randomness is available to all nodes. Moreover, under the assumption that the channels used by the distributed nodes are mixedness-preserving, we prove a matching lower bound. We further demonstrate that shared randomness is necessary to achieve the above complexity, by proving an $Ω(\frac{d^3}{4^{n_q} ε^2})$ lower bound in the private-coin setting under the same assumption as above. Our lower bounds leverage a recently introduced quantum analogue of the celebrated Ingster-Suslina method and generalize arguments from the classical setting. Together, our work provides the first characterization of distributed quantum state certification in the regime of limited quantum communication and establishes a general framework for distributed quantum inference with communication constraints.

We investigate the quantum phases of a half-filled generalized interacting Su-Schrieffer-Heeger model with intracell, nearest-neighbor, and next-nearest-neighbor intercell hoppings, together with an on-site inter-sublattice interaction. In the noninteracting limit, the model hosts one topologically trivial phase and two symmetry-protected topological (SPT) phases, distinguished under periodic boundary conditions by different winding numbers and under open boundary conditions by two-fold and four-fold entanglement-spectrum degeneracies, respectively. When interactions are introduced, these free-fermion SPT phases evolve into distinct interacting topological phases that retain characteristic signatures such as entanglement-spectrum degeneracy structures, boundary modes, and nonzero string order parameters. For strong repulsive interactions, a symmetry-breaking phase with unequal but spatially uniform sublattice densities appears between the trivial and topological regimes. For strong attractive interactions, period-2 and period-4 charge-density-wave phases emerge from particle clustering. At intermediate attractive interactions, the competition between interaction-induced localization and hopping-induced delocalization gives rise to a Luttinger liquid phase, a paired Luttinger liquid phase, and a gapless symmetry-protected topological (gSPT) phase. The gSPT phase is characterized by a gapless charge mode together with symmetry-protected current-carrying edge states. We further characterize the gapless phases and the associated quantum phase transitions through central charges and critical exponents.

Quantum advantage, broadly understood as the ability of quantum systems to significantly outperform their classical counterparts, underpins current interest to quantum technologies and is a topic of active investigation. In many situations, its existence is subject to debate, and the areas of supremacy of large-scale quantum systems are not well defined. Here, we uncover a novel niche where quantum advantage can be clearly defined and proven. We study a time-optimal transfer of excitations in the lattice involving both nearest-neighbor and longer-range couplings. We prove that the quantum-mechanical property of a particle to propagate along several trajectories simultaneously speeds up the transfer process, which takes a shorter time compared to any particular trajectory and thus provides a clear example of quantum advantage.

We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form $H= \sum_{i=1}^K H_i = \sum_{i=1}^K H_{i_1} \otimes H_{i_2} \otimes \cdots \otimes H_{i_M}$. Given that the entries of all $\{ H_{i_1}, H_{i_2} , \cdots , H_{i_M}\}$ (for all $i$) are classically known, we present a procedure (with three variants) in which these operators are classically diagonalized, and then this information is fed into three possible quantum procedures to obtain the block-encoding of $H$. The evolution operator $\exp(-iHt)$ is then obtained using the standard block-encoding/quantum singular value transformation framework. In the case where $\{H_i\}_{i=1}^K$ commute pairwise, our method can be trivially extended to the case with time-dependent coefficients. We provide a detailed discussion of the efficient regime of our hybrid framework and compare it with existing quantum simulation algorithms. Our algorithm can serve as a useful complement to existing quantum simulation algorithms, thereby expanding the reach of quantum computers for practically simulating physical systems. As a side contribution, we will show how the recent technique called \textit{randomized truncation to a quantum state} developed by Harrow, Lowe, and Witteveen [arXiv preprint arXiv:2510.08518, 2025] can be applied to the context of quantum simulation and particularly quantum state preparation, for which the latter can be of independent interest.

We study non-Hermitian quantum mechanics of an inverted triple-well potential within the exact WKB framework. For a single classical potential, different Siegert boundary conditions define three distinct quantum problems: the PT-symmetric, resonance, and anti-resonance systems. For each case, we derive the exact quantization condition and construct the associated trans-series solution. By identifying the resurgent structures and cancellations in these non-Hermitian setups, we obtain the median-summed series, clarifying when the spectra are real or complex in accordance with the physical properties of each system. Establishing explicit links to the semi-classical path integral formalism, we elucidate the roles of bounce and bion configurations in these non-Hermitian systems. This analysis predicts PT-symmetry breaking, which we also verify numerically. Using the median quantization conditions, we prove the existence of this symmetry breaking and establish an exact equation for the exceptional point, which emerges as a remarkably simple algebraic relation between the bounce and bion actions. We further show that the median-summed non-perturbative correction to the spectrum vanishes at the exceptional point, while the resurgent structure survives through a universal minimal trans-series. For the resonance and anti-resonance systems, we find that the exact median-summed spectra are related by complex conjugation, representing time reversal in this setting, are necessarily complex, and do not exhibit an exceptional point. Although their spectra differ significantly from the PT-symmetric case, they share the same minimal trans-series. By maintaining explicit links with the path integral saddles and the formal theory of resurgence, our analysis provides a unified and general perspective on the quantization of non-Hermitian theories.

We investigate the overall optomechanical force experienced by a macroscopic lossy object in free space under external quantum illumination. To this end, utilizing the Modified Langevin Noise Formalism (MLNF), we derive the time-averaged expectation value of the Maxwell stress tensor for a non-equilibrium scenario in which the incoming scattering field is prepared in an arbitrary mixed quantum state, while the medium-assisted field is maintained in local thermal equilibrium. In the limit of full radiation-matter thermal equilibrium, our expression exactly recovers the well-known fluctuation-dissipation relation governing the Casimir effect, and, under coherent illumination, it yields the standard classical radiation pressure. We demonstrate that by driving the scattering field with an anisotropic, multimode squeezed vacuum state, the spatial profile of the electromagnetic quantum fluctuations can be engineered to exhibit broken rotational symmetry, thereby inducing a purely quantum mechanical force acting on the object. Such mechanical interaction is generated in the strict absence of a mean field, $\langle\hat{\mathbf{E}}\rangle=0$, and its non-classical nature is evidenced by its reliance on second-order field correlations $\langle\hat{\mathbf{E}}^2\rangle$, unlike classical optical radiation pressure governed by the squared mean field $\langle\hat{\mathbf{E}}\rangle^2$. Applying this exact formulation to a homogeneous lossy sphere, we demonstrate the experimental feasibility of the effect using realistic material parameters and optical estimations. Ultimately, we establish a general formalism for macroscopic quantum optomechanics that operates beyond the constraints of thermal equilibrium, enabling the prediction of regimes where the purely quantum force circumvents classical mean fields and shot noise while preserving the object's macroscopic quantum coherence.

We study transport dynamics of free fermions subject to the external monitoring of a conserved charge over an extensive region. Focusing on bipartition protocols, we consider monitoring the total particle number over half of the system, and study the profiles of local charges and currents at hydrodynamic scales. While the Lindbladian describing the averaged dynamics is non-local, we show that the profiles can be understood in terms of localized impurities. We present a general framework based on the generalized hydrodynamics (GHD) picture, allowing for a hybrid numerical-analytic solution of the quench dynamics at hydrodynamic scales. We illustrate our approach for domain-wall initial states, showing that monitoring leads to discontinuities in the profiles that become more pronounced as the rate increases and that lead to the absence of transport in the Zeno limit of infinite monitoring rates. Our GHD framework could be naturally extended to interacting systems, paving the way for a systematic study of transport of integrable models subject to extensive-charge measurements.

We investigate the light statistics of an ensemble of independent motionless two-level atoms in a product state. We identify the conditions under which the cold atomic ensemble emits thermal light statistics characterized by the Gaussian Moment Theorem. For the theorem to hold, we derive for each correlation order two conditions on the atom number and the ratio of coherent to incoherent light emission. We further discuss their validity for atoms either in a pure or mixed state. Our results contribute to the understanding of the generation of thermal light by two-level atoms without interactions among the emitters.

Black hole islands are usually diagnosed through the von Neumann entropy, but the full replica saddle contains more information than survives in the limit $n \to 1$. In this paper we show that the capacity of entanglement can detect that extra structure already within the controlled factorized island branch of JT gravity coupled to a large-$c$ bath. In the late-time high-temperature regime, the entropy plateau remains unchanged at the first nontrivial order, while the capacity acquires a definite correction. This provides a sharp semiclassical example in which nearby replica data are physically meaningful even when the entropy itself appears rigid. Our result shows that the factorized island saddle already carries finite-$n$ information beyond the entropy, and that the capacity is a natural observable for exposing it. More broadly, it highlights that the physics of island saddles is not exhausted by the $n=1$ limit: the surrounding replica geometry can contain additional, and observable, information about how the semiclassical saddle is assembled.

Nonlinear processes, mediated by multiphoton interactions rather than single-photon response, drive numerous fundamental phenomena and momentous applications in modern physics. Among these processes, tunneling ionization plays a pivotal role as it drives high-harmonic generation, forming the basis of attosecond science and enabling the visualization and control of electron motion at its natural time scale. Quantum light, with its unique capacity for quantum noise redistribution, offers a transformative solution to boost nonlinear responses. Here, we report the first experiment of nonlinear tunneling ionization of the most fundamental system of atoms boosted by a quantum light -- bright squeezed vacuum (BSV). Remarkably, the tunneling ionization of a single sodium atom induced by a 300 nJ BSV beam matches that achieved with a 7.1 {\textmu}J coherent light source, demonstrating a dramatic boost in nonlinear efficiency from phase-squeezed quantum light. Moreover, the effective intensity of the BSV light and thus the boosted tunneling ionization can be precisely controlled by tuning the degree of phase squeezing while maintaining the average pulse energy. These findings provide fundamental insights into quantum-boosted nonlinear effect and pave the way for efficient frequency conversion and quantum-controlled molecular reactions using tailored quantum light sources.

Amplitude Amplification offers a provable speedup for search problems, which is leveraged in combinatorial optimization by Grover Adaptive Search (GAS). The protocol demands deep circuits that are challenging with regards to NISQ capabilities. We propose a nested Amplitude Amplification protocol for the binary knapsack problem that splits the decision tree at a tunable depth, performing a partial amplification on the first variables before executing a global GAS on the full search space. The partial amplification is implemented by an Inner Iteration Finder that selects the rotation count maximizing marked-subspace amplitude. The resulting biased superposition serves as the initial state for the outer Amplitude Amplification. Using the Quantum Tree Generator for feasible-state preparation and an efficient classical amplitude-tracking scheme, we simulate the protocol on knapsack instances of sizes intractable by statevector simulation. Our results show that the nested approach reduces the cost of improving an incumbent solution compared to baseline GAS, particularly for a specific subset of knapsack instances. As combinatorial problems in domains such as semiconductor supply-chain planning grow in scale, methods that reduce circuit cost are an important step toward eventual quantum advantage for such applications.

Non-equilibrium properties of strongly interacting gauge theories are often intractable with classical simulation methods. Due to recent developments of quantum simulations, studies of their properties in two spatial dimensions are becoming accessible. By demonstrating the existence of an approximate spectrum-generating algebra for a pure gauge plaquette ladder, we predict and verify the existence of Quantum Many-Body Scars in spin-1 Quantum Link Models. The analysis of the model is facilitated by a dualization process that maps the original gauge theory to a constrained spin chain. Was it not for the constraint, the system would have an exact spectrum-generating algebra. We propose a set of observables for diagnosing an approximate spectrum-generating algebra, which is expected to guide quantum simulators toward interesting physical regimes.

Attaining the ultimate precision remains a central objective in the engineering of nanoscale systems and the investigation of nonequilibrium processes. While thermodynamic and kinetic uncertainty relations establish fundamental precision bounds, prior derivations in the quantum regime have remained confined to single-body systems. Consequently, the ultimate precision limits for interacting many-body systems have been unknown. In this Letter, we analytically formulate a kinetic uncertainty relation for a many-body system undergoing collective dissipation, a paradigmatic model of boundary time crystals. By applying a mean-field approximation, we derive lower bounds for relative fluctuations expressed in terms of clear physical quantities. Our analysis identifies a cooperative enhancement mechanism, demonstrating that collective interactions allow the precision to scale with the number of particles. We validate these findings through numerical simulations across the stationary, critical, and boundary time crystal phases. Our work presents the first theoretical description of precision bounds in collective dissipative quantum many-body systems for an arbitrary particle number $N$, providing a solid foundation for designing future quantum technologies that exploit many-body phenomena.

The quantum Rabi model has been a useful and pedagogical quantum model in the past decades, sufficiently simple to be solved analytically and intuitively understood, while sufficiently complex as to provide highly non-trivial eigenstates and a practical description of quantum optical platforms for quantum technologies. The Dirac equation, especially when restricted to 1+1 dimensions, is a simple toy model as well, but its easy diagonalization enabled historically to connect the electron spin to the fermionic statistics, among others. Both models share a symmetry at the purely mathematical level, namely, the spectra of each one has a dual equivalent under energy sign change, that I name a mirror dual symmetry. Usually, one quantizes these equations by assuming a ground state energy for the bosonic mode. But there is another option for the interpretation of the Hamiltonian, as I will argue, that is to assume a total symmetry principle, namely, that the total energy is zero at all times, for either the quantum Rabi model or the Dirac equation, and impose the constraint that every positive energy excitation has a mirror excitation of negative energy. This possibility, which was, apparently, ignored in the times when Paul Dirac was studying the implications of his equation, would avoid the worries in the scientific community that the negative energy solutions would decay until minus infinity, thus obviating the necessity to build a highly artificial Dirac sea, and instead impose what has always been successful in Physics, which is the enforcement of symmetry principles. Assuming a total symmetry principle, many of the problems of current Physics, such as renormalization of quantum gravity, dark matter, and dark energy, may possibly be automatically solved. One obvious result would be the automatic cancellation of the zero point energy.

In several articles, this author has advocated an alternative approach towards quantum foundation based upon a set of postulates, and based upon the notions of theoretical variables and of accessible theoretical variables. It is shown in this article that this basis can be considerably simplified. In particular, the assumption that there exists an inaccessible variable $φ$ such that all the accessible ones can be seen as functions of $φ$, can be dropped. This assumption has been difficult to motivate in the previous articles. From this, I get a simple basis for the main Theorems.The essential assumption is that there in the given context exist two different maximal accessible variables, what Niels Bohr would have called two complementary variables. From this, the whole Hilbert space formalism may be derived. It is also discussed in some detail how this Hilbert space should be chosen. The resulting theory is a purely mathematical theory, but it leads to qunantum mechanics by letting the variables be physical variables. Other applications of the main theory are also considered. The mathematical proofs are mostly deferred to the Appendix.

Parameterized stable homotopy theory organizes local systems of spectra over homotopy types, governed by a "yoga" of six functors. To provide semantics for the recently developed Linear Homotopy Type Theory (LHoTT), good model categories of these spectra are required, preferably monoidal with respect to the external smash product. We focus on the case of parameterized $H\mathbb{K}$-module spectra ($\infty$-local systems), motivated by recent applications of parameterized homotopy to topological quantum computing. While traditionally treated via dg-categories, we leverage combinatorial model structures on simplicial chain complexes to construct the first dedicated global model structure for $\mathbb{K}$-linear $\infty$-local systems, which offers better control than existing models for general parameterized spectra. In particular, when restricted to base 1-types, our model structure is monoidal with respect to the external tensor product, making it a candidate target semantics for the multiplicative fragment of LHoTT.

Quantum circuit complexity quantifies the minimal number of gates needed to realize a unitary transformation and plays a central role in quantum computation. In this work, we investigate the complexity of quantum circuits through coherence and imaginarity resources. We establish a lower bound on the circuit cost by the Tsallis relative $α$ entropy of cohering power, which is shown to be tighter than the one presented by Bu et al.[\textit{Communications in Mathematical Physics} 405, no. 7 (2024):161] under restrictive conditions. As a consequence, we obtain the relationships between the circuit cost and the coherence generating power via probabilistic average in terms of skew information/relative entropy, and present explicit bounds of the circuit cost for typical quantum gates. Moreover, we derive lower bounds on the circuit cost via the imaginaring power of the circuit, induced by the Tsallis relative $α$ entropy and relative entropy. We demonstrate that imaginarity can yield nontrivial constraints on the circuit cost even when coherence-based lower bounds are zero (e.g., for the $T$ gate), which implies that imaginarity may provide advantages under certain circumstances compared with coherence. Our results may help better understand the connections between quantum resources and circuit complexity.

We propose a quantum machine learning framework for estimating classical covariance matrices using parameterized quantum circuits within the Pauli-Correlation-Encoding (PCE) paradigm. We introduce two quantum covariance estimators: the C-Estimator, which constructs the covariance matrix through a Cholesky factorization to enforce positive (semi)definiteness, and a computationally efficient E-Estimator, which directly estimates covariance entries from observable expectation values. We analyze the trade-offs between the two estimators in terms of qubit requirements and learning complexity, and derive sufficient conditions on regularization parameters to ensure positive (semi)definiteness of the estimators. Furthermore, we show that the barren plateau phenomenon in training the variational quantum circuit for E-estimator can be mitigated by appropriately choosing the regularization parameters in the loss function for HEA ansatz. The proposed framework is evaluated through numerical simulations using randomly generated covariance matrices. We examine the convergence behavior of the estimators, their sensitivity to low-rank assumptions, and their performance in covariance completion with partially observed matrices. The results indicate that the proposed estimators provide a robust approach for learning covariance matrices and offer a promising direction for applying quantum machine learning techniques to high-dimensional statistical estimation problems.

The symmetry-resolved Krylov complexity is a useful tool in studying chaotic properties of systems that are endowed with symmetries. We investigate the conditions under which an invariant operator would have the symmetry-resolved Krylov complexity in a charge subspace identical to the Krylov complexity of the full operator. Further, we study the Krylov complexity of the Uncoloured Tensor Model, a disorder-free kin of the SYK Model which has a plethora of symmetries. We find charge subspaces of the same operator in which the equipartition holds as well as where it doesn't. We also find that within the computational limits, the Krylov complexity averaged over the symmetry subspace is bounded above by that of the operator in the full space.

When it comes to discriminating between two quantum states, trace distance is one of the well-known metrics used in quantum computation and quantum information theory. While there are several quantum algorithms for calculating the trace distance between two quantum states, computing it for any two general density matrices remains computationally demanding. In this paper, we propose a quantum algorithm based on the exponentiation of the density matrix and the improved quantum phase estimation (IQPE) to determine the trace distance for both pure and mixed states, with a time complexity of $O(N^8)$ where $N$ is the number of qubits of the given states. We demonstrate its ability to predict the quantity with proof-of-principle simulations and also quantum hardware computations on the IBM quantum computers, confirming its promise for near-term quantum devices.

The natural gradient descent optimisation technique is an efficient optimising protocol for broad classes of classical and quantum systems that takes the underlying geometry of the parameter manifold into account by means of using either the Fisher information metric of the classical probability distribution function or the Fubini-Study tensor of the associated parametrised quantum states in the consequent update rules. Even though the natural gradient descent procedure utilises the geometry of the space of probability or states, it is, however, insensitive to the measure of parametrised distance on the space of possible outcomes when the corresponding optimising problem is considered for the expectation value of a classical or quantum observable with respect to the probability distribution or the quantum state. In this work, we introduce a generic optimising principle, where the intrinsic geometry of the space of outcomes has been taken into account suitably, either by using an ambient space construction with a base statistical manifold with the usual Fisher information metric (or the Fubini-Study tensor), where the loss hypersurface is embedded to, or by means of a first-principle construction from the overlap of nearby quantum states on the projective Hilbert space. This construction as well as a family of conformal variants yields a form of loss-aware natural gradient updates that rescale the effective step size while preserving the descent direction. We benchmark the resulting optimisers on variational quantum circuit examples and on a classical neural network task, finding that, while the standard natural gradient remains the most robust on average, the proposed conformal schemes can improve best-case convergence in favourable regimes.

Quantum memories for optical states are essential resources for quantum communication and information processing. We propose a quantum memory protocol based on coherent photon-phonon transduction in a Brillouin-active optical waveguide supporting traveling acoustic modes. A pulsed pump drives an effective beam-splitter interaction between optical and acoustic fields, enabling the mapping of a propagating optical quantum state onto a traveling phononic excitation and its subsequent retrieval on demand. Using a continuum optoacoustic model, we show that the protocol enables broadband quantum state storage in a distributed medium without relying on discrete cavity modes. Analytical and numerical results demonstrate high-fidelity storage and retrieval of squeezed and entangled states under experimentally realistic parameters. The memory bandwidth is set by the Brillouin interaction and can reach hundreds of MHz. Our results identify continuum Brillouin optomechanical systems as a scalable platform for broadband quantum memories and multimode quantum signal processing.

For quantum algorithms for problems in which the task is to compute an entire field of values, like e.g. computational fluid dynamics (CFD), it is often proposed amplitude encoding w.r.t. multiple qubits; however, the efforts implied by it for initialization and read-out are not addressed. This work is devoted specifically to this issue: It reviews different encoding schemes in quantum computing, discussing their computational costs for initialization and read-out as well as resulting aspects for their usage via minimal examples. The considerations in previous literature on the required computational resources for amplitude encoding w.r.t. multiple qubits are extended in the presented quantification by explicitly deducing the circuit depth that results for the decomposed initialization procedure of V. V. Shende et al. [1, 2] and deriving an upper bound for the necessary number of executions of a quantum algorithm to extract the encoded values with a specific accuracy. For these two results, an empirical verification via the means provided by IBM's quantum computing simulation framework $\textit{Qiskit}$ [3] is given. In the framework of the study on the required number of runs to achieve a desired accuracy, it is however found that the derived upper bound, scaling like $ {\tilde{n}^2} ~ {\ln( {\tilde{n}} )} $ with the number of encoded values $ {\tilde{n}} $, is too conservative to be used for precise estimations. Therefore, a corresponding study of the required runs for the reference distribution of equal probabilities for all basis states is done in particular, which suggests $ {\tilde{n}} ~ { \ln( {\tilde{n}} ) } $ as an empirical scaling law. Since the view regarding CFD applications is taken here, it is presented in particular that the insights from this work lead to a new encoding approach, which is proposed specifically for a quantum algorithm for the lattice Boltzmann method.

A fundamental problem in quantum physics is to establish whether a multiparticle quantum state can be uniquely determined from its local marginals. In theory, this problem has been addressed in the exact case where the marginals are perfectly known. In practice, however, experiments only have access to finite statistics and therefore can only determine the marginals of a quantum state up to an error. In this Letter, we prove that unique determinability universally survives such local imperfections: specifically, for every uniquely determined state, we show that deviations of local marginals propagate to global states strictly bounded by a power law with exponent $α\in(0,1]$. This result induces a classification of multipartite quantum states by their power-law exponents, with linear scaling $α=1$ as the most favorable regime. We derive a necessary and sufficient criterion for linear robustness and translate it into an executable semidefinite-programming certification. Applying our theory, we prove that stabilizer states are inherently square-root robust and provide a complete robustness classification for the Dicke family. Finally, we exploit these results to construct a scalable two-local genuine multipartite entanglement witness, demonstrating the viability of this framework for broad practical applications.

As quantum computing moves from isolated experiments toward integration with large-scale workflows, the integration of quantum devices into HPC systems has gained much interest. Quantum cloud providers expose shared devices through first-come first-serve queues where a circuit that executes in 3 seconds can spend minutes to an entire day waiting. Minimizing this overhead while maintaining execution fidelity is the central challenge of quantum cloud scheduling, and existing approaches treat the two as separate concerns. We present Qurator, an architecture-agnostic quantum-classical task scheduler that jointly optimizes queue time and circuit fidelity across heterogeneous providers. Qurator models hybrid workloads as dynamic DAGs with explicit quantum semantics, including entanglement dependencies, synchronization barriers, no-cloning constraints, and circuit cutting and merging decisions, all of which render classical scheduling techniques ineffective. Fidelity is estimated through a unified logarithmic success score that reconciles incompatible calibration data from IBM, IonQ, IQM, Rigetti, AQT, and QuEra into a canonical set of gate error, readout fidelity, and decoherence terms. We evaluate Qurator on a simulator driven by four months of real queue data using circuits from the Munich Quantum Toolkit benchmark suite. Across load conditions from 5 to 35,000 quantum tasks, Qurator stays within 1% of the highest-fidelity baseline at low load while achieving 30-75% queue time reduction at high load, at a fidelity cost bounded by a user-specified target.

We demonstrate a mechanism for the production of massive excitations in graphs. We treat the number of neighbors at each vertex in the graph (degree) as a scalar field. Then we introduce a mechanism inspired by the Higgs mechanism in quantum field theory(QFT), that couples the degree field to a vector-like field, introduced via the graph edges, represented mathematically by the incident matrices of the graph. The coupling between the two fields produces a massless ground state and massive excitations, separated by a mass gap. The excitations can be treated as emergent massive particles, propagating inside the graph. We study how the size of the graph and its density, represented by the ratio of edges over vertices, affects the mass gap and the localization properties of the massive excitations. We show that the most massive excitations, corresponding to the heaviest emergent particles, localize on regions of the graph with high density, consisting of vertices with a large degree. On the other hand, the least massive excitations, corresponding to the lightest emergent particles localize on a few vertices but with a smaller degree. Excitations with intermediate masses are less localized, spreading on more vertices instead. Our study shows that emergence of matter-like structures with various mass properties, is possible in discrete physical models, relying only on a few fundamental properties like the connectivity of the models.

Spontaneous emission of a quantum emitter, such as an excited atom, is a fundamental process in quantum electrodynamics (QED), typically associated with exponential decay to the ground state accompanied by irreversible photon emission. This simple Markovian picture, however, is profoundly modified in the presence of time-delayed feedback, structured continua, or cooperative emission, as occurs when an emitter radiates in front of a mirror, when several emitters radiate collectively, or in the case of a giant atom. In such regimes, strong non-Markovian dynamics arise from photon reabsorption and interference effects, leading to pronounced deviations from exponential decay. Here we demonstrate the emergence of exceptional points (EPs) in these highly non-Markovian waveguide-QED environments, i.e., non-Markovian EPs. These EPs appear directly in the relaxation dynamics as sharp transitions to oscillatory behavior, manifested by the appearance of real zeros in the excited-state amplitude. We analyze in detail the spontaneous emission of giant atoms with two or more coupling points, highlighting the mechanisms leading to non-Markovian EPs, and show that similar phenomena arise in other waveguide-QED settings, such as the collective spontaneous emission of spatially separated point-like emitters. Our results reveal waveguide-QED systems as experimentally accessible platforms for realizing and exploring non-Markovian EP physics.

From gravity to electromagnetism, apparent action at a distance has always been resolved by deeper, local explanations. Yet today, Bell's theorem is widely interpreted as the death knell for local reality. In this chapter, I present the theorem in accessible terms, examine the three main strategies that attempt to preserve hidden variables, and argue that they share a common defect: the attempt to explain the quantum from the classical rather than the other way around. In unitary quantum mechanics, classicality itself is given a quantum account, and, when the Bell scenario is formulated in the Heisenberg picture, a strictly local explanation emerges. This chapter serves as a non-technical front-end to 'Explaining Bell Locally' (Proc. R. Soc. A).

Contextuality and measurement incompatibility are two fundamental aspects of nonclassicality, and their manifestations in observed quantum correlations are often deeply interconnected. Recently, measurement incompatibility has been studied in connection with nonlocality, particularly in terms of their robustness under various quantum channels. This line of investigation helps establish a connection between the channels that break nonlocality and those that break incompatibility. In this study, we focus on an asymmetric bipartite Bell scenario involving three and four inputs on Alice and Bob sides, respectively, with each of these inputs having dichotomous outcomes. Under the assumption of locality, the observed statistics in this asymmetric scenario obeys the Elegant Bell inequality (EBI). Here, we use a different version of the EBI that relies on the assumption of the preparation noncontextuality. By taking the violation of this noncontextual version of EBI as a witness of preparation contextuality we establish a connection between the channels that break contextuality and the channels that break triple-wise measurement incompatibility. Our results suggest that any channel which breaks EBI contextuality will also break Clauser-Horne-Shimony-Holt (CHSH) nonlocality; however, the reverse does not hold. We also show that a depolarising channel that breaks N-wise incompatibility can also break a certain form of contextuality, witnessed by a generalised inequality involving N measurements on one wing of a bipartite Bell scenario.

Recently, Yamaguchi and Kempf [Phys. Rev. Lett. 136:010801, arXiv:2501.02757] proved that encrypted qubits can be cloned. In this work, we generalize the encrypted cloning protocol and prove that it also applies to higher-order quantum systems. Given that a straightforward generalization of the protocol using the exponential of the shift and phase operators fails to satisfy the unitary requirement for a quantum gate, we propose a different approach. We introduce a new operator to be used in the encryption process and show that it is unitary. We adapt the decryption operator from the reference paper to fit in the framework of multi-level quantum systems. We analyze the circuit implementation of the proposed operators and show that the overhead imposed by larger dimensions scales linearly with qudit dimension.

The Boltzmann-Loschmidt dispute of 1876 questioned the possibility of a statistical irreversible description by time reversible classical equations of motion of atoms. Here we show analytically and numerically that the quantum chaos diffusion of cold atoms, or ions, in a harmonic trap and pulsed optical lattice can be inverted back in time with up to 100\% efficiency. This is in sharp contrast to classical evolution where exponentially small errors break time reversibility. We argue that the existing experimental skills allow highlighting the Boltzmann-Loschmidt dispute from a quantum perspective.

Quantum coherence provides a controllable thermodynamic resource that can raise or lower the effective temperature of a cavity mode, enabling efficiency tuning in quantum heat engines. Here, we derive analytic expressions for the effective engine temperature, demonstrating the enhanced temperature tunability achievable via $N$-level ground-state coherence. We further unify ground- and excited-state coherence within a single analytic framework, revealing their interplay as a mechanism for thermodynamic control. Such quantum resources serve as tunable parameters that enable switching between heating, cooling, and cancellation regimes, driving the effective temperature from near-zero to divergence. Ultimately, our framework connects and generalizes previous models of quantum heat engines, and we identify rubidium atoms as a promising candidate for experimentally realizing these coherence-assisted effects.

We propose a globally-admissible phenomenological spectral density of the bath for the non-Markovian Brownian motion of an optomechanical resonator, motivated by the near-resonance experimental observation of a non-Ohmic spectrum in [Nat. Commun. 6, 7606 (2015)]. To avoid divergences arising from a naive global extrapolation, we construct this phenomenological bath spectral density that reproduces the observed local-power-law behavior near the mechanical resonance while remaining well defined globally, ensuring the finiteness of the bath-induced renormalizations and quadrature fluctuations of the resonator. The corresponding model of the structured environment produces a nonlocal mechanical susceptibility whose analytic pole structure encodes the observed linewidth. The resulting dissipation kernel exhibits a power-law-modulated exponential decay with transient negativity, signaling strong memory effects. In the weak-coupling regime, the optical readout based on homodyne detection enables near-resonance spectroscopy and, with a calibrated drive on the resonator, permits, in principle, the reconstruction of the full mechanical susceptibility, thereby providing access to both the dissipative and dispersive bath contributions. Our results provide a consistent route from locally-inferred spectral properties to globally-admissible open-system descriptions and establish a framework for probing structured environments in cavity optomechanics.

Simulating lattice gauge theories on quantum computers presents unique challenges that drive the development of novel theoretical frameworks. The orbifold lattice approach offers a scalable method for simulating SU($N$) gauge theories in arbitrary dimensions. In this work, we present three improvements: (i) two new simplified Hamiltonians, (ii) an encoding of the SU(2) theory with smaller number of qubits, and (iii) a reduction in the requirement for large scalar masses to reach the Kogut-Susskind limit, achieved via the inclusion of an additional term in the Hamiltonian. These advancements significantly reduce circuit depth and qubit requirements for quantum simulations. We benchmarked these improvements using Monte Carlo simulations of SU(2) in (2+1) dimensions. Preliminary results demonstrate the effectiveness of these developments and further validate the use of noncompact variables as a promising framework for scalable quantum simulations of gauge theories.

Data-driven surrogates can replace expensive multiphysics solvers for parametric PDEs, yet building compact, accurate neural operators for three-dimensional problems remains challenging: in Fourier Neural Operators, dense mode-wise spectral channel mixing scales linearly with the number of retained Fourier modes, inflating parameter counts and limiting real-time deployability. We introduce HQ-LP-FNO, a hybrid quantum-classical FNO that replaces a configurable fraction of these dense spectral blocks with a compact, mode-shared variational quantum circuit mixer whose parameter count is independent of the Fourier mode budget. A parameter-matched classical bottleneck control is co-designed to provide a rigorous evaluation framework. Evaluated on three-dimensional surrogate modeling of high-energy laser processing, coupling heat transfer, melt-pool convection, free-surface deformation, and phase change, HQ-LP-FNO reduces trainable parameters by 15.6% relative to a classical baseline while lowering phase-fraction mean absolute error by 26% and relative temperature MAE from 2.89% to 2.56%. A sweep over the quantum-channel budget reveals that a moderate VQC allocation yields the best temperature metrics across all tested configurations, including the fully classical baseline, pointing toward an optimal classical-quantum partitioning. The ablation confirms that mode-shared mixing, naturally implemented by the VQC through its compact circuit structure, is the dominant contributor to these improvements. A noisy-simulator study under backend-calibrated noise from ibm-torino confirms numerical stability of the quantum mixer across the tested shot range. These results demonstrate that VQC-based parameter-efficient spectral mixing can improve neural operator surrogates for complex multiphysics problems and establish a controlled evaluation protocol for hybrid quantum operator learning in practice.

Contextuality and nonlocality are distinct manifestations at the foundation of quantum mechanics, yet their coexistence within a single quantum state remains subtle. In a hybrid CHSH--KCBS scenario involving the entanglment of a qubit and a qutrit, the qutrit supports the KCBS contextuality test, and the CHSH nonlocality arises from correlations between the qubit and qutrit. Here, we derive the analytical closed-form expressions for both inequalities and also simulate this physics on a quantum circuit. We show that contextuality is governed solely by a population parameter $p_2$, associated with the occupation of the qutrit subsystem in the $|2\rangle$ level, which plays a distinguished role in the KCBS structure. In contrast, nonlocality depends irreducibly on coherence, involving both amplitudes and phases encoded in parameters $(X_i, Y_i)$. This separation of physical resources reveals parameter regimes that optimize KCBS violation while suppress CHSH violation, and vice versa. As a result, the optimal regions do not overlap, and coexistence is restricted to a narrow intermediate regime in parameter space.

PulsePol is an elegantly designed pulse-sequence-based quantum control scheme that enables polarization transfer between electron and nuclear spins, for example, in nitrogen-vacancy (NV) centers. However, previous analyses of PulsePol assumed very strong, near-ideal, instantaneous microwave pulses, which is rarely achievable at higher magnetic fields. We revisit the PulsePol scheme under finite-pulse constraints and show that its performance significantly degrades due to finite-pulse effects. Using bimodal Floquet theory, we identify the symmetry-breaking mechanism responsible for this deterioration in fidelity. By phase adjustment, we reestablish the proper symmetry of the interaction-frame spin Hamiltonian, leading to a sequence called Q-PulsePol, where "Q" reflects the restored quadrature symmetry. Our results demonstrate robustness to finite-pulse effects and improved polarization transfer efficiency, establishing Q-PulsePol as a practical and reliable scheme for bulk hyperpolarization of nuclear spins in solids using a single-mode (zero-quantum or double-quantum) transfer. This work bridges idealized quantum control with realistic pulse engineering, establishing design rules for spin-based quantum control protocols.

This paper presents a quantum search approach to combinatorial constraint satisfaction problems, demonstrated through the generation of magic squares. We reformulate magic square construction as a quantum search problem in which a reversible, constraint-sensitive oracle marks valid configurations for amplitude amplification via Grover's algorithm. Classical pre-processing using the Siamese construction and partial constraint checks generates a compact candidate domain before quantum encoding. Rather than integrating classical and quantum solvers in an iterative loop, this work uses the classical component for structured initialisation and the quantum component for search, and benchmarks the quantum approach against classical brute-force enumeration and backtracking. Our Qiskit implementation demonstrates the design of multi-register modular arithmetic circuits, oracle logic, and diffusion operators. Experiments are conducted on small grid instances, as larger grids are intractable on classical statevector simulators due to exponential memory growth. The results validate the correctness of the proposed quantum search pipeline and confirm the theoretical quadratic query advantage over classical search.

We establish fundamental uncertainty relations for the hydrodynamic variables arising from the Madelung representation of quantum fields in curved spacetime. Through canonical quantization of the density $n$ and phase $θ$ variables and their conjugate momenta, we derive exact uncertainty principles that depend on spacetime geometry through the lapse function $N$ and spatial metric $γ_{ij}$. These relations reveal how gravitational fields modulate quantum fluctuations and provide first-principles constraints for scalar field dark matter models and stochastic quantum gravity.

We present QCommute, a software tool implemented in C++ for symbolic computation of nested commutators between a Hamiltonian and local observables in quantum many-body spin-1/2 systems on one-, two-, and three-dimensional hypercubic lattices. The computation is performed algebraically directly in the thermodynamic limit, and the Hamiltonian parameters are kept symbolic. Importantly, this way the entire parameter space is covered in a single run. The implementation supports extensive parallelization to achieve high computational performance. QCommute enables the investigation of quantum dynamics in strongly correlated regimes that are inaccessible to perturbative approaches, either through direct Taylor expansion in time or via advanced techniques such as the recursion method.

The phrase ``buy a quantum computer'' hides several different procurement problems. An institution may be seeking cloud access for teaching, reserved capacity for research, a local instrument for hardware training, an optimization appliance, or a strategic installation that reshapes facilities, staffing, and budgets. Because these choices differ in purpose, operating burden, and useful lifetime, the decision should be framed as acquisition of \emph{quantum capability} rather than selection of a presumed hardware winner. This manuscript develops a practical procurement framework that distinguishes five capability layers, separates peer-reviewed results from commercial offerings, pricing anchors, and public roadmaps, and compares the main commercial platform families -- superconducting circuits, trapped ions, neutral atoms, quantum annealing, and photonics -- through the lens of institutional fit, access model, and refresh pressure. The main conclusion is that most institutions should begin with the smallest layer of capability that produces repeatable near-term value, builds internal expertise, and preserves strategic flexibility. Large on-premises systems are justified only when mission requirements, site readiness, staffing, governance, and upgrade paths are already clear.

Theories of the measured homodyne current generated by a stochastic Schrödinger equation (SSE) can be tested in a simulation of the Einstein-Podolsky-Rosen (EPR) correlations for a two-mode squeezed state. We carry out such a simulation, and determine the correct stochastic term for the measured current in the broad-band limit. Stratonovich rather than Ito stochastic noise agrees with experiment. We show that this is relevant to measurement noise and errors in quantum technologies. By analyzing the SSE trajectories as measurement settings are changed, we propose a modern version of Schrodinger's gedanken experiment, where one measures position and momenta simultaneously, ``one by direct, the other by indirect measurement''.

The phenomenon of interaction-free measurement (IFM) enables the probabilistic detection of an absorbing object with reduced photon absorption. We report the experimental implementation of a simultaneous IFM of multiple objects using a single quantum probe on the cloud-based Ascella photonic processor of company Quandela. We demonstrate sequential IFM of up to 5 objects using a single photon, significantly extending the original IFM scheme for a single object. The experimental error-mitigated results confirm the theoretical predictions for this sequential IFM setup, and demonstrate a practical approach to scaling IFM to more complex quantum interrogation tasks.

We propose a quantum measurement-based framework for probabilistic transformation of grayscale images using adaptive positive operator-valued measures (POVMs). In contrast, to existing approaches that are largely centered around segmentation or thresholding, the transformation is formulated here as a measurement-induced process acting directly on pixel intensities. The intensity values are embedded in a finite-dimensional Hilbert space, which allows the construction of data-adaptive measurement operators derived from Gaussian models of the image histogram. These operators naturally define an unsharp measurement of the intensity observable, with the reconstructed image obtained through expectation values of the measurement outcomes. To control the degree of measurement localization, we introduce a nonlinear sharpening transformation with a sharpening parameter, $γ$, that induces a continuous transition from unsharp measurements to projective measurements. This transition reflects an inherent trade-off between probabilistic smoothing and localization of intensity structures. In addition to the nonlinear sharpening parameter, we introduce another parameter $k$ (number of gaussian centers) which controls the resolution of the image during the transformation. Experimental results on standard benchmark images show that the proposed method gives effective data-adaptive transformations while preserving structural information.

Combinatorial optimization problems become computationally intractable as these NP-hard problems scale. We previously proposed extraction-type majority voting logic (E-MVL), a quantum-inspired algorithm using digital logic circuits. E-MVL mimics the thermal spin dynamics of simulated annealing (SA) through controlled sparsification of spin interactions for efficient ground-state search. This study investigates the performance potential of E-MVL through systematic optimization and comprehensive benchmarking against SA. The target problem is the Sherrington-Kirkpatrick (SK) model with bimodal and Gaussian coupling distributions. Through equilibrium state analysis, we demonstrate that the sparsity control mechanism provides a consistent search of the solution space regardless of the problem's coupling distribution (bimodal, Gaussian) or size. E-MVL not only achieves the best performance among all tested algorithms-solving exact solutions up to 1600 spins where the best SA baseline is limited to 400 spins-but also provides insights that significantly improve SA's own temperature scheduling. These results establish E-MVL's dual contribution as both an efficient optimizer and a practical methodology for enhancing SA performance. Moreover, FPGA implementation achieved an approximately 6-fold faster solution speed than SA.

We present a systematic numerical investigation of the "entanglement geometry gravity" chain in random tensor networks (RTN) established by the ER EPR conjecture and Jacobson's thermodynamic derivation. First, we verify the kinematic foundation: the entanglement first law $δ\langle K\rangle=δS$ (slope=1.000), the encoding of geometry by mutual information (correlation=0.92), and the locality of holographic perturbations (3.3x). We also confirm that gravitational dynamics (JT gravity) does not emerge, identifying a sharp kinematics-dynamics boundary. Second, and more importantly, we discover that many-body localization (MBL) is the mechanism that protects emergent holographic geometry from thermalization. Replacing Haar-random evolution (geometry lifetime $t\sim6$) with an XXZ Hamiltonian plus on-site disorder, we observe a finite-size crossover at disorder strength $W_c\approx10-12$ above which mutual-information-lattice correlations persist indefinitely ($r>0.5$ for $t>50$). We map the full parameter space: the optimal regime is a near-Ising anisotropy $Δ\approx50$ with $W=30$ yielding $r=0.779\pm0.002$ (confirmed by a fine scan over $Δ\in[30,70]$); only holographic (RTN) initial states sustain geometry, while product, Néel, and Bell-pair states do not. MBL preserves the spatial structure of entanglement (adjacent/non-adjacent MI ratio ~2.6-4.2x vs. 1.0x in the thermal phase), rather than its total amount. A comparison with classical cellular automata reveals that MBL uniquely breaks the entanglement-structure trade-off imposed by quantum monogamy: classical systems achieve spatial structure only at the cost of negligible mutual information, while MBL sustains both.

We formulate a global-position colored-permutation encoding for the capacitated vehicle routing problem. Each of the $K$ vehicles selects a disjoint partial permutation, and the sum of these $K$ color layers forms a full $n\times n$ permutation matrix that assigns every customer to exactly one visit position. This representation uses $n^2K$ binary decision variables arranged as $K$ color layers over a common permutation structure, while vehicle capacities are enforced by weighted sums over the entries of each color class, requiring no explicit load register and hence no extra logical qubits beyond the routing variables. In contrast, many prior quantum encodings introduce an explicit capacity or load representation with additional qubits. Our construction is designed to exploit the Constraint-Enhanced QAOA framework together with its encoded-manifold analyses. Building on a requirements-based view of quantum utility in CVRP, we develop a routing optimization formulation that directly targets one of the main near-term bottlenecks, namely the additional logical-qubit cost of vehicle labels and explicit capacity constraints. Our proposal shows strong algorithmic performance in addition to qubit efficiency. On a standard benchmark suite, our end-to-end pipeline recovers the independently verified optima. The feasibility oracle may also be of independent interest as a reusable polynomial-time decoding and certification primitive for quantum and quantum-inspired routing pipelines.

This thesis develops a decision-theoretic framework for extracting thermodynamic work from temporal correlations in quantum systems. We model a classical agent -- lacking quantum memory -- performing adaptive work extraction through continuous inference and decision-making under uncertainty. By introducing $ρ^*$-ideal protocols, we demonstrate that exploiting memory effects allows adaptive strategies to surpass non-adaptive bounds. We formalize this via the Time-Ordered Free Energy (TOFE), a novel upper bound for causal, adaptive operations that reveals a thermodynamic gap linked to adaptive ordered discord. Additionally, we tackle work extraction from unknown sources using reinforcement learning. By adapting multi-armed bandit algorithms, we show an agent can simultaneously learn an unknown i.i.d. quantum state and extract work, achieving polylogarithmic cumulative dissipation that significantly outperforms standard tomography. Overall, this work lays the foundation for predictive and learning-based quantum thermodynamics.

Characterizing quantum states is essential for validating quantum devices, yet conventional quantum state tomography becomes prohibitively expensive as system size grows. Direct tomography offers a distinct route by enabling selective access to individual complex density-matrix elements, with a particular advantage for sparse target states and some verification tasks. Here we introduce a direct quantum state tomography scheme combining strong-measurement estimation with a fan-out coupling architecture. It enables mutually commuting interactions between system qubits and a single meter qubit, thereby achieving constant circuit depth, independent of system size. Notably, the involutory fan-out coupling reduces to the identity under repetition, enabling straightforward noise scaling for quantum error mitigation. We experimentally validate the scheme on a superconducting quantum processor via the IBM Quantum Platform, demonstrating four-qubit state reconstruction and single-circuit GHZ-state fidelity estimation up to 20 qubits with error mitigation. Consistent results with standard tomography and improved efficiency establish our scheme as a promising approach to reconstructing full quantum states and scalable verification tasks.

Quantum clock synchronization (QCS) aims to establish a shared temporal reference between distant nodes by exploiting uniquely quantum phenomena such as entanglement, single-photon interference, and quantum correlations. In contrast to classical synchronization and time-transfer techniques, which are limited by signal propagation delays, atmospheric disturbances, and oscillator drift, QCS protocols offer the potential to surpass classical precision bounds and enhance resilience against adversarial manipulations. As precise and secure time synchronization underpins distributed quantum networks, navigation systems, and emerging quantum Internet infrastructures, understanding QCS principles, capabilities, and implementation challenges has become increasingly important. This survey provides a unified and critical overview of the rapidly growing QCS research landscape, highlighting fundamentals, protocol types, enabling resources, performance constraints, security considerations, and practical implementations of QCS. We first introduce the theoretical underpinnings of QCS, including entanglement-assisted time transfer, Hong-Ou-Mandel interference-based synchronization, and quantum slow-clock transport. We then categorize the main QCS protocols, ranging from ticking-qubit and entanglement-based schemes to time-of-arrival correlation methods, conveyor-belt synchronization, and quantum-enhanced two-way time transfer. This organization clarifies the relationships between protocol families and their achievable precision advantages over classical methods. Key quantum resources such as spontaneous parametric down-conversion-based entangled photon pairs, Greenberger-Horne-Zeilinger and W multipartite states, squeezed and frequency-entangled light, quantum frequency combs, and quantum memories are reviewed in the context of scalability and robustness.

Quantum machine learning (QML) stands at the intersection of quantum computing and artificial intelligence, offering the potential to solve problems that remain intractable for classical methods. However, the current landscape of QML software frameworks suffers from severe fragmentation: models developed in TensorFlow Quantum cannot execute on PennyLane backends, circuits authored in Qiskit Machine Learning cannot be deployed to Amazon Braket hardware, and researchers who invest in one ecosystem face prohibitive switching costs when migrating to another. This vendor lock-in impedes reproducibility, limits hardware access, and slows the pace of scientific discovery. In this paper, we present a framework-agnostic quantum neural network (QNN) architecture that abstracts away vendor-specific interfaces through a unified computational graph, a hardware abstraction layer (HAL), and a multi-framework export pipeline. The core architecture supports simultaneous integration with TensorFlow, PyTorch, and JAX as classical co-processors, while the HAL provides transparent access to IBM Quantum, Amazon Braket, Azure Quantum, IonQ, and Rigetti backends through a single application programming interface (API). We introduce three pluggable data encoding strategies (amplitude, angle, and instantaneous quantum polynomial encoding) that are compatible with all supported backends. An export module leveraging Open Neural Network Exchange (ONNX) metadata enables lossless circuit translation across Qiskit, Cirq, PennyLane, and Braket representations. We benchmark our framework on the Iris, Wine, and MNIST-4 classification tasks, demonstrating training time parity (within 8\% overhead) compared to native framework implementations, while achieving identical classification accuracy.

A common view in monitored quantum dynamics is that local measurements suppress entanglement growth. We show that this intuition can fail in a one-dimensional spinful fermionic chain governed by a BCS Hamiltonian with pairing strength $Δ$ and subject to continuous, on-site, spin-resolved charge measurements at rate $γ$. Using free-fermion simulations and quasiparticle analysis, we show that pairing suppresses entanglement growth, while measurements suppress pairing. Their competition yields measurement-enhanced entanglement: for $Δ>0$, the steady-state entanglement $S_s$ increases with $γ$ over a finite interval $0<γ<γ_{\rm peak}$. This occurs because stronger measurements suppress pairing correlations, which would otherwise suppress entanglement growth. Using a nonlinear sigma-model calculation and free-fermion simulations, we provide evidence that for $Δ>0$ and small but finite $γ$, the steady-state entanglement scales as $S_s\sim \ln^2 L$. This implies that, in this setting, measurement-enhanced entanglement does not persist in the thermodynamic limit.

Beyond ground state energy estimation, quantum phase estimation (QPE) applied to many-electron systems has the potential to output a projection on the ground state, that would enable the evaluation of observables other than the energy. In this article, after recalling the role of QPE free parameters, we detail the derivation of first-order and unified conditions on unitaries that allow us to control the energy estimation precision and lead to tighter bounds than in previous works. We then introduce a novel condition that allows us to also control the state projection precision. We apply these conditions to a Trotterization case, leading to tighter bounds than the previous ones. The main results in this article are formal, with a first numerical illustration on the H2 molecule that allows us to derive useful insights.

Parametrised quantum circuits are a central framework for near term quantum machine learning. However, it remains challenging to determine in advance how architectural choices, such as encoding strategies, gate placement, and entangling structure, influence both the expressive capacity of the model and its trainability during optimisation. We introduce a data-agnostic framework, one requiring no knowledge of a training dataset or optimisation trajectory, that maps a broad family of circuits into a single architecture matrix built over learnable features and parameters. We show that this framework provides an explicit link between circuit structure, the correlations among learnable features, and the geometry of training kernels through the factorisation of each of these objects as quadratic forms in terms of these matrices. We show how correlations between learnable features arise from shared parameter-induced harmonics generated by non-commuting gate-observable interactions during Heisenberg back-propagation, and how these correlations are encoded directly in the architecture matrix. From this perspective, kernel structure and coefficient statistics can be reconstructed analytically from circuit design alone, without reference to a dataset or optimisation trajectory. The resulting framework makes circuit-induced structure explicit, separating architectural effects from data-dependent ones, and provides a principled foundation for analysing and comparing parametrised quantum circuits based on intrinsic, design-level signatures.

Unitary $k$-designs are central to quantum information and quantum many-body physics as efficient proxies for Haar-random dynamics. We study how chaotic Hamiltonian evolution can generate unitary $k$-designs. Standard approaches typically rely on many independent Hamiltonian realizations or fine-tuning evolution times. Here we show that unitary designs can instead arise from a quenched temporal ensemble, where Hamiltonians are sampled once and held fixed, while randomness enters only through the evolution times. We analyze a two-step protocol (2SP), applying $H_1$ for time $t_1$ and $H_2$ for time $t_2$, and a three-step protocol (3SP) with an additional quench, with all times randomly drawn from a prescribed distribution. Time averaging imposes energy-index matching in the frame potential (FP), which quantifies the distance to Haar random. Analytically and numerically, we show that 2SP cannot realize a general unitary $k$-design, whereas 3SP can do so for arbitrary $k$. The advantage of 3SP is that the additional random phases impose stronger constraints, eliminating independent permutation degrees of freedom in the FP. For Gaussian unitary ensemble Hamiltonians, we prove these results rigorously and show that under imperfect time averaging, 3SP achieves the same accuracy as 2SP with a parametrically narrower time window.

This paper completes a previous work by constructing a class of positive-energy relativistic spatial localization observables in Minkowski spacetime within quantum field theory, using the stress-energy-momentum tensor smeared with suitable test functions. For each timelike direction, the construction yields a family of positive operator-valued measures (POVMs) on spacelike hypersurfaces, well defined on every n-particle sector and satisfying a natural relativistic causality condition excluding superluminal propagation of detection probabilities. These observables arise from local or quasi-local field-theoretic quantities and provide a rigorous version of earlier heuristic proposals. In the one-particle sector, the construction reduces to the observable introduced previously, and its first moment reproduces the Newton-Wigner position operator under suitable normalization conditions. Because the normally ordered stress-energy-momentum tensor is not positive on the full Fock space, as implied by the Reeh-Schlieder theorem, we study quantum energy inequalities and derive lower bounds controlling deviations from positivity. This leads to regularized families of positive operators approximating the localization effects. We also construct conditional localization observables for finite laboratories using modified local energy operators and their Friedrichs self-adjoint extensions. Using Haag duality and Kadison's result on affiliation, we show that the resulting conditional POVMs belong to local von Neumann algebras and therefore commute for causally separated regions, in agreement with the Araki-Haag-Kastler framework. These results support the view that commutativity of localization observables is recovered at the level of conditional measurements in finite spacetime regions.

Mutually Unbiased Bases (MUBs) constitute a fundamental geometric structure in quantum theory, known for providing an optimal measurement scheme for quantum state tomography. In prime and prime-power dimensions, analytical constructions of maximal sets of MUBs are well-known and standard construction relies on the Weyl-Heisenberg (WH) group and finite fields. In non-prime-power dimensions, on the other hand, the existence of such maximal sets remains an open question. We present a generalized numerical method of constructing MUBs without any reliance on a priori group structure or specific algebraic frameworks. Formulating the problem at the level of Gram matrix, we reduce the search for complete sets of $d+1$ MUBs in dimension $d$ to a phase space optimisation problem. We use the fact that the MUB Gram matrix is a projection matrix, and the third- and fourth-order trace constraints are necessary and sufficient conditions for a valid projection matrix. We further develop a classification framework based on third-order Bargmann invariants and automorphism groups, allowing us to probe the underlying algebraic and geometric structure of the resulting configurations. Numerical applications of this method in dimensions $3$, $4$, and $5$ demonstrate that all numerically constructed solutions are mutually isomorphic, are isolated points in phase space, and possess automorphism groups that coincide exactly with the Clifford group, the normalizer of the WH group. Though the scope of the search was limited, in dimension $d = 6$ our numerical search yielded no MUBs within explored parameter space.

The development of quantum networks (QNs) relies on efficient mechanisms for distributing entanglement among multiple quantum users (QUs) under practical system constraints. This paper investigates the problem of entanglement rate maximization in a dual-connectivity (DC) wireless quantum network comprising multiple quantum base stations (QBSs). Under the DC architecture, each QU can associate with up to two QBSs, thereby enhancing resource utilization compared to conventional single-connectivity (SC) schemes. The joint QBS-QU association and entanglement generation rate allocation problem is formulated as a mixed-integer nonlinear programming problem that incorporates practical constraints, including limited QBS entanglement generation capacity as well as heterogeneous minimum entanglement rate demands and fidelity requirements for QUs. To efficiently solve this challenging problem, an alternating optimization (AO) algorithm is developed, which decomposes the original formulation into entanglement rate allocation and association subproblems. Simulation results demonstrate that the proposed DC architecture significantly outperforms SC schemes, while the AO algorithm achieves near-optimal performance with substantially reduced computational complexity.

We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply organize classical transport, become finite-width phase space structures under quantum fluctuations, and their overlap provides a geometric mechanism consistent with tunneling as fluctuation-induced delocalization of transport barriers. We demonstrate this approach for the Hamiltonian saddle, where path integral sampling reveals manifold broadening and barrier penetration. This establishes a geometric framework for studying phase space transport and tunneling beyond the classical regime, while also providing a natural route toward the application of LDs to field theory.

Combining optical tweezers with fluorescence microscopy is a powerful tool for single-cell analysis, playing a pivotal role in disease diagnosis, cell sorting, and the investigation of cellular dynamics. However, fluorescence detection faces challenges such as blinking, photobleaching and autofluorescence in biotissues. To address these limitations, we developed a magnetic detection strategy by integrating quantum magnetometry using nitrogen-vacancy centers into optical tweezers, demonstrating precise trapping and manipulation of individual cells in microfluidic environment. We detected a magnetic signal of 89 μT from a single cell labeled with magnetic nanoparticles, compared to a noise floor of 3.9 μT observed in unlabeled cells. This platform provides a promising approach for high-precision single-cell analysis and holds significant potential for probing cellular activities within biological microenvironments.

The rapid integration of Large Language Models (LLMs) into scientific writing fundamentally challenges traditional definitions of authorship, responsibility, and scientific integrity. As researchers transition from using computers as deterministic tools to managing them as ``virtual collaborators,'' the nature of human contribution must be re-evaluated. Using the drafting process of a recent computational physics manuscript as a case study, this essay explores the indispensable role of the Human-in-the-Loop (HITL). We demonstrate that while AI excels at structural organization and syntax generation, the human author bears the ultimate responsibility for enforcing rigorous physical logic, maintaining academic diplomacy, and anticipating peer-review critiques. In this paradigm, the human contribution shifts from writing boilerplate text to acting as a Principal Investigator who actively mentors and steers the AI's reasoning. To ensure accountability and preserve the integrity of the scientific record in this new era, I argue that the community must mandate the publication of full, unedited AI interaction transcripts as standard supplementary material.

Information flow is central to contemporary accounts of cognition, yet its physical basis in living neural matter remains poorly specified. Here, we develop a multiscale resource-theoretical framework motivated by the \textit{thermocoherent effect}, where heat flow is reciprocally coupled to a delocalized information flow carried by shared coherence and not reducible to local subsystem variables. Extending this line of work in light of recent results on correlation-enabled Mpemba-type thermal relaxation, we argue that the operational relevance of correlations depends less on their taxonomy than on their dynamical accessibility under the underlying interaction geometry. Relational structure encoded in the state of a single composite system -- including quantum entanglement, quantum discord, and classical correlations -- may therefore act as a usable physical resource that remains hidden from local subsystem descriptions. We propose that electrical, chemical, ionic, and thermal transport processes in neural matter may, under suitable microscopic conditions, generate or transduce partially hidden relational resources whose mutual coupling can progressively build larger-scale thermocoherent organization across spatial or spatiotemporal partitions in neural tissue. Ion-channel interfaces, hydrogen-bonded proton networks, aromatic $π$-electron architectures, and phosphate-rich motifs emerge as plausible substrate classes in which such resources may arise, become transiently accessible under environmental coupling, and leave coarse-grained signatures in neural dynamics. The resulting picture is neither a claim of macroscopic quantum cognition nor a reduction of cognition to abstract coding, but a falsifiable framework in which microscopic relational resources can bias transport, relaxation, signaling, and cross-scale neural coordination.

We introduce the notion of dismagicker: non-Clifford unitary gate designed to reduce the non-stabilizerness (also called magic) of quantum many-body states. Although both entanglement and non-stabilizerness are fundamental quantum resources, they require distinct control strategies. While disentanglers (unitary operations that lower entanglement) are well-established in tensor network methods, analogous concept for non-stabilizerness suppression has been largely missing. In this work, we define dismagicker as non-Clifford unitary operation that actively suppresses non-stabilizerness, steering states toward classically simulatable stabilizer states. We develop optimization method for constructing dismagickers within the Matrix Product States framework. Our numerical results show that the non-stabilizerness reduction procedure, when combined with entanglement reduction steps with Clifford circuits, significantly improves the accuracy for both classical simulation of many-body systems and quantum state preparation on quantum devices. Dismagicker enriches our toolkit for the manipulation of many-body states by unifying non-stabilizerness and entanglement reduction.

Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for complete sets of mutually unbiased bases in multipartite scenarios. We present lower and upper bounds of the quantum uncertainties based on the complementarity of the observables, the purity of the measured state, the (conditional) von-Neumann entropies, the Holevo quantities and mutual information. The results are illustrated by several representative cases, showing that our bounds are tighter than and outperform previously existing bounds.

Recently, studies have explored the statistics of matrix elements of local operators in the Lieb-Liniger model. It was found that the probability distribution function for off-diagonal matrix elements $\langle \boldsymbolμ|\mathcal{O}|\boldsymbolλ \rangle$ within the same macro-state is well described by the Fréchet distributions. This represents a significant development for the Eigenstate Thermalization Hypothesis (ETH). In this paper, we investigate a similar phenomenon in another solvable model: the disorder-free Sachdev-Ye-Kitaev (SYK) model. The Hamiltonian of this model consists of 4-body interactions of Majorana fermions. Unlike the conventional SYK model, the coupling strengths in this model are fixed to a constant, earning it the name ``disorder-free.'' We evaluate the matrix elements of operators constructed from products of $n$ Majorana fermions: $\mathcal{O} = χ_{a_1}χ_{a_2}\ldots χ_{a_n}$. For a general choice of indices and $n \geq 4$, we find that the statistics of the off-diagonal matrix elements are well-fitted by a generalized inverse Gaussian distribution rather than Fréchet distributions.

Tensor network methods, particularly those based on Matrix Product States (MPS), provide a powerful framework for simulating quantum many-body systems. A persistent computational challenge in these methods is the selection of the bond dimension chi, which controls the trade-off between accuracy and computational cost. Fixed bond dimension strategies either waste resources in low-entanglement regions or lose fidelity in high-entanglement regions. This work introduces an adaptive bond dimension management framework that uses von Neumann entropy feedback coupled with a Proportional-Integral-Derivative (PID) controller to dynamically adjust chi at each bond during simulation. An Exponential Moving Average (EMA) filter stabilizes entropy measurements against transient fluctuations, and a predictive scheduling module anticipates future bond dimension requirements from entropy trends. The per-bond granularity of the allocation ensures that computational resources concentrate where entanglement is largest. The framework integrates GPU-accelerated Singular Value Decomposition (SVD) via CuPy and the cuSOLVER backend, achieving individual SVD speedups of 4.1x at chi=256 and 7.1x at chi=2048 relative to CPU-based NumPy for isolated matrix factorisations (measured on an NVIDIA A100-SXM4-40GB GPU with CuPy 13.4.1 and CUDA 12.8). At the system level, benchmarks on the spin-1/2 antiferromagnetic Heisenberg chain demonstrate a 2.7x reduction in total DMRG wall time compared to fixed-chi simulations, with energy accuracy within 0.1% of the Bethe ansatz solution. Integration with the Density Matrix Renormalization Group (DMRG) algorithm yields ground-state energies per site converging to E/N = -0.4432 for the isotropic Heisenberg model at chi = 128. Validation against Amazon Web Services (AWS) Braket SV1 statevector simulator confirms agreement within 2-5% for small systems.

We present an analytical theory for the most subradiant modes in a finite one-dimensional emitter array coupled to either an ideal or a nonideal waveguide. Using an effective non-Hermitian Hamiltonian together with a Bragg-edge open-boundary ansatz, we derive compact eigenvalue expressions showing that the linewidths of the most subradiant states exhibit a universal N^{-3} scaling in both cases. However, in the deep-subwavelength regime, the decay rates display even-odd oscillations due to boundary interference. Furthermore, we demonstrate that the collective energy shift of the most subradiant state approaches a constant value that depends on the atomic separation, with the leading finite-size correction scaling as N^{-2}. These results unify the roles of Bragg-edge interference, finite-size effects, and near-field dipole-dipole interactions in shaping ultranarrow, strongly shifted subradiant resonances, providing a transparent framework beyond the ideal-waveguide limit and opening potential applications in subradiant spectroscopy and waveguide-QED-based sensing.