Quantum Physics Paper Analysis

Significant efforts are currently being directed toward the implementation of large-scale quantum information processors, but realizing useful quantum advantage also requires the development of efficient quantum algorithms. While for many practical problems the dominant resource costs are associated with a small set of computational primitives, optimizing them in the quantum setting presents unique challenges, including a reversibility constraint absent from ordinary classical computation. Here we introduce an evolutionary framework in which large language models (LLMs) propose circuit designs and an independent evaluator verifies and scores them. We apply this framework to tasks spanning numerical computation, chemistry, optimization, quantum simulation, and number theory. In seven of the eight tasks, the discovered circuits significantly reduce both Toffoli and qubit counts relative to the state of the art. In the eighth, the search discovers a new reversible architecture for prime-field modular inversion. By handling reversibility differently, the architecture makes divsteps -- a classical algorithm previously impractical for reversible integer arithmetic -- viable and substantially improves the Toffoli-qubit trade-off for modular inversion. These results open the door for evaluator-guided LLM co-design of new algorithmic structures for quantum computation.

Quantum low-density parity-check (qLDPC) codes have a canonical mixed state---the normalized projector onto the code space---that lies at the intersection of quantum error correction and quantum many-body physics, yet the stability of its information-theoretic structure under local noise remains poorly understood. Recent progress on mixed-state phases of matter has identified the spatial decay of conditional mutual information (CMI) $I(A:C|B)$ as a key diagnostic of such stability, analogous to the role of the spectral gap for quantum ground states. We prove that, for the normalized code-projector state of a $\mathbb{Z}_d$ qLDPC stabilizer code under local Pauli noise, the CMI across a buffer $B$ separating $A$ from $C$ decays exponentially with the width of $B$ in two complementary noise regimes independent of system size. At weak noise, this holds for full-system tripartitions, where correlations between the two sides require an error cluster to cross the buffer, an exponentially unlikely event. At strong noise, exponential decay holds whenever the buffer supports no logical operator, since correlations can persist only along rare chains of buffer qudits that remain informative. Under an additional space-uniformity assumption, we establish the robustness of Levin--Wen topological entropy. On finite-dimensional lattices of size $n$, the weak-noise bound further implies a constant-layer quasi-local Petz recovery channel of range $O(\poly(\log n)/\varepsilon)$ that recovers the noiseless state within trace-distance error $\varepsilon$. Both CMI bounds apply to general qLDPC interaction graphs, including geometries where such constant-depth quasi-local recovery need not exist. Thus, the exponential decay of the noise-induced CMI provides a general criterion for mixed-state phase stability.

The quantum-trajectory description of a noisy quantum circuit is not unique: every Kraus representation of the noise channel defines a different unraveling, i.e., a different ensemble of pure states that averages to the same density matrix. While all unravelings share the same expectation values of observables, they generally differ in the amount of quantum resources carried by the individual trajectories. Here we study non-stabilizerness, or magic, quantified by the stabilizer Rényi entropy, in quantum-trajectory unravelings of Haar-random and $T$-doped random Clifford brickwork circuits subject to local dephasing noise of strength $p$. The canonical unraveling in terms of Pauli jumps is Clifford and leaves magic untouched, so that trajectories retain the Haar-random value of non-stabilizerness. Exploring the full two-parameter family of minimal unravelings, we find that the trajectory-averaged magic can be substantially reduced by a state-independent choice of Kraus operators, and that the optimal choice is not in general the projective-measurement unraveling, but a two-outcome generalized measurement in which the Kraus operators correspond to a weak measurement of the noisy qubit. The optimal unraveling reduces the extensive magic density of the trajectories by a $p$-dependent factor without altering its linear scaling with system size. At the same time, it produces a very broad distribution of magic over trajectories, with a sizable fraction of trajectories retaining Haar-random magic. Since the cost of stabilizer-based classical simulation grows exponentially with the magic of the state, these high-magic trajectories, rather than the average, control the simulation cost. Our results delineate the potential and the limitations of unraveling optimization as a route to the classical simulation of noisy quantum dynamics with stabilizer methods.

Classical simulation of magic state factories, including distillation, cultivation, and code switching, is challenging because of their substantial non-Clifford content. We introduce $\texttt{magna}$ (magic-state-factory assessment via global network algebra), a classical simulator that simulates such protocols as cheaply as Clifford circuits. $\texttt{magna}$ expresses the figures of merit of a protocol, namely the acceptance rate and the fidelity of the accepted states, as tensor networks, which it reduces globally by exploiting a structural correspondence with transversal gates on quantum codes. $\texttt{magna}$ further supports feedforward conditioned on arbitrary functions of mid-circuit measurement outcomes, including decoder outputs. We simulate Bravyi--Haah distillation with up to 100 output magic states at a cost that does not grow exponentially in the number of outputs, and achieve state-of-the-art sampling times for distance-5 magic state cultivation on both color codes and RP$^2$ surface codes. Finally, we validate nonlinear feedforward on a logical-level distillation protocol with 15 rounds of decoder-dependent feedforward. $\texttt{magna}$ aims to contribute to the key infrastructure for the large-scale evaluation and optimization of magic state factories.

The classical capacity of a noisy optical channel is the maximum rate at which information can be transmitted reliably, given a constraint on the mean input energy. For the ubiquitous bosonic Gaussian channels, which include standard models of loss and noise in fibre and free-space optical links, determining this rate requires addressing whether entanglement between channel uses or non-Gaussian signals can outperform Gaussian encodings. More precisely, the question is whether the energy-constrained Holevo information is additive across arbitrarily many channel uses and coincides with its Gaussian counterpart. We answer these fundamental questions in the affirmative for every single-mode bosonic Gaussian channel at every input energy. Namely, we prove that independently prepared Gaussian states with Gaussian-distributed random displacements achieve the capacity, including in the low-energy regime where squeezing the signals competes with encoding information in their displacement. Our proof connects an entanglement inequality to a sharp, additive lower bound on output entropy. We then characterise communication above capacity: under a strict total photon-number cutoff, the probability of correct decoding decreases exponentially with the number of channel uses, and we derive explicit bounds on the decay exponent. When only the mean photon number is constrained, a simple energy-rescaling formula determines exactly the entire asymptotic rate--error trade-off: the capacity at mean photon number $N$ and allowed average decoding error $ε$ equals the vanishing-error capacity at mean photon number $N/(1-ε)$. Together, these results identify the ultimate limits of classical communication for some of the most fundamental models of optical communication.

Capturing static and dynamic electron correlation simultaneously at manageable computational cost remains a key challenge in electronic structure theory. Motivated by the recurring role of effective temperature in self-consistent field methods we extend the adiabatic connection mechanism from density functional theory to include a temperature dimension. This gives rise to thermally enhanced hybrid functionals, in which static correlation is captured via fractional occupations generated by an effective "correlation temperature" within thermal Hartree-Fock, while dynamic correlation is described by established density functional approximations. The framework formally unifies information-density matrix functional theory (i-DMFT) and thermally-assisted-occupation (TAO-)DFT as special cases, clarifying their theoretical basis and the respective prescriptions for the temperature parameter. We assess the performance of several thermally enhanced hybrids for different cases where i-DMFT was previously shown to fail. Furthermore, we discuss and test different schemes for determining the correlation temperature and investigate the accuracy of different such choices for a benchmark set derived from biphenyl. The results help to clarify the achievable balance of accuracy, generality, and efficiency, establishing thermally enhanced hybrids as a systematic route toward low-cost treatment of both correlation types.

Fault-tolerant quantum computing (FTQC) introduces substantial systems-level complexity through quantum error correction (QEC), making debugging FTQC programs challenging. Existing quantum debugging approaches primarily target logical-level circuits and do not naturally support debugging within realistic FTQC execution flows. We present SynDebug, the first systems-level debugging framework for FTQC programs. SynDebug introduces lightweight assertion-based debugging primitives that operate directly within encoded FTQC infrastructures while avoiding additional logical surface area and minimizing temporal overhead. We evaluate SynDebug across multiple QEC code families, code distances, and encoded workloads, including state preparation, entanglement validation, and Shor-style programs. Our results demonstrate that SynDebug enables practical FTQC debugging with an average 1.8% additional circuit depth overhead (0% in most cases) and no measurable increase in the logical error rate, showing that systems-level debugging for large-scale FTQC applications is both feasible and practical.

We investigate the fate of quantum many-body scars in the PXP model subject to Markovian dissipation. We show that when local jump operators respect the same symmetries of the Hamiltonian the full Liouvillian spectrum displays a tower of states with properties analogous to standard quantum scars: large overlaps with Néel states and equally spaced gaps in the imaginary part of the eigenvalues, set by a single frequency. Whether the long-time dynamics is dominated by scars is determined by the real parts of the eigenvalues, which are set by the ratio between the two relaxation rates $γ_{\pm}$ describing spin flips down-to-up or up-to-down respectively. For asymmetric dissipation ($γ_+ > γ_-$) the scarred eigenvalues have the smallest real parts: the resulting enhanced fidelity oscillations are further stabilized by staggered jump operators. In contrast, replacing the full projection operator in the dissipators with a partial one breaks the symmetries of the problem and is seen to destroy dissipative scars altogether.

Fault tolerant quantum computers greatly benefit from having both high fidelity entangling gates and a non-local qubit connectivity. However, most entangling gates for neutral atoms are local, requiring separated atoms to be moved using optical tweezers to yield entanglement between them. Here, we design a high fidelity Mølmer Sørensen-like entangling gate between neutral atoms coupled to a photonic cavity, enabling a programmable all-to-all connectivity through the shared cavity coupling. The gate is both robust to changes in cavity photon number, and enables selective entanglement between any subset of separated atoms through local laser addressing. This eliminates the need to physically move atoms to perform the gate, and therefore motional errors and erasure are suppressed. Using experimentally realistic parameters we demonstrate gate fidelities exceeding $F > 0.99$, with higher fidelities achievable through optimal control of the pump amplitudes.

We develop a technique to perform efficient unitary time evolution of a general spin Hamiltonian based on the system with identical qubits, as naturally realized by permutation symmetric atomic ensembles. We employ Cartan decomposition method to the associated Hamiltonian Lie algebra and construct the symmetry adapted generators to implement unitary operator of the ensemble Hamiltonian. This enables the compact circuit representations of the system dynamics in terms of experimentally accessible collective spin operations and exploits the Dicke basis structure of the ensembles as an effective qudit representation. We benchmark Cartan based evolution against both exact time evolution and the Suzuki Trotter product formula. Our results show that the Cartan protocol accurately reproduces the operator dynamics, spin expectation values, and fluctuation observables with zero error that are substantially smaller than those obtained through Trotterization while maintaining an optimized circuit structure. In addition, scaling analysis with the ensemble size demonstrates that the Cartan error remains independent of the atom number while the corresponding Trotter error increases with the system size, highlighting the improved efficiency of the Cartan approach for a larger system size.

The paradigm of a simple unstable theory in the sense of Shelah is the theory of the random graph, the Fraïssé limit of the finite graphs. Quantum error correction has a paradigm of its own, and we show that it is the counterpart of the random graph: the Pauli group on countably many qubits, taken modulo phases and with commutation as its relation, is the Fraïssé limit of the finite alternating spaces over the two-element field, and its form computes the syndromes of stabilizer codes. Seen through this correspondence, simplicity theory turns out to be a theory of error correction. Clifford encoding circuits implement the homogeneity of the Pauli group, forking recognizes the logical errors, and the independence theorem of Kim and Pillay is the gluing of syndromes. The two paradigms look alike as first-order structures, and they part company only when observables enter. Each defines a bipartite observable, and we prove that, once preparations are mixed, both acquire the tree property of the second kind in real-valued logic. They reach it by different roads, however, and we show that the probes decide which. The probes of the Pauli observable are the Pauli channels; for them the indicator of each syndrome sector is the difference of the responses of two uniform mixtures, and actual mixtures already witness the tree. The probes of the Rado observable see only marginals; conditions given by actual mixtures remain compatible on disjoint blocks, and the tree must be sought among idealized preparations.

Semiconductor spin qubits offer a promising route to compact and scalable quantum computers, combining long coherence times in isotopically purified silicon with compatibility with semiconductor manufacturing. Beyond computational speedup, their energy efficiency is an important consideration for future large-scale systems. We evaluate the power and energy requirements of a Loss-DiVincenzo spin-qubit quantum computer by analyzing the Quantum Fourier Transform (QFT) and benchmarking it against the classical Fast Fourier Transform (FFT). We develop a detailed energy budget, identifying cryogenic cooling as the dominant baseline contribution before quantum error correction (QEC). The comparison between the QFT and the classical FFT reveals that, for any quantum workload operating under a polynomially bounded sampling regime, the crossover in energy consumption occurs at smaller problem sizes than the crossover in execution time. Thus, quantum computing can become energetically competitive before achieving a speedup in execution time. We then incorporate surface-code QEC and analyze the energy costs of QEC cycles, gate synthesis, and decoding. At scale, instrumentation and decoding become dominant contributions, while cryogenic cooling imposes a constraint on scalability. We show that optimizing the control-signal demultiplexing ratio can reduce the overall energy cost by approximately two orders of magnitude. For a system with about one million physical qubits, we estimate a power consumption of approximately 100 kW, at least one order of magnitude below that of today's highest-performance classical computing systems.

Greenberger-Horne-Zeilinger (GHZ) states are multipartite entangled quantum states that play a central role in quantum information theory, with applications in quantum communication, cryptography, and distributed quantum computing. A major experimental goal is to create high-dimensional GHZ states using multiple entangled parties. Krenn, Gu and Zeilinger discovered a surprising bridge between these quantum-optical experiments and graph theory: certain photonic experiments can be represented by edge-coloured, edge-weighted graphs, and the dimension of the produced GHZ state equals the number of feasible monochromatic inherited vertex colourings. This led Krenn and Gu to conjecture that every GHZ graph with more than four vertices has dimension at most $2$. A counterexample would give a new high-dimensional multipartite GHZ construction, while a proof would clarify fundamental resource limitations in quantum optics. It is known that the conjecture holds for graphs of vertex connectivity at most $2$ [MFCS 2024], and that simple GHZ graphs with $n>4$ vertices have dimension less than $n/\sqrt{2}$ [Quantum 2024]. However, no general upper bound depending only on vertex connectivity was known. We prove that every simple connected GHZ graph $G$ with at least four vertices has dimension at most $2^{κ(G)-1}+\binom{κ(G)}{2}$, where $κ(G)$ is the vertex connectivity of $G$. We also prove new bounds in terms of edge connectivity and maximum degree.

Assuming only the solubility of Kirchhoff's laws, the conservation of energy, and the form of the constitutive relations, we present a flux-charge symmetric Hamiltonian formalism that always admits a symplectic reduction for nonsingular, well-posed circuits involving gyrators, inductors, and capacitors (LCG circuits) with arbitrary non-linearity. The formalism introduces a notion of circuit duality on non-linear non-reciprocal circuits and a family of point transformations that inserts, removes, and moves reciprocal elements across gyrators while preserving the Hamiltonian spectrum. With these transformations, we extend Tellegen's classic result that gyrators make reciprocal elements behave as their dual to non-linear reciprocal elements such as the Josephson junction and quantum phase slip. Furthermore, we present conditions under which non-reciprocal circuits can be transformed to dynamically equivalent reciprocal circuits.

It is common wisdom that a better understanding of how to quantify electron correlation should lead to more efficient treatments of the correlation problem. Here, we not only substantiate this view but turn it into a concrete, systematic framework for ground states. Since prominent correlation measures such as the nonfreeness depend only on the one-particle reduced density matrix, modeling the correlation energy as a function of such a measure naturally places the framework within reduced density matrix functional theory, while keeping the cost at mean-field level. Strikingly, the variable conjugate to the measure emerges as a ``correlation temperature'', thereby connecting correlation measures, functional theory, and effective temperatures. The framework rationalizes methods such as i-DMFT, and we illustrate its key concepts analytically for the Hubbard dimer and numerically for small molecular systems. This brings a fundamental question within reach: how much of the correlation problem can be solved at mean-field cost?

We introduce patchwork, a lattice-surgery compiler for arbitrary multi-qubit Pauli measurements on a prescribed narrow-corridor two-dimensional surface-code layout. Systematic geometric rules simplify stabilizer placement and gate scheduling, including for logical $Y$ measurements implemented using twist defects. We introduce measurement circuits and schedules that, together with protruding lobes of $Y$-extension patches, preserve the full effective code distance for all numerically tested code distances. To support parallel decoding, we develop a wavefront algorithm that partitions merged lattice-surgery patches into space-time commit, buffer, and cleanup regions. Simulations of three sequential multi-qubit Pauli measurements acting on ten logical qubits show that staged decoding achieves total failure probabilities close to those of monolithic decoding over the parameters tested. These methods provide an automated framework for fault-tolerant lattice surgery and a route toward scalable, real-time decoding.

Tests of gravity-mediated entanglement aim to determine whether two massive objects in spatial superposition can become entangled through their mutual gravitational interaction. In an ideal model, the two objects are often treated as pointlike branches, but real wave packets have a finite width and are also exposed to dephasing and residual non-gravitational forces. We study these effects in a two-branch gravitational cat-state model with Gaussian wave packets. The Newtonian interaction is averaged over the finite wave-packet width, and spatially correlated dephasing is included phenomenologically. We then ask a practical question: when does the generated state remain useful rather than merely entangled? To answer this, we examine Bell violation, teleportation fidelity, coherent information, Fisher information, and state distinguishability. We find finite parameter windows where the same state is Bell-nonlocal and teleportation-useful, but these windows shrink as the wave packets become broader or the dephasing becomes stronger. We also show that a residual electrostatic branch interaction can coherently cancel the gravitational nonlocal phase and strongly suppress the operational signal. The results identify finite-width and electrostatic tolerance boundaries that should be considered in future tests of gravity-mediated entanglement.

On a chain of exchange-coupled quantum dots a Heisenberg exchange pulse of area pi is a SWAP, so the parallel bubble-sort SWAP network of superconducting chains is native to exchange-only (EO) spin qubits, and any other pulse area fuses routing with an entangling interaction. We build a variational "bubble-sort exchange network" (odd-even transposition, one parameter per pulse) and study it as a Born machine read out by Pauli spin blockade. Exchange conserves total spin, so the reachable readout distributions are fixed by the total-spin content of the initial product state. For the two-spin singlet-triplet encoding we derive a selection rule -- outcomes with k triplet pairs are bounded by the initial weight in sectors S <= k (S = 0 excluded for k = 1) -- and prove by a transportation argument that it is also sufficient: the reachable distributions form the polytope cut out by the rule, and its total-variation floor is attained. Products of singlets and T0's forbid whole outcome classes; the Neel state forbids none; the three-spin EO code has no floor. We then distil, in noise-free simulation, next-token distributions of GPT-2 over restricted vocabularies into the network, with matrix-product-state (MPS) Born machines as classical control. At six logical qubits the three-spin chain reaches KL = 0.011 nat at depth N and 0.004 at 2N, below the bond-dimension-4 MPS; the two-spin chain from the Neel state reaches 0.014 at 2N and 0.004 at 3N, against 0.28-1.5 from singlet/triplet products for the first teacher. Final states lie largely outside the code space: leakage is a resource, not an error. No arrangement of disjoint pulses meets every pair in fewer than N-1 rounds, and at depth 2N the chain distils as well as a 2D array or non-local couplings. Sector-restricted simulation extends this to 10-14 logical qubits (up to 30 dots).

Classical simulation of quantum many-body dynamics is challenged by the rapid growth of operator complexity, particularly in higher dimensions where tensor-network methods become increasingly demanding. We develop state-adapted Pauli-weight propagation based on generalized $m$-body mean-field projections, which compress many-body observables into optimal low-body representations in a covariance geometry induced by the initial state. Combined with adaptive Krylov-like restricted Heisenberg dynamics, this provides an alternative to conventional Hilbert--Schmidt Pauli-weight truncation. We derive necessary and conditional sufficient bounds on low-body approximation accuracy using standard operator complexity measures and characterize possible dynamical failure mechanisms of the state-adapted method. Numerical benchmarks demonstrate substantial state-dependent accuracy gains, while identifying regimes of reduced accuracy or violations of Pauli spectral bounds. For a three-dimensional system of $80$ interacting spins, our method achieves strong body-order convergence, close agreement with independently converging tensor-network simulations, and substantially smaller sparse Pauli representations. These results establish state-adapted Pauli propagation as a promising approach to classical simulation of higher-dimensional coherent many-body dynamics.

We examine how a finite many-body system can function as an effective charger for a single-qubit quantum battery, using the Lipkin-Meshkov-Glick model as a paradigmatic setting. As our figure of merit, we consider the battery ergotropy while explicitly resolving the energetic flows across the composite system. In the absence of intra-charger interactions, we show that the generation of non-zero ergotropy is controlled by the competition between collective coupling and spectral mismatch. We further demonstrate that even passive positive-temperature charger states can generate finite battery ergotropy, provided the charger is sufficiently large and sufficiently hot. Intra-charger interactions restructure the charger spectrum and qualitatively modify the available energetic pathways. While they can enhance the amount of energy accessible for charging, they can simultaneously divert energy into internal many-body and battery-charger interaction channels, producing an energetic impedance to direct charger-to-battery transfer. Consequently, battery ergotropy alone is insufficient to characterize an effective many-body charger: the useful work generated and its energetic provenance must be assessed together.

In this work we study the application of two-photon correlated quantum states for high-precision time estimation. To achieve this, photon pairs were fed into a Hong-Ou-Mandel polarization interferometer to generate N00N entangled states with $N = 2$. Two- and four-detector schemes were considered, and the achievable time estimation precision of each was studied, with particular emphasis on the system's Fisher information in each case. Our results reveal that using a four-detector scheme, enabling the measurement of both coincidence and photon-bunching terms, achieves the maximum precision given by the quantum Fisher information, without the need of characterizing system losses. We also show that correlations between repetitions arise due to systematic errors, limiting the precision enhancement that can be obtained by increasing the number of repetitions. Taking these correlations into account, we show that the four-detector scheme outperforms the two-detector scheme in the precision of time-delay estimation. With the experimentally determined calibration uncertainties, the four-detector scheme improves the dispersion by a factor of 2 for the repetitions performed, reaching up to a factor of 4 as both schemes approach their systematic floors.

Realistic non-Gaussian operations, which can be implemented by mixing a nonclassical Gaussian state with a Fock state at a beam splitter and then heralding on a photon-number-resolving detector, are known to improve phase estimation in a Mach-Zehnder interferometer. The existing studies have considered the single-mode squeezed vacuum for difference-intensity and parity detection, and the two-mode squeezed thermal state for parity detection alone as the initial Gaussian resources. However, a real squeezer in the lab actually produces single-mode squeezed thermal light, which has not been studied in a coherent-plus-resource interferometer. We take up this case and using the phase space Wigner picture, we obtain the heralded state produced by photon subtraction, addition and catalysis on a single-mode squeezed thermal resource, and evaluate the corresponding phase sensitivities. Single-photon catalysis, which is useless on squeezed vacuum, becomes a useful operation for any thermal occupation above $\nth\simeq0.2$, and since it heralds with a probability near one-half, it turns out to be the best success-weighted operation over the whole thermal range. In the vacuum limit our results reproduce the known hierarchy, where two-photon catalysis is the best operation. The quantum Fisher information computations confirms that thermal noise enhances the phase information encoded in the catalyzed state, demonstrating that difference-intensity detection closely approaches the ultimate precision bound across most operational regimes, and, together with a loss analysis, verifies the robustness of the effect.

The use of reinforcement learning (RL) in the design of quantum control strategies for pulse level control of NISQ era quantum devices is attracting growing interest. Model-free RL, not requiring preexisting knowledge of the physical system, acts as a black-box optimization tool well suited for noisy devices. In this work, we provide a simulation-based analysis of the performance of model-free RL for state preparation and qubit gate design in a challenging setup: indirect control of NV nuclear spins in a spin-bath. In particular, the spin-bath is modeled via the generalized cluster correlation expansion accounting for magnetic impurities and intra-bath interactions. We analyze the performance of the RL agents by performing simulations with minimally observable environments and noisy, sparse rewards as introduced in (Phys. Rev. X 12, 011059), and compare them to other state-of-the-art black-box optimization tools.

We completely classify connected Cayley graphs over finite abelian groups that exhibit perfect state transfer in Grover walks. First, we show that a Cayley graph over any finite group exhibiting perfect state transfer has valency $1$, $2$, or $4$. For valency $4$, we prove that an abelian Cayley graph $\operatorname{Cay}(Γ,S)$ exhibits perfect state transfer if and only if $S=\{a,-a,a+h,-a+h\}$, where $h$ has order $2$, and $4\nmid |Γ|/2$. Combining this characterization with the valency-one and valency-two cases, we explicitly determine all pairs $(Γ,S)$ for which $\operatorname{Cay}(Γ,S)$ exhibits perfect state transfer. Our results extend the classification of circulant graphs of valency at most four obtained by Kubota and Yoshino [Circulant graphs with valency up to 4 that admit perfect state transfer in Grover walks, \emph{J. Comb. Theory Ser. A.}, 216 (2025) 106064] to Cayley graphs over arbitrary finite abelian groups and to all valencies.

Quantum computing offers a promising approach to non-perturbative simulations of quantum field theories, particularly for real-time dynamics and systems affected by the sign problem. Yet translating continuum field theories into quantum computations remains a challenging interdisciplinary task. Here we introduce \texttt{Jianmu-Q}, a multi-agent framework that transforms natural-language descriptions of quantum field theories into quantum simulation workflows. Specialized agents handle theoretical formulation, lattice discretization, qubit mapping, and circuit design, while physical consistency checks and independent numerical calculations provide validation throughout the workflow. We benchmark the framework on three field theories of increasing complexity: the $(1+1)$-dimensional Nambu--Jona-Lasinio and Schwinger models, and a $(2+1)$-dimensional $\mathbb{Z}_2$ gauge theory. Across these systems, noiseless quantum-circuit simulations converge toward independent exact-diagonalization and tensor-network results, while selected circuits are executed on IBM quantum hardware, demonstrating an end-to-end, validation-guided approach to quantum simulation of field theories.

Far-detuned frequency allocations in fixed-frequency superconducting processors mitigate spectral crowding but constrain cross-resonance interactions at practical drive amplitudes. Here, we demonstrate that a single strong drive induces a large $XX-YY$ interaction in the far-detuned regime, while a weak second tone tunes the accompanying $ZZ$ phase. The interaction realizes a 150-ns $\sqrt{\mathrm{bSWAP}}$ gate, which can directly prepare a maximally entangled state from the ground state. For the implementations on the same qubit pair at matched drive strengths, cross resonance gives a shorter CNOT operation, while $\sqrt{\mathrm{bSWAP}}$ gives a 33% shorter SWAP operation with a higher IRB fidelity. The multilevel theory further predicts a regime where stronger driving can yield a speed advantage for CNOT as well, a possibility absent in the two-level model. As an application of the $XX-YY$ interaction, we also demonstrate two-spin squeezing beyond the standard quantum limit through two-axis countertwisting. The interaction realized here complements cross resonance and offers a route to efficient gate synthesis and quantum simulation of interacting spin systems.

Protecting quantum batteries from environmental noise remains a challenge. Using exact Burshtein-Kubo equations, we study a two-spin quantum battery with Dzyaloshinskii-Moriya (DM) coupling under indepen dent local longitudinal random telegraph noise (RTN). At a fixed effective noise scale, the DM-assisted slow switching protocol yields a superadditive transient ergotropy gain and near-maximal ergotropy during the initial charging stage, while the no-DM slow-switching control reaches comparable ergotropy only in a later revival. A finite superadditive region persists at fixed RTN amplitude, with protocol-dependent location and gain. In the Ising model, the enhancement is nonmonotonic in DM strength, with intermediate coupling giving near-optimal performance. Dressed-channel analysis associates this enhancement with changes in transition frequencies and longitudinal-noise matrix elements that reduce slow-RTN spectral weight. Superadditivity also persists in the tested anisotropic XY model.

The quantum Buridan's ass problem concerns a network of interconnected nodes in which transitions between the nodes are governed by the laws of quantum mechanics. In such situations interference between probability amplitudes plays a key role in determining whether the probability of leaving the initial node is large or small and also the speed at which the associated transitions occur. In this paper we extend this idea to consider transitions between one given set of coupled nodes and the remainder of the network. We have in mind a quantum analogy to changing an opinion, in which the initially occupied set of nodes is one opinion bubble, with the remaining parts of the network corresponding to a different opinion. We find that quantum interference again plays a crucial role in the dynamics. A further key component is the role of symmetry between the nodes and their interconnections, as it is symmetry that lies at the heart of the Buridan's ass puzzle. In the classical Buridan's ass paradox it is symmetry between competing alternatives that freezes the ass into indecision. In the quantum case, however, interference results in a far richer dynamics.

Hong-Ou-Mandel interference underpins many photonic quantum information protocols and is commonly characterized by a single visibility parameter. This quantity is typically obtained by averaging over a fixed coincidence window, thereby discarding details of the underlying temporal structure that are critical in continuous-wave processes. Four-photon interference with continuous-wave sources furthermore requires photon pairs with long coherence times, which we generate in microring resonators and measure with ultrafast time-resolved detection. Here, we model and resolve their interference and temporal structure by recording all four photon arrival times and mapping their relative delays onto a three-dimensional coincidence histogram relative to a trigger detection. The resulting structure preserves relative arrival-time correlations that are usually discarded and enables post-processed optimization of coincidence windows to trade off visibility against count rate. This method provides a general benchmark for continuous-wave sources in interference-based quantum network protocols.

Selected configuration interaction (SCI) obtains accurate many-body solutions by variationally diagonalising the Hamiltonian in a sparse, iteratively selected set of configurations, but can lose compactness when the target state has broad configurational support. We introduce selected stabilizer interaction (SSI), a fully classical, SCI-inspired method that instead iteratively constructs a nonorthogonal subspace spanned by a systematically enlargeable set of selected stabilizer states. A single stabilizer, generated by Clifford operations, can encode a structured superposition of (possibly exponentially) many configurations, shifting the relevant compression from configurational to stabilizer sparsity. We benchmark ground-state energies, fidelities, superposition degrees and required expansion lengths against exact diagonalization and equivalent SCI schemes for the transverse-field Ising, XXZ Heisenberg, and Hubbard models, finding particularly strong compression from the stabilizer representation in the spin models, and increasing advantage with system size for these systems. The results establish a proof of principle for heuristic selected stabilizer diagonalization, while also identifying particular challenges in symmetry handling and effective exploration of the stabilizer space.

Emergency-priority traffic signal control requires reducing emergency-vehicle delay while limiting disruption to ordinary traffic. This work investigates a finite-horizon QUBO formulation and compares Exact QUBO optimization, QAOA, CVaR-QAOA, a quantum machine-learning policy, fixed-time control, and max-pressure control in a three-intersection corridor. The study evaluates three traffic-demand regimes, examines the effect of the emergency-priority weight, and compares quantum solutions with the exact QUBO optimum. The optimization-based controllers achieved reliable emergency progression across all tested demand regimes, while max-pressure produced lower ordinary-traffic delay. Increasing emergency priority reduced emergency travel time but increased congestion, with diminishing improvements at larger weights. CVaR-QAOA reproduced the exact QUBO solution more accurately than standard QAOA, although the resulting differences in closed-loop traffic performance were comparatively small.

Together with a right-handed neutrino, the fermions of one generation of the Standard Model are labelled by five bits, a combinatorial structure tied to anomaly cancellation. We make this precise. Anomaly cancellation is the vanishing of a cubic form, the defining property of triorthogonal codes, the quantum error-correcting codes behind magic state distillation. Removing the right-handed neutrino gives a $[[15,1,3]]_p$ code for every prime $p$, including the Bravyi-Kitaev code for $p = 2$. For qutrits it is the unique shortest distance-three triorthogonal code.

Understanding the microscopic environment of superconducting qubits is a central challenge for quantum technologies. Parasitic two-level systems (TLSs) of various microscopic origins are ubiquitous and limit qubit performance through decoherence, frequency drifts, and leakage. Recently, long-lived TLSs with lifetimes exceeding those of state-of-the-art qubits have been shown to induce correlated qubit dynamics, with direct implications for quantum error correction. Here, we perform wide-band quantum-jump correlation spectroscopy on flux-tunable transmon qubits and identify microscopic degrees of freedom that outlive the qubit by orders of magnitude. Pump-probe measurements at varying detunings from these objects reveal intrinsic lifetimes exceeding one second. Their weak coupling to the qubit, in the kilohertz range, is consistent with positional defects described by the standard tunneling model, without excluding other microscopic origins such as magnetic spin impurities or trapped quasiparticles. More broadly, these results establish superconducting qubits as a sensitive probe of exceptionally long-lived microscopic degrees of freedom and open a route toward their controlled access and functionalization.

Cold-atom quantum memories require a near-zero magnetic environment (residual field <1 microtesla) to mitigate Zeeman decoherence. Conventional three-axis active compensation suffers from inter-coil crosstalk and geomagnetic drift, which degrade the uniformity and long-term stability of the zero-field region. To address this, we propose a spatiotemporally cooperative feedback-controlled suppression architecture for magnetic interference. An integrally printed three-dimensional orthogonal coil frame mechanically suppresses inter-axis flux leakage. A spatial feedforward inverse matrix is introduced to algorithmically eliminate first-order cross-coupling. A dual-threshold hysteresis incremental-PI controller filters magnetometer quantization fluctuations and avoids frequent small jitter adjustments of coil driving currents. Hardware ablation experiments, long-duration stability tests and spatial magnetic-field mapping were conducted. Experimental results show that during a 714.4 s continuous steady-hold stage, the mean and maximum residual fields at the central point reach 0.112 microtesla and 0.224 microtesla, respectively. The overlapping Allan deviations of all three components remain below 5 nT for averaging times of 1.9-178.2 s. Based on differential-ferrofluid lattice-scan measurements combined with centre-constrained quadratic vector reconstruction and soft Maxwell regularization, a weak-field spatial distribution with an RMS variation of 5.65 microtesla is fitted within a spherical region of interest of radius 5 mm, where 67.5% of the model volume meets the sub-5 microtesla coverage criterion. For a prolate ellipsoidal region matching the atomic-cloud distribution with full axis lengths of 10, 5, and 5 mm, the upper field bound within 93.7% of the volume is 2.68 microtesla.

We determine the finite-horizon identification limits of a \(d\)-dimensional memory when the control interface is restricted to four shared, time-homogeneous generators. A writer encodes a message by applying a prefix word to a common root state. The verifier then applies a candidate-dependent query word followed by a shared terminal binary test, with each word of length at most \(T\). For fixed error tolerances \(λ_2>0\) and \(λ_1+λ_2<1\), the optimal identification sizes satisfy \(\ln N_{\mathsf Q,4}=Θ_{λ_1,λ_2}(\min\{d^2,T\})\) for arbitrary CPTP generators and \(\ln N_{\mathsf S,4}=Θ_{λ_1,λ_2}(\min\{d,T\})\) for stochastic maps. Four unitary letters and four permutation letters attain these respective bounds, showing that a four-letter reversible alphabet reaches the static code-size orders in optimal quadratic and linear word length. In the fully dimension-limited regime, this yields \(\ln N_{\mathsf Q,4}=Θ(d^2)\) versus \(\ln N_{\mathsf S,4}=Θ(d)\), establishing a quadratic quantum--classical separation in logarithmic code size. Low-overlap Grassmann and agreement-code packings supply the orbit endpoints, while exact inverse query words match each encoded state to its designated test. At the sharp boundary \(λ_2=0\), \(0\leqλ_1<1\), all four model classes satisfy \(\ln N=Θ(\min\{\ln d,T\})\). Thus any fixed positive false-acceptance tolerance activates the metric-packing regime, whereas zero false acceptance imposes an exclusive-witness constraint and yields the logarithmic-dimension boundary.

Riemannian optimization provides a natural geometric framework for designing quantum algorithms for ground-state preparation, most notably through quantum imaginary-time evolution. However, existing geometry-aware approaches primarily employ steepest-descent updates, leaving more advanced methods from classical Riemannian optimization largely unexplored. In this work, we introduce quantum conjugate gradient descent (QCGD), a quantum-compatible implementation of Riemannian conjugate gradient that combines the steepest descent direction with information retained from previous search directions. In our numerical experiments, the proposed approach achieves faster convergence per iteration than the baseline double-bracket quantum imaginary-time evolution (DB-QITE) algorithm, and we quantify the associated circuit cost with gate counts produced by Qrisp. This improvement, however, comes at the cost of increased circuit depth for each update step, revealing a trade-off between convergence rate and implementation complexity. Nevertheless, since the circuit depth for those algorithms grows exponentially with the number of iterations, the proposed method may offer practical advantages, particularly in the early fault-tolerant regime.

Angle-encoded variational quantum circuits implement truncated Fourier series. For one-dimensional inputs, a single-qubit re-uploading (serial) circuit represents every function that a multi-qubit circuit with the same encoding budget $E$ can; we find that this exchange of width for depth is not free in first-order training. Because its state lives on the Bloch sphere, all parameters of the serial circuit move the state, at each input, along one complex direction, which we call \emph{phase-locking}. We prove that this costs no Fourier direction but leaves no direction to spare: however many parameters it has, the serial circuit has at most $2E+2$ tangent directions, one more than its $2E+1$ Fourier coefficients need, while a two-qubit control with the same encoding budget and model class generically has at least $6E+6$. The cost in training is measured against this control, as the number of runs out of 100 that reach the optimum within a fixed step budget. On an exact loss with flat-spectrum targets the gap grows with $E$; at $E=32$ the serial circuit converges in 3, 53 and 83 runs under gradient descent, Adam and Levenberg--Marquardt, the control in 99, 100 and 100. On three real-world series, at matched parameter counts, the serial circuit reaches the least-squares optimum in at most 9 runs under Adam and in 32 to 93 under Levenberg--Marquardt, the control in at least 98 and in all 100; its held-out error is up to about $1.5$ times that of the control under Adam, but no larger in the typical run under Levenberg--Marquardt.

Finite rate randomness expansion (RE) which is secure against quantum adversaries is a crucial information processing task which is well studied in the case of two non-communicating parties sharing Bell non-local correlations in a device independent manner. In this paper we show that contextual correlations with only a single localized party are sufficient for RE in a semi-device independent (SDI) manner. We propose a template SDI-RE protocol which is applicable for arbitrary $N$-cycle non-contextuality (NC) inequalities and derive its RE rate under finite statistics. As a special case, we also highlight the advantages of the situation when RE is constrained by Clauser-Horne-Shimony-Holt (CHSH) inequality but with characterized measurements implemented by only a single party. Our template protocol also incorporates non-ideal statistics which may not satisfy perfect commutativity and perfect repeatability, both of which are necessary in a loophole-free test of NC inequalities. As such, several recent experimental implementations of significantly loophole-free tests of NC inequalities can be modified for secure RE following our approach.

A deconfined quantum critical point (DQCP) is a continuous transition between ordered phases with unrelated broken symmetries, beyond the Landau-Ginzburg-Wilson paradigm. In one dimension, such a transition between a $z$-polarized ferromagnet (zFM) and a valence-bond solid (VBS) is well established numerically in a frustrated spin-$1/2$ chain. Here we ask whether a superconducting quantum processor can resolve this transition and its signatures despite finite-size effects and device noise. The ground states are prepared by ancilla-projected quantum imaginary-time evolution (QITE), whose exact target states are compressed by tensor-network optimization into shallow depth quantum circuits. The hardware data distinguish the phases through their order parameters, spin and dimer correlations, structure factors, correlation ratios, and snapshot distributions. The crossing of the order parameters locates the transition, and its finite-size extrapolation lies close to the thermodynamic-limit value obtained from large-scale numerics. A noise model based on the device calibration accounts quantitatively for the reduced amplitudes measured on hardware. Our findings demonstrate that a Landau-forbidden transition between competing orders can be resolved on current quantum processors.

Distributing entanglement directly between error-corrected logical qubits is an important capability for scalable quantum networks. We propose a heralded protocol for generating remote entanglement between Gottesman--Kitaev--Preskill qubits encoded in the motional modes of spatially separated trapped ions, using the internal electronic states to interface the motional qubits with emitted photons. We derive the protocol for single-rail and polarization photonic encodings and evaluate the effects of finite GKP squeezing, photon loss, photon recoil, motional heating, and motional dephasing on the decoded logical state. Moreover, we numerically analysed the fidelity of distributed logical Bell-pair fidelity. We find that one can achieve more than 95% of fidelity in the realistic situation. The protocol combines motional-control and photonic-networking operations that have already been demonstrated in trapped-ion experiments.

We study the von Neumann operator-space entanglement entropy (OSEE) of initial product operators evolved under random gaussian dynamics, as modeled by a Brownian SYK$_2$ model. By exploiting a mapping to a domain-wall melting problem, we derive an exact expression for the time-dependent bipartite OSEE in the thermodynamic limit, and obtain an analytic characterization of the corresponding gaussian Page curve emerging at late times. Our results build on recent work on the entanglement dynamics in the all-to-all quantum simple exclusion process, leveraging tools from RMT, including the Coulomb-gas approach and a mapping to the free Jacobi process. Finally, based on our results, we discuss the possibility of relating the OSEE with non-gaussianity measures in the Heisenberg picture.

Quantum programs pass through compilers, transpilers and vendor services before execution. However, the distance between what was written and what runs is rarely measured. We call this distance realization divergence: the observable difference in how an identical source circuit is realized and behaves across quantum software stacks. We report a hardware study across three vendors and four devices, combining pre-registered predictions with explicitly identified exploratory analyses and amendments. In a compilation experiment with assigned placement policies, embedding radius correlates with two-qubit overhead at Spearman 0.805, against 0.492 for circuit size. Under a fixed lowest-index policy, an eight-qubit Bernstein-Vazirani circuit exhibits greater execution divergence than a twelve-qubit circuit on IQM Emerald. The opposite ordering occurs on IQM Garnet. Both comparisons replicate across two repetitions with disjoint confidence intervals. These results support a placement-dependent explanation, without isolating individual hardware noise mechanisms. The same ordering inversion is absent on the all-to-all IonQ control. On Rigetti Cepheus, a follow-up using topology-aware native placement found no consistent advantage in correct-answer probability for either submission track, but did not establish equivalence between the tracks. Structural comparisons depend on metric weighting, placement and device generation. Provider interfaces also limit observability: Rigetti's supported-operation list remained unchanged across a device generation that replaced the native entangler. We classify silent interface failures in composed toolchains and identify checks at toolchain boundaries, connecting valid cross-provider comparisons with concrete software-quality practices.

High-order harmonic generation from molecules is highly sensitive to molecular geometry and strong-field electron dynamics, providing a powerful route for probing and controlling ultrafast processes in extended systems. In this work, we systematically investigate the influence of molecular chain length on HHG from linear carbon-chain molecules C$_2$H$_2$, C$_6$H$_2$, and C$_{10}$H$_2$ driven by an 800 nm linearly polarized laser field. To isolate the molecular-size effect from the influence of different ionization potentials, the laser intensities are adjusted to maintain the same Keldysh parameter for different molecules. Real-time time-dependent density functional theory simulations are performed with the molecular axis aligned parallel to the laser polarization direction. The results show that increasing the molecular chain length significantly enhances the harmonic yield and tends to extend the cutoff region. In particular, C$_{10}$H$_2$ exhibits much stronger plateau harmonics than C$_2$H$_2$, while the intermediate molecule C$_6$H$_2$ shows harmonic intensities between those of C$_2$H$_2$ and C$_{10}$H$_2$. Time-frequency analysis and charge-density evolution reveal that the enhanced HHG emission in longer chains originates from the enlarged electron acceleration distance and increased probability of multi-center recollision, especially near the terminal carbon atoms. These findings demonstrate that molecular-size engineering offers an effective strategy for controlling harmonic emission and optimizing attosecond light sources in extended molecular systems.

Previous studies on the vibrational structure of carbon dioxide isotopologues have revealed a correlation between the strength of Fermi interactions and a recently defined normal-mode parameter. In this contribution, we investigate how the Raman intensities of the most intense bands evolve across the complete series of carbon dioxide isotopologues at room temperature. To this end, we introduce a general scheme for simulating Raman intensities in linear triatomic molecules, based on the computation of the mean polarizability surface up to cubic terms for all twelve stable species. For the first time, we establish correlations between the degree of normality and the Raman transition intensities, mean polarizability derivatives, and variational Raman shift errors across the CO$_2$ isotopologue series. The observed trends are further analyzed by considering rotational contributions, which may partially account for the deviations observed in the correlations. Our study is supported by experimental Raman spectra of isotopically enriched samples and theoretical simulations. Although this study focuses on carbon dioxide, similar behavior is expected for other series of isotopologues.

Driven-dissipative collective spin systems can host several long-lived metastable states; rare switching between them governs slow relaxation and first-order dissipative phase transitions associated with changes in the dominant stationary state. In the companion Letter [arXiv:2604.15091], we introduced a quantum instanton framework based on exact quasiprobability dynamics to describe this switching and illustrated it with a minimal model possessing a simplifying symmetry. Here we develop its numerical implementation, combining collocation and shooting methods, and apply it to two microscopically motivated systems: the Lipkin-Meshkov-Glick model with purely collective dissipation and the cooperative resonance fluorescence with collective and local dissipation. By determining the leading exponential scaling of switching rates between metastable attractors, we predict the stationary magnetization, the first-order dissipative phase-transition point, and the exponential scaling of slow relaxation rates. These predictions agree with quantum master-equation calculations and an exact analytical result for the second model without dephasing. We also examine how the choice of quasiprobability representation affects numerical convergence and find that the alternative semiclassical Wigner approach, based on Gaussian truncation, has varying accuracy across models and parameter regimes. These results substantiate the framework's applicability to experimentally relevant collective spin systems with both collective and local dissipation.

Diffusion language models generate text by reversing a classical diffusion process over token sequences. We show that their continuous-time forward and reverse dynamics can be embedded in the framework of open quantum systems, which describes quantum systems interacting with their environment. This connection provides a basis for extending diffusion sampling to superpositions of sentence states and for modifying the underlying generation dynamics. We construct a $τ$-leaping unraveling scheme that simulates stochastic trajectories of these states while updating multiple token positions at each step. This enables generation conditioned on superposed prompts or thoughts, which we call Superposition of Prompts (SoP) and Superposition of Thoughts (SoT). The same formulation yields Quantum-Inspired Remasking (QIR): perturbing the masked-diffusion dynamics produces a confidence-based rule for revising previously generated tokens. Experiments with pretrained diffusion language models show that superposition-based generation can retain information from conditioning components not selected at the final measurement, while QIR improves LLM-assessed text quality when applied at an appropriate stage of generation.

We present the theoretical description of a resistive nanoswitch designated for a change-over between the two operation modes by calculating the electri elastic, dispersion (van der Waals and Casimir), and also exchange repulsive forces in its configuration with an account of surface roughness. The dispersion forces are described by means of the Lifshitz theory and, at the shortest separations between the interacting bodies, where this theory is inapplicable, by the method of additive summation of the interatomic potentials corrected for the role of the effects of nonadditivity. The exchange repulsion is also found by a summation of the interatomic potentials and using the proximity force approximation. It is shown that the nanoswitch possesses the equilibrium closest separation between a cantilever tip and a ground plate calculated as a function of the actuation voltage and operates in a cyclic manner with no pull-in when this voltage is switched on and off. We have found the tunnel current between a cantilever tip and a plate and investigated distortions appearing in the signal transmitted through a nanoswitch. According to our results, the amplitude distortions arising in the low-frequency information signal can be made sufficiently small by increasing a difference between the amplitudes of the carrier and information signals. Possible applications of the obtained results are discussed.

The quantum random energy model (QREM) is a paradigmatic model for studying delocalization-localization transitions at finite energy density in Fock space. In the computational basis, its diagonal energies are independent Gaussian random variables, in contrast to the correlated energies of local interacting models such as the disordered XXZ chain. In this work, we construct a potential energy shell associated with a basis state, defined through its energy variance, and investigate its connectivity on the Fock-space hypercube. As the transverse field is varied, this energy-selected subgraph undergoes a finite-size geometric crossover between fully connected and fragmented regimes. Furthermore, we observe a correlation between the shell connectivity and the finite-size fractal dimension of the eigenstates, as extracted from the participation entropy. For the QREM, the statistical independence of the diagonal energies allows the shell connectivity to be analyzed as an effective independent site percolation problem on the hypercube, with its crossover scale estimated within a one-hop approximation. At finite energy density, this estimate gives a nonmonotonic dependence of the crossover scale on system size $L$: increasing $L$ initially favors connectivity, while beyond an energy-dependent scale $L^*(\varepsilon)$ the trend reverses towards fragmentation.

Assembling defect-free arrays of neutral atoms requires real-time rearrangement of stochastically loaded optical tweezers. Conventional rearrangement methods shuttle atoms sequentially, whereas high-speed spatial light modulators (SLMs) can move all atoms in parallel, which scales more favorably as the array size grows. For fast parallel rearrangement, the sequence of holograms displayed on the SLM should be computed more rapidly than the SLM refresh rate, and there should be phase continuity between successive holograms to minimize transient intensity fluctuations. We calculate holograms analytically by adding together the complex fields needed to produce each individual trap, and we ramp the phase of each trap linearly as it moves to its target location. Trap positions enter as continuous variables, rather than tied to points on a grid, so the method provides high positioning accuracy. Using a single GPU, we compute each intermediate hologram in 0.284 ms, considerably faster than the SLM refresh time of 0.696 ms, so the rearrangement speed is hardware-limited. In each step, we use the free processing time to iteratively optimize the holograms for equal intensity across the traps, decreasing trap non-uniformity to 1.24% during rearrangement at no cost in total time. Starting from an array of 256 sites loaded stochastically with $^{87}$Rb atoms, we assemble a 100-atom array in under 20 ms with a rearrangement survival probability of 99.31(12)% per atom. This rearrangement increases the temperature of the atoms by 9(3) $μ$K, which is small compared to the trap depth of 480 $μ$K. Our method can also move individual atoms axially, enabling transport in different planes. We demonstrate this capability with a rearrangement protocol where one set of atoms leapfrogs over another.

It is known that under particular hypotheses anomalous thermalization processes can occur, such as the Mpemba effect, consisting in a faster cooling down when the system is prepared in a hotter initial condition, thus making convenient to warm up the system before the freezing process in order to make it freeze in a shorter time. It is shown here that the action of a Markovian classical noise during the freezing process can accelerate the approach to the zero-temperature thermal state. This prediction is counterintuitive, especially after observing that a classical noise can be considered equivalent to the action of an infinite-temperature reservoir, since both drive the system toward the same state. These facts lead to the statement that warming up the system during the contact with a low-temperature reservoir can accelerate the cooling process.

Logical CCZ states enable Toffoli gates, a central building block of fault-tolerant quantum arithmetic. We introduce an end-to-end protocol for direct CCZ-state preparation on bivariate tricycle and bicycle (BT/BB) codes. Our factory combines the cup-product CCZ gates native to BT codes with two novel ingredients, both enabled by engineering the logical coupling between BT and BB codes through projection-preserving lifts. Index-2 lifted BB ancillas enable selective $Z$-basis initialization, allowing the native cup-product gates to directly prepare two disjoint logical CCZ states. The prepared CCZ states are faithfully transferred to index-3 lifted BB memories with high code distance. We use decoder-based postselection to obtain high-fidelity output states with low overhead. We perform exact simulations of our factory under a circuit-level noise model motivated by neutral-atom hardware, obtaining joint infidelities of $1.84\times10^{-5}$ at $21.94\%$ acceptance and $4.10\times10^{-7}$ at $8.89\%$ acceptance for single-qubit, CZ, and CCZ error rates of $0.01\%$, $0.1\%$, and $0.5\%$, respectively. At the output-infidelity target of our smallest factory, its estimated spacetime cost per CCZ state is lower than that of $T$-state cultivation followed by CCZ conversion, providing an efficient route to logical CCZ states for fault-tolerant quantum computation.

Side-channel attacks on block ciphers rarely recover the key outright: they leave a residual key space ordered by subkey posteriors, and evaluation laboratories report the key rank of the true key against thresholds near 2^48 and 2^60. No evaluation framework models an adversary who collects traces classically and finishes the search on a quantum computer, although quantum search with advice provides exactly that. We give such an adversary a cost model and a metric. For a device whose key has rank r, any quantum algorithm with classical access to the posteriors needs Omega(sqrt(r)) cipher evaluations, and block search achieves O(sqrt(r)); the per-instance advantage is exactly quadratic, and the super-quadratic exponents reported for search with advice are averages over the prior that apply to no single device. Under the NIST MAXDEPTH budget D and a Grover iteration of g gates and depth d, the quadratic advantage holds only for ranks up to (4D/(pi d))^2 and collapses to a constant factor beyond; with the best published AES-128 oracle and D = 2^40 the window closes near rank 2^58.6. We define the quantum-aware key rank, the classical rank of equal cost, computable from the rank estimators laboratories already run, and derive the classical rank a device must retain to keep a given threshold against each depth budget. Block search and amplitude amplification from the product-form posterior state are within a factor of two to four of each other on Hamming-weight posteriors, so the cost of coherent indexing decides between them. Experiments on simulated leakage and a toy cipher confirm the predicted window: at SNR 0.125 a depth-limited quantum adversary is worth about 22 traces to a classical one, however large its gate budget.

A quantum memory can preserve a subsystem perfectly while discarding information needed by a later operation. We study the total intermediate dimension required for channel synthesis when the first stage protects a $b$-dimensional subsystem and has a prescribed noncommutative graph imposing full confusability on an $a$-dimensional control register. For a finite family of classically controlled branches, exact synthesis is possible if and only if the target graph contains the prescribed graph of the first stage. For every feasible family, we construct a single processor that implements all branches exactly. The processor uses pairwise nonorthogonal pure program states in a register of dimension at most $a$. A target graph may be realizable with a carrier of dimension $b$, while synthesizing a channel with that graph can require dimension $ab$. We also characterize the closure of the attainable channels, distinguishing exact synthesis from arbitrarily accurate approximation. Finally, for a family built from the trine communication task, a four-dimensional carrier permits exact synthesis with quantum programs under output depolarization. At the same total carrier dimension and without free shared randomness, classical programs have optimal normalized diamond error $(1-η)/4$, where $0\leqη\leq1$ is the depolarization strength. For $η<1$, the gap persists under sufficiently small perturbations of the target branches.

We demonstrate that the one-time measurement scheme is more consistent than the standard two-time measurement scheme with respect to the fundamental symmetry of entanglement, namely entanglement-assisted invariance (envariance). In particular, the work statistics obtained from the one-time measurement scheme arise naturally as a direct consequence of envariance for any driving unitary, without involving an explicit measurement postulate, whereas the analogous identification for the two-time measurement scheme is possible only for a Haar-measure-zero set of unitaries. This envariance-based formulation eliminates the ambiguity in work statistics related to the energetic cost of measurement.

The Petz recovery map provides a near optimal decoder for approximate quantum error correction, but its inverse square-root normalization complicates circuit implementation. We use the polar structure of the Petz recovery isometry to implement recovery through a single quantum singular value transformation (QSVT). We give explicit block-encoding circuits and an extended recovery isometry that yields approximate Petz recovery without postselection. We bound the diamond distance between the approximate and ideal Petz encoding-recovery channels in terms of a spectrum-weighted loss, which provides a channel specific objective for optimizing the QSVT angles. Uniform polynomial approximation yields an asymptotic error bound that decays exponentially with the number of QSVT iterations, at a rate controlled by the smallest nonzero scaled singular value. Applications to Haar-random encoding and the Hayden-Preskill protocol illustrate the tradeoff between circuit depth and recovery accuracy and place existing scrambling decoders within a common Petz recovery framework.

Trapped-ion devices are being investigated for transportable applications, including the transfer of exotic charged particles between laboratories and the development of portable quantum technologies. To date, ion transport has been demonstrated only in magnetic (Penning) traps, whereas radiofrequency (Paul) traps are the predominant platform in quantum science. Here, we report the first transport of a few thousand ions confined in a linear Paul trap over distances of several kilometers, with transport durations of 15 and 45 min. These results establish a foundation for mobile trapped-ion quantum devices capable of operating while in motion and may enable the transport of exotic ions in Paul traps between experimental facilities.

We study quantum spectrum and eigenstate property estimation using multiple initial states and generalized Hadamard tests. Building on the QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra) framework, we introduce a new method that samples evolution times independently for each initial-state pair. Under the stated assumptions, when statistical error determines the sampling cost, the total Hamiltonian simulation cost required for fixed-accuracy eigenvalue and observable estimation is independent of the number of initial states, up to logarithmic factors. This improves scalability when many initial states are needed to explore the target eigenspaces. The method also reduces the cost of multiplicity recovery and retains Heisenberg-limited scaling for eigenvalue estimation. Numerical experiments support the predicted statistical error scalings.

At zero temperature, a dilute Fermi gas with an attractive contact interaction forms a superfluid with gapped fermionic excitations. We show that the gap at weak coupling can be organized as a trans-series expansion in the interaction strength and the asymptotic Gor'kov-Melik-Barkhudarov gap. Low-energy virtual quasiparticles generate corrections that are linear in the gap with a leading coefficient nearly 25$\times$ larger than the other known coefficients. This substantially increases the gap at intermediate densities, highlighting that systematic corrections are crucial for quantitative predictions.

Kemp and Ramgoolam proposed a basis of monomials for a commutative semisimple algebra with generators \(C_1,\ldots, C_L\), constructed from a degeneracy graph which records how the eigenspaces of \( C_1\) are successively split by \( C_2,\ldots, C_L\). They showed that the basis property is equivalent to the non-vanishing of the determinant of the matrix of values of these monomials on the projector basis, and conjectured a factorised formula for this determinant, as a product of powers of eigenvalue differences. We prove this formula for any number of generators. The proof uses graph analogues of Newton polynomials. Their evaluation matrix is not triangular in general, but expanding the rows of the children of each node of the penultimate layer in a Newton basis of their eigenvalues makes it block triangular, with diagonal blocks given by smaller degeneracy graphs in which the final layer is removed. The formula then follows by induction on the number of layers. We show that the exponents in the determinant are overlap volumes of higher-dimensional Young diagrams attached to the nodes of the graph: intervals, ordinary Young diagrams, plane partitions and their higher analogues. Finally, the block triangular structure gives an explicit recursive inversion of the evaluation matrix, expressing the projectors in the monomial basis.

A well established approach to describe open quantum system dynamics is the celebrated Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. In this article we aim to shed light on semigroup dynamics that are not of this form. Such dynamics may appear in real physical systems describing asymptotic long-time dynamics. Thus, they correspond to semigroup dynamics applicable to a restricted set of initial states only. As a way of motivating our studies, first we review known results about the single-mode Gaussian Quantum Brownian motion channel and corresponding master equations. Next we discuss a conceptually simpler family of qubit semigroup generators and identify parameter regions of completely positive, merely positive, and non-positive dynamics. We then focus on the latter case to which we will refer to as restricted-positive, as the semigroup generator may well be physically meaningful when applied to a restricted set of admissible initial states.

Hong-Ou-Mandel (HOM) interference offers robustness in high-noise environments due to its phase-insensitive nature, while N00N-state interference provides enhanced phase sensitivity for precision measurements in low-noise settings. However, their realizations have typically required separate experimental platforms. Here, we report a single hybrid quantum interferometer that can dynamically transition between HOM and N00N-state interference by adjusting two time delays, $τ_1$ and $τ_2$. This tunability enables operation in phase-insensitive, phase-sensitive, or hybrid modes within a unified setup, as confirmed by theoretical analysis and experimental demonstration. Our system offers a versatile platform with potential for quantum sensing applications, paving the way for integrated quantum technologies capable of adapting to diverse noise conditions.

Solving linear systems of equations is a fundamental task in machine learning and optimization. In this work, we extend the original WZP algorithm from real symmetric linear systems to complex Hermitian linear systems. We then study the success probability of the modified WZP algorithm from a resource-theoretic perspective. By expressing the postselection success probability as the expectation value of a positive operator, we derive upper and lower bounds of the maximal success probability over separable, incoherent, and real pure states. These bounds further establish connections between the maximal success probability and geometric entanglement, coherence, and imaginarity. We further show that, under permutation averaging, the averaged success probability is an affine function of the coherence fraction, with its dependence determined by the alignment between the success operator and the equal-superposition state. We also investigate the preprocessed WZP algorithm under subgroup-constrained preprocessing. For the two-level family, the optimal success probability is determined by the maximal projection weight onto the orbit of the target projector. Our results provide a unified perspective on the WZP success probability under different operational constraints.

A recent graph-theoretic criterion for a Hamiltonian to exhibit a free-parafermion spectrum is that its frustration graph be an indifference graph. We show that an arbitrary finite indifference graph can be realized as a frustration graph of the quantized six-vertex model at odd roots of unity, by a suitable choice of the defining wiring diagram and parameters. This provides a concrete realization of the criterion through the quantum Frobenius property of the quantized six-vertex model, recently established from its three-dimensional integrable structure.

We revisit the effective radial Schrödinger equation for a charged spinless particle in collinear static electric and magnetic fields that was formulated in our earlier work within the tridiagonal representation approach (TRA). In that model the angular factor of the electric coupling is replaced by the orientation parameter $C=\cosθ$, the linear Zeeman term is diagonal in the azimuthal quantum number, and the effective field-modified central potential takes the form $V(r)=\Vt(r)+qECr$. Here we show that the same equation can be solved exactly without the TRA, by the Nikiforov--Uvarov (NU) method, once the potential component $\Vt(r)$ is prescribed. Three examples are worked out in closed form: a Kratzer-type component, which yields a linear-plus-Coulomb-plus-inverse-square central potential; a pseudoharmonic-type component, which yields a linear-plus-harmonic-plus-inverse-square potential; and a Hulthén-type component with a repulsive core (Manning--Rosen form), which yields a screened confining potential with a finite number of $s$-wave bound states. For each case we obtain the energy spectrum, the normalized eigenfunctions in terms of Laguerre or Jacobi polynomials, the location of the potential minimum, and closed-form radial moments. The spectra are independent of the orientation $θ$ and of the electric field, in agreement with the structure found by the TRA, while the field enters through the shape of $V(r)$, the radial moments, and the expectation value $\langle V\rangle_k$. All analytical results are confirmed by an independent finite-difference diagonalization.

We demonstrate that a single repulsive impurity enhances directional confinement of a high-energy wavepacket in a finite two-dimensional lattice of quantum wells. At energies far above the interwell barriers, the impurity suppresses transverse dynamical tunneling while preserving propagation along a principal lattice axis, even as the corresponding classical regular region shrinks. Confinement is strongest at impurity amplitudes comparable to the barrier height and weakens for stronger perturbations. Spectral analysis links this nonmonotonic pinning to the wavepacket's overlap with eigenstates concentrated along the launch direction, consistent with impurity-induced variational scarring. These results show that a single local defect can control quantum propagation over distances far exceeding its own spatial extent.

We investigate directional quantum steering harvesting by two uniformly accelerated non-identical Unruh-DeWitt detectors coupled to a massless scalar field in the Minkowski vacuum. We show that the Unruh effect does not simply degrade harvested steering, but can reshape its directionality in a strongly parameter-dependent manner. At low detector energy scales, acceleration predominantly suppresses steering, whereas at higher energy scales, moderate acceleration can enhance steering and even activate an initially absent steering direction. Most strikingly, within a finite acceleration window, the Unruh effect enhances steering in one direction while simultaneously suppressing it in the opposite direction, revealing an intrinsically directional influence of relativistic acceleration. Detector non-identicality provides an additional control mechanism: a moderate energy-gap mismatch can enhance or activate one steering direction while suppressing the reverse one, whereas sufficiently large energy-gap mismatch suppresses the harvested steering. Moreover, the maximal steering asymmetry approximately marks the transition from two-way to one-way steering. Our results establish relativistic acceleration and detector non-identicality as means of controlling the strength and directionality of vacuum-harvested quantum correlations.

We propose a loss-tolerant measurement-device-independent quantum key distribution (MDI-QKD) protocol using time-bin-multiplexed single photons entangled with local qubits stored in nitrogen-vacancy (NV) centers. In each round, Alice and Bob each send a single multiplexed photon to an untrusted intermediary, Charlie. Each photon first becomes entangled with Charlie's NV-center qubits; Charlie then performs entanglement swapping between his NV qubits to establish EPR pairs between Alice's and Bob's local qubits. With $d$ time bins per photon, $\log_2 d + 1$ EPR pairs can be generated per transmitted photon, substantially increasing the probability of EPR-pair creation under limited channel bandwidth. To further mitigate the effects of prolonged memory storage, the protocol employs a memory-insensitive (MI) architecture, where multiple banks of qubits and multiplexed photon routing reduce the effective memory lifetime requirements. This approach enhances loss tolerance, enabling higher secret key rates and secure key distribution over longer distances compared to conventional single-photon protocols. Using the Lo-Chau EPR-QKD framework and Shor-Preskill reduction, we prove that the protocol is secure without trusting intermediate nodes, making it suitable for quantum networks with untrusted repeaters.

Ionizing radiation produces correlated errors in superconducting qubits, posing some challenges to quantum error correction. In addition, it causes background events in other superconducting cryogenic devices, such as kinetic inductance detectors and superconducting nanowire single-photon detectors. Cosmic muons are a component of this background that can only be partly shielded against at ground level, but can be tagged by an independent detector inside the cryostat, so that the affected data can be vetoed, or the muon tags incorporated into error correction. We present a low-cost, compact muon detector consisting of two plastic scintillator modules, each read out by a silicon photomultiplier (SiPM), operated in coincidence. We characterize the SiPMs from room temperature down to 10 mK, including the breakdown and upper-limit voltages that define the operating bias range. Operated as a muon counter, the detector measures a coincidence rate that, as expected, is independent of temperature within uncertainties and agrees with analytical and Monte Carlo predictions. Below approximately 8 K, each muon event produces two pulses, one narrow and one broad, an effect that, to our knowledge, has not been reported before. Coincidences with an independent muon detector outside the cryostat confirm that muons are still counted reliably in this regime. By studying the appearance of double pulses as a function of temperature and magnetic field up to 4.5 T, we find a behavior consistent with the phase diagram of a type-II superconductor. This links the double pulses to a superconducting material in the SiPM, likely an adhesion layer or diffusion barrier introduced during manufacturing. The mechanism by which the superconducting state produces the second pulse is not yet understood.

We classify strong subadditivity for the canonical topological Rényi functional at finite positive orders on an unpunctured torus in the topological quantum field theory of any finite unitary modular tensor category. Universal validity means validity for all pure ground states and all regular region pairs with transverse or disjoint boundaries and compatible corner rounding. At von Neumann order one, the inequality holds universally. For each fixed order strictly between zero and one, universal validity is equivalent to pointedness, meaning that every simple anyon type has quantum dimension one. For every nonpointed category and each finite positive order other than one, we construct a violating pure state and an allowed pair. For a fixed pointed category and fixed order above one, universal validity is equivalent to a same-order modular Fourier entropy bound for every pure state. Global homological constraints on actual unions and intersections and established weighted modular uncertainty prove the order-one theorem. For parallel annuli at fixed flux distribution, the order-one functional is affine in their positive count. At other orders, unequal quantum dimensions on the occupied support induce strict curvature that suitable overlapping regions convert into negative deficits. Under the boundary-charge cutting prescription, the von Neumann theorem extends to arbitrary logical density matrices in the same ground space.

We study the extended Dicke model obtained from the scalar--vector--tensor polarizability of open-shell atoms coupled to a shared cavity mode. For a single electric-dipole channel, rotational symmetry fixes the tensor to vector ratio; we use $^{168}\mathrm{Er}$ with $J=6$ as a product-state example. A circular pump produces a chiral Raman vertex whose tensor-dependent matrix elements select the occupied Zeeman sector. The resulting first-order transition occurs before the empty-cavity branch loses local stability, and the ordered state is read out through $\langle\hat J_z\rangle$. A linear pump instead produces an empty-cavity $\pm x$ cat and a continuous transition into an even-$m$ cat-like state with order parameter $\langle\hat J_z^2\rangle$. With cavity loss alone, the circular trajectory emits a photon burst and approaches a Raman-dark Zeeman pole rather than a finite-field condensate. In the linear geometry, cavity-bright modes are damped toward the cat-like branch while a dark spin mode remains undamped. These are phenomena of that model; the vector-only controls show that they depend on the channel-fixed tensor coupling.

Cavity optomechanics represents a frontier research direction in quantum science and technology, centered on the control and exploration of interactions between electromagnetic fields and mechanical motion. Rooted in quantum mechanics, this field realizes efficient coupling and precise manipulation of optical fields and mechanical vibrations through the structural design and precise regulation of optical microcavities and mechanical oscillators, thereby revealing and harnessing novel quantum phenomena. In recent years, cavity optomechanics has evolved into an interdisciplinary frontier integrating quantum optics, condensed matter physics, and quantum precision measurement, exhibiting profound application in both fundamental physics research and quantum information science. With advancements in technologies such as nanomanufacturing and laser cooling, optomechanical interactions have been successfully demonstrated in various experimental systems. Among these platforms, cavity cold-atom systems stand out as one of the ideal platforms for implementing quantum optomechanics. Featuring exceptional environmental isolation, long quantum coherence times, and strong light-matter interaction, these systems provide a crucial testbed for exploring strong and even ultrastrong optomechanical coupling effects as well as rich nonlinear quantum phenomena. This paper reviews the recent progress in optomechanical control and manipulation based on cavity cold-atom systems. We first outline the fundamental principles of standard cavity optomechanical systems. Then, we describe the experimental realization of linear and nonlinear optomechanical couplings in cold-atom systems. After that, we focus on the representative applications of this platform in high-precision quantum sensing, quantum memory, and the preparation of macroscopic nonclassical states. Finally, we give an outlook and challenges in this field.

In quasi-Hermitian mixed-state quenches, the initial and final Hamiltonians generally possess different positive-definite metrics, so post-quench evolution is not quasi-unitary in the initial physical space. Choosing the preparation/measurement space as reference, we derive from first principles a normalized mixed-state Loschmidt amplitude using metric-compatible purifications. The resulting biorthogonal trace representation contains a normalization factor given by the norm of the evolved purification in the initial metric; this factor is essential for comparing states from different physical Hilbert spaces and directly encodes the metric mismatch. We prove that this normalization function is strictly positive on the real-time axis, so real-time criticality arises solely from destructive interference in the dynamical overlap. In complex time, zeros of the normalization factor generate branch singularities distinct from Fisher zeros. For a general two-level system, we derive analytic expressions for the Fisher and normalization zeros and analyze exceptional-point scaling together with the temperature- and quasi-Hermiticity-dependent DQPT critical times in two solvable quench protocols. In contrast to metric-stationary quenches, where non-Hermitian effects may be absorbed into an equivalent Hermitian description, the metric mismatch here produces genuine non-Hermitian dynamics: a time-dependent normalization factor and complex-time branch structure that cannot be removed by any global similarity transformation.

We study the relation between the exact-WKB Delabaere--Dillinger--Pham Stokes jumps and the multi-instanton expansion of a one-dimensional potential with $N$ equal-depth minima. For a single barrier this relation is the Bogomolny--Zinn-Justin cancellation between the instanton--anti-instanton ambiguity and the Borel ambiguity of perturbation theory, and we extend it to every consecutive barrier interval and to the integration contours themselves. In the dilute large-$T$ regime at fixed nonperturbative grade, we derive the quasi-zero mode integral over the instanton separations from the Euclidean path integral and reduce it to Gamma and Hankel periods. With the local Weber level function of each well and one normalization per well fixed by the local Weber connection matrix, these periods reproduce the two lateral connected exact-WKB coefficients. The two lateral contours of each instanton--anti-instanton separation differ by exactly one Hankel cycle, and this linear Picard--Lefschetz relation reproduces the Stokes jump of the connected coefficient. A numerical solution of the Schrödinger equation for a symmetric triple well confirms the resulting two-barrier level splitting. At higher fixed grade, the map from ordered event sequences to normalized scalar coefficient products is not one-to-one. At leading dilute order the scalar weight of a closed event sequence depends only on the numbers of barrier crossings, $\mathcal I\bar{\mathcal I}$ pairs, and $\mathcal I\mathcal I$/$\bar{\mathcal I}\bar{\mathcal I}$ pairs. We construct two inequivalent grade-six triple-well event sequences with the same product of local Weber amplitudes, which embed in every potential with $N\ge3$ wells. Our results hold within the regular dilute, one-loop, local Weber approximation.

We characterize a source of photon pairs simultaneously entangled in polarization and in the transverse spatial degree of freedom, with the spatial measurements performed in intermediate planes of the fractional Fourier transform. The source consists of two crossed type-I crystals in a non-collinear geometry, such that the transverse variables carry information about the crystal of origin. Detection in the crystal plane reveals this information completely and destroys the polarization entanglement, so that a scheme using the near and far fields as conjugate spatial bases cannot support a parallel polarization channel. In intermediate planes both spatial bases combine position and momentum, such that the which-crystal information is partially erased, and the polarization entanglement survives in all four combinations of spatial bases. Applying Bell and Einstein-Podolsky-Rosen criteria to the same photon pairs certifies both degrees of freedom simultaneously. We evaluate quantum bit error rates and asymptotic secret key rates in each degree of freedom, and find that the source delivers two simultaneously usable channels per photon pair.

Preserving the underlying statistical properties of light during frequency transduction is essential for interfacing spectrally disparate quantum systems. To do this successfully, the process needs to be highly efficient, broadband and noiseless. Despite significant progress in this field, satisfying all these conditions remains challenging. Recently, molecular modulation-based transduction in hollow-core fibers has emerged as a promising approach, where biphoton correlations were proven to be preserved during frequency up-conversion. However, beyond this previous demonstration of correlation-maintaining conversion, whether molecular modulation can preserve more general statistical properties of light remains experimentally unexplored. Here, we demonstrate the conservation of photon-number statistics during selective frequency transduction by Raman molecular modulation in a hydrogen-filled hollow-core fiber. As a proof of concept, weak 585-nm signals are selectively converted to 773 nm in the near-infrared and to 471 nm in the blue spectral region with near-unity efficiencies. Phase matching between the generated coherence waves and the transitions of interest is achieved through the effective dispersion of the system, enabling independent selection of the frequency up- and down-conversion processes. The preservation of the photon-number statistics of the shifted signals, along with the large frequency shifts, broad tunability and compatibility with quantum-optical fields, provides a versatile fiber-based platform for quantum frequency transduction. In particular, the demonstrated interfacing between visible and near-infrared wavelengths using low pump energies and low gas pressures offers a route towards connecting spectrally distinct quantum systems, including quantum emitters, sensors and atomic quantum memories, within hybrid quantum networks.

The graph isomorphism problem asks whether two graphs are equivalent up to a permutation of their vertices. Its precise computational complexity remains unresolved, and it is still unknown whether a polynomial-time algorithm exists. We investigate whether simple graph-dependent Instantaneous Quantum Polynomial-time (IQP) and Quantum Approximate Optimisation Algorithm (QAOA) circuits can distinguish non-isomorphic graphs. We first show that suitable IQP and QAOA constructions allow the underlying graph to be reconstructed using a polynomial number of samples. Building on previous work using the QAOA energy, we show that Hamming weight distributions can distinguish graph pairs at circuit depths for which the numerically computed energy gap is zero. We then apply graph invariants to the matrix of ZZ correlators on the output distribution. For the specific case of the graph spectrum, at QAOA depth $p=2$, this invariant numerically distinguishes all $10{,}486$ cospectral regular graph pairs tested on up to 18 vertices. For IQP circuits, we introduce a finer invariant based on probability multiplicities within Hamming weight sectors, which distinguishes every non-isomorphic graph pair tested numerically. Finally, we derive exact graph-theoretic characterisations of the IQP output distribution at $θ=π/2$ and $θ=π/4$. These results show that simple graph-dependent quantum circuits encode substantial structural information, while leaving open whether this information can be extracted efficiently for general graph isomorphism.

The analysis of charge fluctuations in a mesoscopic device can shed light on the fundamental question of whether or not a single-particle picture of electron transport is appropriate, even in the presence of Coulomb interaction. It has been shown on general grounds that mapping the interacting system onto a fermionic single-particle description is subject to strict constraints on the charge-transfer statistics. These constraints can be formulated in terms of a sign rule for the factorial cumulants of the full counting statistics. We report here on the experimental observation of a sign-rule violation in a most elementary model system, i.e. a single-level quantum dot, and provide theoretical modeling that can quantitatively reproduce the experimental data. This reveals the presence of correlations introduced by electron-electron interaction.

The Unruh response thermalizes accelerated detectors, but the entanglement remaining in a register does not by itself specify what distributed measurements can recover. We study this distinction for a four-qubit cluster state whose two assisting nodes independently undergo generalized amplitude damping, while the target nodes remain isolated and the environments are inaccessible. We derive the exact joint-assisted concurrence and the exact one-way value for arbitrary local measurements. The joint optimum equals the bipartition negativity, and computational-basis measurements attain the one-way optimum. A polar-decomposition argument, together with compactness, establishes a necessary and sufficient condition for separable measurements to attain the joint optimum and proves a strict gap whenever this condition fails. For assisting detectors at equal Unruh temperature with relaxation-rate ratio $r>1$, joint advantage exists precisely when the thermal excitation factor satisfies $q<1/r$. At finite positive temperature it ends at a unique finite time, while the remaining entanglement is nonzero. For $r=2$, both the transition time and remaining resource have closed expressions. These results identify when joint assistance is necessary within the independent weak-coupling thermalization model.

Entropy estimation of discrete probability distributions is a fundamental problem in statistical inference and quantum property estimation. In this paper, we study the problem of estimating Rényi entropy $H_α(\mathbf{p})$ for any distribution $\mathbf{p} = (p_i)_{i=1}^n$ given its purified quantum query-access. For non-integer $α> 1$, our algorithm estimates $H_α(\mathbf{p})$ to within additive error $ε$ using only $\widetilde{\mathcal{O}}\big(n^{\max\{1/2,1-1/α\}}/ε\big)$ queries, which improves the best known upper bound for dependence on both $n$ and $1/ε$. For $0<α<1$, our algorithm has query complexity $\widetilde{\mathcal{O}}\big(n^{1/(2α)}/ε^{\max\{1,1/(2α)\}}\big)$, which improves the dependence on $1/ε$ of the current best upper bound without incresing its $n$ dependence. Our approach adapts the multi-level estimation framework to relative approximation of the power sums and leverage binary search to remove the requirement of prior knowledge of them. We also strengthen the precision-dependent lower bound to $Ω\big(1/ε^{\max\{1,1/(2α)\}}\big)$ for $0<α<1$, which identifies the optimal precision dependence of our algorithm.

Spatial sectioning of the far-field noncollinear field from spontaneous parametric down-conversion (SPDC) is a promising approach for multiparty quantum communication. Although demonstrations with six pairs of users have been reported, the fundamental limits remain unknown. These include the maximum number of channels, the required degree of channel optimization, and the dependence on input parameters. In this paper, we provide a practical framework that answers these questions by connecting input parameters and invoking a design theorem. For a representative configuration, we realize 12 user-pair channels with routing consistency exceeding $0.9999$ at a $12\%$ reduction in photon flux. We further show that sectioning improves the accidental-coincidence budget linearly with the number of channels $N$, allowing the aggregate key rate to scale with the user count. These results provide a design strategy for spatial-division multiplexing of entangled photons analogous to the channel-spacing standards used in wavelength-division networks.

Entanglement in multiphoton graph states is an important resource with various applications, such as measurement-based quantum computing and memory-less quantum repeaters. While some primitive instances have been successfully prepared, scalable generation of large-scale graph states with programmable connections remains an outstanding challenge. Fusion provides a promising "divide-and-conquer" approach by linking smaller resource states into larger, more complex graphs. However, its practical scalability has been limited by the probabilistic nature of conventional fusion protocols, which necessitates extensive hardware overhead and feed-forward resources to achieve deterministic outcomes. Here, we introduce and experimentally demonstrate a deterministic fusion operation with built-in error mitigation, capable of connecting small time-bin-encoded cluster states--originally generated on-demand from a quantum emitter--into larger, reconfigurable photonic graph states of increased sizes. The fusion operation is realized by nondestructively projecting pairs of flying microwave photonic qubits into Bell states using superconducting circuits with in-situ programmability. Crucially, the protocol features active reset and reuse of matter qubits during graph state generation, thereby circumventing the coherence constraints of the quantum emitter and enabling the generation of genuine multipartite entanglement across 13 photonic qubits. Our results establish a scalable framework for photonic graph-state synthesis, paving the way for fault-tolerant measurement-based quantum computation and distributed quantum networks.

Recent progress in programmable quantum simulators motivates exact benchmarks for nonequilibrium dynamics in topological quantum matter. We study the Kitaev honeycomb model driven through its critical regions by a linear ramp of the bond coupling $J_z$ over a ramp time $τ$, comparing zigzag and armchair ribbons with fully periodic tubes. The production of excitations exhibits a geometry-dependent finite-size crossover controlled by $N_2/\sqrtτ$, the ratio of the ribbon width to the Kibble--Zurek length. Periodic tubes obey the expected critical-line Kibble--Zurek scaling and serve as the boundary-free benchmark. Zigzag ribbons follow the same scaling until defect production is exponentially suppressed by a finite-width algebraic gap floor associated with the formation of Majorana edge modes, whose occupation is pinned by inversion parity. Armchair ribbons instead support transient Majorana edge modes with exponentially small gaps, producing width-parity-dependent defect plateaus: exactly one defect per unit length for odd widths and an approximate, transient plateau near one half for even widths. The quench-generated entanglement entropy and fermionic logarithmic negativity inherit the same geometry-dependent structure, and the negativity further distinguishes the coherence-borne entanglement of the Kibble--Zurek regime from the population-borne entanglement of the edge-mode plateaus. These results identify boundary Majorana modes as the mechanism controlling departures from ideal Kibble--Zurek dynamics and provide geometry-resolved benchmarks for programmable simulations of topological matter.

Quantum subspace diagonalization (QSD) with a Krylov space spanned by Chebyshev polynomials of the Hamiltonian is a natural ground-state method for fault-tolerant quantum computers, but every guarantee it offers---convergence rate, noise floor, and the cost of turning its classical output back into a physical state---is controlled by the overlap of the reference state with the true ground state, which decays exponentially with system size for any product state and non-trivial Hamiltonian. We propose quantum folding: for a system governed by a local Hamiltonian, seed the QSD with the product of the ground states of its subsystems, which differs from the target only through the interface terms. We prove a nonasymptotic error bound for the Chebyshev QSD that is linear in the measurement noise, by transplanting Kirby's effective-Hamiltonian analysis to the Chebyshev--Krylov basis, and identify the block-encoding rescaling of the Hamiltonian as a parameter of the guarantee. Exact simulations of antiferromagnetic Heisenberg chains show that the folded reference state reduces the Krylov dimension for a given accuracy severalfold and lowers the error under noise by two to five orders of magnitude relative to the Néel state. We show how the Ritz vector is prepared as a physical state and that the ground-state generation probability obeys a tight ceiling set by the overlap, so that recursive folding prepares ground states at polynomial cost. Taken together, these results allow for a scalable QSD framework that avoids the exponentially small ground-state overlaps associated with conventional product-state initialization. Finally we compute the fold fidelity itself: a slow power law for the gapless spin-1/2 chain, a size-independent constant for the gapped spin-$1$ chain, and an exact closed form converging to 1/4 for the AKLT chain.

Bound-entangled states with positive partial transpose (PPT) can exhibit quantum steering and Bell nonlocality, disproving the long-standing Peres conjecture and its stronger steering counterpart. These counterexamples, obtained through explicit constructions or numerical searches, raise the question of whether they share a common structural origin. We address this question in the low-rank regime by asking whether known counterexamples can be obtained, up to invertible local filtering, from the complement of an unextendible product basis (UPB). We find that the answer depends crucially on the local dimension. In $3\otimes3$, the rank-four structure of PPT entangled states implies that both the steerable PPT state of Moroder \textit{et al.} and the Bell-nonlocal PPT state of Vértesi and Brunner can be obtained from UPB-complement states under invertible local filtering. For three qubits, in contrast, rank-four states that are PPT across every bipartition are separable across each cut. Moreover, comparison of the product-vector structure of the relevant kernels shows that the known three-qubit Bell-nonlocal PPT states cannot be obtained by invertible local filtering from the complement of any three-qubit UPB. Going beyond rank four, we further show that a known rank-eight three-qutrit state, supported on the complement of a UPB and PPT across every bipartition, is genuinely multipartite entangled. These results show that UPBs provide a unifying structural origin for important low-rank PPT entangled states in $3\otimes3$, but that nonlocal bound entanglement is not, in general, a UPB phenomenon.

We study quantum van der Pol oscillator in which single-photon pumping competes with a nonlinear two-photon dissipative channel to produce a quantum limit cycle, and the question of how two such oscillators with non-identical intrinsic frequencies synchronize in the sense of phase locking when coupled dissipatively to one another. For a single oscillator, starting from a Lindblad description of the dynamics, we derive the exact Wigner-function evolution equation, and show that its Fokker--Planck approximation admits in the appropriate regime an equivalent classical Itô stochastic description that reproduces remarkably well the full Lindblad dynamics. Notably, the stochastic approach provides an efficient means of capturing system dynamics in the semiclassical regime, where a large number of energy eigenstates contribute and direct numerical simulations become computationally demanding. Restricting to the three lowest Fock states and using a parity symmetry, we obtain in closed form the stationary-state density matrix and its Wigner-function representation that displays pronounced nonclassical features. For two non-identical oscillators, we study the full Lindblad dynamics numerically and characterize synchronization through the stationary-state order parameter as a function of frequency mismatch and dissipative coupling. We find that increasing the effective nonlinear dissipative strength suppresses the synchronized region. Restricting the two oscillators to the three-level qutrit subspace, a parity symmetry reduces the stationary-state problem to an exact $41$-dimensional linear system, allowing to compute the synchronization order parameter. In this reduced description, results in the limit of large dissipation agree closely with those from the full dynamics, while exhibiting in the limit of small dissipation a double-peak synchronization structure accompanied by a phase reversal.

Energy is arguably the main resource in classical physics; coherence is the prototypical quantum resource. In this paper, we study the interplay between these two resources in the task of optimal mode discrimination. This task, motivated by cryptography and metrology, consists of finding in which mode a signal has been encoded, for a given finite set of possible modes. After recalling that the task can be cast as a semi-definite program, we solve completely the case of two-mode discrimination under a hard energy constraint $n\leq N$. Specifically, we identify the region of modes overlap, for which the maximal energy state (the Fock state with N excitations) is the best choice for discrimination. For other overlaps, having access to coherence leads to better discrimination.

Scattering of sound waves propagating in a compressible fluid is linked to the quantum dynamics generated by a class of non-Hermitian Hamiltonian operators. The scattering amplitude is expressed in terms of the corresponding evolution operator. This is used to provide a new proof of the reciprocity theorem in acoustic scattering, conduct analytic low-frequency acoustic scattering calculations, and study the scattering of sound waves by a finite planar array of delta-function point scatters embedded in an infinite acoustic slab. A detailed discussion of acoustic scattering properties of a homogeneous acoustic slab including a pair of delta-function point scatters on one of its faces is provided.

Coherent noise poses a fundamentally greater challenge to quantum error correction than independent s- tochastic Pauli errors, because unitary errors preserve interference between error paths, can accumulate over multiple quantum error correction rounds, and leave the encoded logical channel with a residual coherent com- ponent. If the parameters of such coherent noise can be accurately determined, this knowledge can be exploited to inject correlated priors into the decoding graph, and to perform maximum-likelihood decoding under poly- nomially tractable structures, significantly improving the accuracy of syndrome-based decoding. In this work, we introduce one protocol to determine the model and parameters of coherent noise, and reduce the complexity of the experiment from 16nto O(16), which is of great significance for correcting coherent noise in quantum error correction.

Fiber-optic sensors enable high-sensitivity measurements of various physical parameters. Here, we demonstrate a quantum-enhanced interrogation of an all-fiber-optic Fabry-Perot resonator, employing entangled two-photon interference to probe directly strain-induced optical phase shifts. The resonator is interrogated by a narrow-linewidth laser that is frequency-locked to its resonance mode, thereby exploiting the cavity's inherent sensitivity to variations in the fiber length. To access the phase fluctuations transferred to the interrogation field due to external perturbations on the sensor, we implement an in-fiber Mach-Zehnder interferometer readout. This configuration allows the sensor to operate both with classical coherent light and with entangled photon pairs generated via spontaneous parametric down-conversion. Harnessing two-photon entangled states corresponding to an N = 2 NOON state, we experimentally demonstrate a reduction of the measurement noise below the standard quantum limit. These results provide clear evidence of the quantum advantage in enhancing fiber-optic sensors under practical constraints on optical power.

We present a quantum-enhanced search for the Galactic dark-photon background (GDPB), a relativistic and anisotropic vector field that can be produced by dark-matter decay or annihilation in the Milky Way halo. We reinterpret an existing quantum-enhanced dark-photon dataset obtained with a superconducting circuit QED platform originally developed for wave-like dark-photon dark-matter searches, consisting of a high-$Q$ niobium cavity in the $\mathrm{TM}_{010}$ mode dispersively coupled to a transmon qubit. By preparing four-component cat states and performing repeated quantum non-demolition parity measurements, analyzed with a hidden Markov model, we extract photon-transition probabilities for multiple cat amplitudes and integration times. The coupling to the GDPB is governed by a polarization- and angle-dependent cavity overlap function, which predicts a distinctive diurnal modulation of the excitation rate for both longitudinal and transverse polarizations. From the absence of such modulation, we set 90\% confidence-level bounds on the kinetic-mixing parameter $ε$ for two benchmark production mechanisms (parametric and cascade decay) over the relativistic mass range $m_X \ll ω_c$.

Through-substrate interconnects are a key technology for scaling surface-electrode ion traps (SEITs) toward large electrode counts and complex architectures. Dielectric substrates such as fused silica offer superior RF performance compared to silicon, but the reliable fabrication of void-free through-glass vias (TGVs) remains challenging. In this work, we demonstrate a SEIT fabricated on a fused silica substrate incorporating TGVs. The via-holes are formed using Selective Laser-Induced Etching and subsequently metallized with gold by electroplating. A patent-pending geometry-assisted bottom-up plating approach enables void-free filling using constant-current electroplating without electrolyte additives or pulsed deposition schemes. Electrical characterization across multiple wafers confirms a TGV-level yield above 98.8 %, demonstrating the robustness and reproducibility of the developed TGV technology. The TGVs are combined with multilayer SEIT fabrication, enabling vertical signal routing to all electrodes while maintaining an unaffected trapping surface without wire bonds. To interface the trap with external control electronics, a glass interposer providing signal fan-out to a larger pitch is designed and fabricated. The trap chip and the interposer are integrated using thermocompression bonding, forming a compact chip-to-chip assembly. The presented technology demonstrates the first fully integrated multilayer SEIT on fused silica incorporating void-free TGVs.

Inserting a resolution of the identity between two operators turns a matrix element of their product into a phase-space integral. For unbounded operators the product need not exist on the vector at hand, while the integral may still converge. We follow this gap through the chain $e^{μa^2}e^{λa^{\dagger2}}$ of two-photon exponentials, where it can be traced completely. Five regions of parameter space appear: where the Bochner conditions of the strong formulation hold, where the product exists as a vector, where it exists as a sesquilinear form, where the coherent-state integral converges, and where the Fock-space series converges. The first three are strictly nested inside the intersection of the last two, and these two overlap without either containing the other. A single Hermite-type function agrees with the matrix element where it exists and with the integral and the series wherever they converge, so the integral carries the analytic continuation of the matrix element beyond the domain of the product and beyond the convergence of its Fock series. On the real slice of parameter space, an iterated form of the integral also reaches every point where the series converges. The analysis rests on a weak composition lemma whose hypotheses concern only the bra, the ket and the resolving family. For bounded chains the same identity is unconditional, and worked examples of that kind are given in a companion paper.

Encoding quantum information in $d$-dimensional systems (qudits) with $d>2$ offers appealing new directions for resource-efficient quantum computing. However, protecting the coherence of nonclassical qudit resource states remains an open challenge. Dynamical decoupling (DD) is a well-established technique for extending coherence, but its application to qudits is hindered by the quadratic scaling of the decoupling sequence overhead with the dimension $d$. As a result, demonstrations of qudit DD have so far been limited to low-dimensional qudits. Here, we show that noise-biased qudits enable a nontrivial reduction of this overhead, for example, from quadratic to linear. We perform qudit DD on a model $d=8$ qudit, the nuclear spin of an antimony donor in silicon. We benchmark DD performance on highly nonclassical states such as uniform superpositions, cat states, and Haar random states and measure coherence improvements up to a factor $5$ to $10$. For a spin-cat error correction code, continuous DD extends the coherence time of the logical superposition $|+\rangle_L$ to $225$~ms, compared to $19$~ms under free evolution and $85$~ms with a Hahn echo. This improvement shows that DD sequences tailored to a system's noise bias can significantly enhance the lifetime of encoded logical qubits.

Strong eigenstate thermalization (ETH) in operationally mean-ergodic, non-chaotic systems provides an opportunity to investigate whether Floquet eigenstates retain information about classical transport beyond their leading thermodynamic behavior. We address this question using the double kicked top (DKT), which exhibits nonmixing transport and dynamics consistent with weak mixing transport under variation of its control parameters. We show that the coefficient $m$ of the leading finite-size correction to the normalized eigenstate entanglement entropy (EE) $s$ tracks the restructuring between these transport regimes even when the thermodynamic-limit entropy $c$ becomes nearly insensitive to them. This coefficient $m$ is positive for nonmixing transport and negative when dynamics consistent with weak mixing transport dominate. The coefficient's sign reversal in the coexistence regime remains stable as the semiclassical resolution increases. Our results demonstrate that finite-size eigenstate structure can encode signatures of classical transport that are invisible in the thermodynamic-limit entropy, providing an eigenstate-based diagnostic of dynamical organization beyond the leading thermodynamic behavior associated with strong ETH.

This paper proposes a scheme and design of cryogenic multiplexing control chip (MCC) which enables one microwave cable to control many superconducting qubits. Designed based on adjustable inductor, MCC is a non-reciprocal device which generates microwave signals between 4 and 8 GHz and constructs XY control circuit to operate qubits. The effects of filters, isolators, power splitters, qubits and load impedance on MCC are analyzed in the frequency-domain simulation. And in time-domain simulation, the response time, Gaussian pulses, single-sideband, amplitude and frequency compensation of MCC are examined. The MCC can be integrated with the superconducting qubits on the same package at 20 mK temperature stage, and output specific microwave pulses used to drive the superconducting qubits without crosstalks. The MCC can greatly reduce the number of microwave control lines and is beneficial to the development of large-scale superconducting quantum processor.

This paper reconstructs the Michelson interference phenomenon based solely on the binary (on-off) statistics of a single-photon counter and macroscopic path-difference data, without the a priori assumptions of complex wave superposition or prior spectral information. In contrast to the conventional approach that assumes light as a continuous complex wave function and considers interference between them, this study focuses on the algebraic properties inherent in discrete detection statistics. We verify that the discrete response data collected across various path differences form a positive semi-definite matrix, and apply Herglotz's theorem to this result. Consequently, we show that the harmonic form of the interference fringe is not a consequence of adopting a wave model as an axiom, but rather it is uniquely decomposed into a cosine average of wavenumbers dictated by testable algebraic constraints satisfied by the statistical data. Through this approach, the logical basis of the interference phenomenon can be described by the characteristics of the binary data itself, perfectly aligning with the modern optical experimental environment that relies entirely on discrete event statistics.

Pauli correlation encoding (PCE) encodes $m$ binary variables in the signs of $k$-body Pauli correlators of $n=O(m^{1/k})$ qubits, and trains a parameterized circuit on a relaxed loss of sharpness $α$. The strongest published schedules sharpen this loss aggressively and are benchmarked with exact expectation values, whereas a quantum computer estimates correlators from a finite number of shots. We show that the sharpness is a hidden shot budget. Since the expected sign of a correlator estimated from $S$ shots, $\mathrm{erf}(c\sqrt{S/2})$, agrees with $\tanh(0.851\sqrt{S}\,c)$ to within $0.019$, the edge term of the relaxed loss at $α=0.851\sqrt{S}$ approximately equals, up to a constant, minus twice the cut expected from decoding $S$ shots. This explains why schedules tuned with exact expectation values lose their advantage at realistic budgets, and yields a shot-aware schedule whose final sharpness is set by the shot budget. On five G-set graphs with $800$ variables on $13$ qubits, this schedule outperforms every published schedule at its target budget in all $150$ paired comparisons of the decoded circuit output, owing to the sharpness at $1.6\times10^4$ shots and mostly to switching off the regularization at $10^3$; after a classical bit-swap search, it remains the best on average at $1.6\times10^4$ shots. Device noise damps the correlators by a factor $s$, which amounts to a smaller shot budget $s^2S$. On the IBM Heron processor ibm_fez, an all-to-all ansatz of the type used for the best published G-set results compiles to $835$ CZ gates and decodes to a random cut, while our $96$-CZ hardware-native circuit, trained in simulation and sharpened to $α\simeq0.65\,s\sqrt{S}$, retains up to $0.919$ of the best-known cut. For new circuits, a damping and an offset calibrated on other circuits of the same graph predicted the decoded cuts at $10^3$ shots to within $0.002$.

Magneto-optical traps (MOTs), indispensable to cold-atom-based quantum computing and quantum precision measurement, are increasingly desired in compact and stable form. Particularly, the six-beam 3D-MOT, distinguished by symmetric geometry and superior trapping performance, finds particularly broad applications. Conventional implementations, however, rely on complex and bulky free-space optics, hindering miniaturization, practical assembly, and long-term stability. Here, we demonstrate a compact six-beam 3D-MOT system that employs two multifunctional optical metasurface chips to implement the optical-field functionalities required for cooling and trapping atoms. By combining two metasurface chips and a vacuum cell, a photonic-integrated cell module (PICM) is implemented as the core assembly and the volume is only" 73*73*107 mm^3" . In success, 1.3 * 10^3 Rb atoms are trapped and cooled to the temperature of ~183 μK. It should be noticed that the laser beam is guided to the metasurface through optical fiber, thus such fully fiber-coupled architecture enables straightforward and stable operations. We believe that this work would pave a practical route toward compact and portable 3D-MOT.

Frequency inhomogeneity can obscure the metrological advantage of squeezed spin states, making the choice of readout crucial. We study interacting spin-1/2 ensembles with static local frequency disorder and optimize a common collective readout over independent disorder realizations. Using Bayesian optimization of the full measurement-outcome distribution, we identify observables combining dipole and quadrupole operators that yield greater classical Fisher information than the optimized dipole readout considered here. For ensembles of up to 17 spins, their disorder-averaged CFI surpasses the standard quantum limit at both disorder strengths studied, including a regime where the dipole readout remains below it. For the larger ensembles studied, fixing the encoding axis to the direction that maximizes the disorder-averaged quantum Fisher information retains nearly the same performance. These results identify a route to extracting metrological information from frequency-disordered spin ensembles through the choice of collective observable.

We construct quantum codes from codewords of a cyclic code and the minors of a polynomial matrix. The construction uses a two-row, three-column matrix whose minors yield a second matrix satisfying the CSS orthogonality condition. We derive the code dimension from the greatest common divisors of the entries and minors, with a simplified formula for odd lifting factors. A residue characterization identifies additional common factors of the minors and leads to a method for controlling the dimension through polynomial selection. We also give a condition for changing the minor generator without changing the code. Explicit polynomial constructions yield 13 quantum codes with verified minimum distances, including a $[[255,80,12]]$ code of rate $80/255$.

Loss and noise limit the use of light to distribute entanglement, transmit quantum information, and establish secret keys. Gaussian states have a compact description in terms of means and covariance matrices, but their entanglement still requires global optimization. We develop a framework for computing Gaussian-restricted versions of the relative entropy of entanglement and Rains entanglement. An integral representation reveals a convex geometry under matrix geometric means and reduces Gaussian Rains entanglement to relative entropy minimized over Gaussian states with positive partial transpose. We obtain unique optimal reference states and additivity for independent Gaussian input states. Our convex-majorization algorithm has an explicit geometric convergence rate, uniform in the faithful regularization parameter and valid for pure input states. Controlled numerical integration and approximate convex subproblem solutions give a bit-complexity bound that is polynomial in accuracy bits for each fixed rational input covariance matrix, with explicit dependence on covariance size. These calculations bound extractable entanglement and, through the relative entropy of entanglement, extractable secret key. Teleportation simulation, energy allocation, and a convex optimization of passive-basis loss cores give bounds on quantum and private communication under an input-energy constraint, allowing arbitrary two-way classically assisted protocols. Two- and three-mode examples compare the bounds with achievable rates, including matching pure-loss benchmarks. Finally, we separate the Gaussian-restricted quantities from their unrestricted counterparts and give a photon-number truncation method with controlled error for computing the latter.

It is proved that every Borel ensemble of pure states on a separable bipartite Hilbert space with finite average entanglement admits a countable ensemble with the same barycenter and arbitrarily small additional average entanglement. Consequently, the discrete and continuous versions of the Entanglement of Formation coincide on the whole space of states of infinite-dimensional bipartite quantum system (with infinite values allowed). The main idea of the proof (realized with the AI-assistance) is the identification of a Borel ensemble of pure bipartite states with a Borel probability measure on the unit sphere of the space of Hilbert--Schmidt operators followed by dividing the support of this measure into appropriate cells and replacing each cell by its conditional barycenter. The resulting countable ensemble is obtained by a recursive construction.

A series of recent works has established EFI pairs as the "minimal" assumption for quantum cryptography. Recently, Cavalar et al. [CCC+26] showed that EFI pairs are equivalent to non-uniform expanding single-copy pseudorandom state generators (1PRS), and obtained a non-uniform meta-complexity characterization of EFI pairs. We remove the non-uniformity in their construction and prove that EFI pairs are equivalent to expanding 1PRS. As a corollary, we obtain the first uniform meta-complexity characterization of EFI pairs. Together with the equivalence of statistically verifiable one-way state generators and commitments proved by Batra and Jain [BJ24], this gives a quantum analogue of the classical equivalence between one-way functions, commitments, and pseudorandom generators.

We develop and analyze an entropic descent method for a nonconvex optimization problem on probability simplices arising in classical and quantum secure communication. The optimization variables describe a randomized encoder, allowing its input distribution and stochastic preprocessing to be optimized jointly. An exact relative-entropy identity yields a channel-independent majorization bound and an explicit mirror-descent iteration with a fixed unit step size. We establish quantitative descent, convergence of objective values, and stationarity of accumulation points on their support faces for arbitrary finite classical channels, without assuming degradedness or less noisiness. For strictly positive transition matrices, a square-root parametrization and a Kurdyka--Łojasiewicz argument establish finite length of the transformed trajectory and convergence of the entire sequence, including limits on the simplex boundary. For less-noisy channels, a restricted convex formulation admits global convergence with an explicit \(O(1/t)\) objective-error bound. We extend the relative-entropy construction to noncommuting quantum outputs and derive monotone alternating updates for covariant encoders, including correlated preprocessing over a fixed block. Numerical experiments compare the method with analytic benchmarks and constrained optimization, reveal multiple attracting values, and demonstrate strict improvements from stochastic preprocessing.

Multimode mechanical resonators offer a large set of densely packed, long-lived bosonic modes within a single compact device, making them attractive for quantum simulation, quantum information processing, and quantum-enhanced sensing. Many such applications rely on multipartite entanglement, yet deterministic mechanical entanglement has so far been largely limited to pairs of modes. Here we demonstrate the deterministic and programmable preparation of multipartite entangled states among the phonon modes of a high-overtone bulk acoustic wave resonator coupled to a superconducting transmon qubit. By sequentially applying optimal-control-engineered isometries between the qubit and successive modes, we generate matrix product states of bond dimension two, including $W$, Greenberger-Horne-Zeilinger (GHZ), and cluster states. We fully characterize these states via quantum state tomography and certify genuine multipartite entanglement among up to four modes. We further demonstrate correlated-noise sensing by exploiting the complementary decoherence responses of the stored $W$ and GHZ states, isolating inter-mode phase correlations from local decoherence and placing quantitative bounds on collective dephasing. Our results establish a scalable approach to preparing multipartite entangled states in mechanical systems, with promising applications in multiparameter sensing and tests of quantum mechanics with massive objects.

Massive mechanical oscillators couple directly to forces, accelerations and gravity, making them attractive probes of new physics and of quantum mechanics at macroscopic scales. Pushing sensitivities beyond the standard quantum limit for signals of unknown phase requires non-Gaussian quantum states, whose metrological advantage has so far been confined to lighter systems such as trapped ions. Here we operate a microgram-scale acoustic mode of a high-overtone bulk acoustic wave resonator as a phase-insensitive quantum-enhanced sensor. A transmon qubit prepares the mode in Fock states of up to seven phonons by optimal control, and resolves its phonon-number distribution after interaction with a weak resonant signal. Bayesian analysis yields a Fisher information five times the vacuum value, a 7.0 dB gain in signal-amplitude sensitivity over any classical probe state, irrespective of its energy, currently limited by state preparation infidelities. We then train a neural network on the measured sensor response to perform Bayesian estimation without any analytical model of the system, showing the same sensitivity gain with half the systematic bias. Our results establish acoustic resonators prepared in non-Gaussian states as quantum-enhanced probes for high-frequency gravitational waves, dark matter and wave-function collapse.

We study quantum communication, entanglement distribution, and secret-key generation through multimode bosonic loss and fading channels, assisted by local quantum operations and two-way classical communication. Using sector teleportation, we determine the exact two-way quantum and secret-key capacities of multimode pure-loss channels under a mean photon-number constraint, allowing arbitrary adaptive quantum protocols. We extend these results to continuous frequency-dependent loss under a power constraint and identify the optimal allocation of photons among optical modes. For constant loss over an unlimited bandwidth, we obtain a closed-form capacity proportional to the square root of power. For randomly varying loss, we determine exact finite-energy capacities when the channel realization is publicly revealed, distinguishing knowledge before and after transmission. When fading remains unobserved, we derive capacity bounds and explicit formulas for an on/off channel. We also establish strong-converse bounds, with exact thresholds for the deterministic loss models considered here, observed fading, and unobserved fading with finitely many possible transmissivities. Under mean energy constraints, these thresholds generally exceed the corresponding finite-energy capacities. These results guide energy allocation and provide benchmarks for energy-constrained optical quantum communication with multimode signals and variable loss.

We introduce PULSUS, a direct frequency-domain framework for multidimensional spectroscopy of open quantum systems beyond the impulsive rotating-wave approximation. Coherence-frequency intervals are represented through Liouvillian resolvents, while finite Gaussian pulses are incorporated through operator-valued functions of the field-free Liouvillian. This enables direct evaluation on Cartesian grids or arbitrary spectral coordinates while retaining molecular evolution during the pulse envelopes and, when required, the complete light--matter interaction. The implementation is validated against analytical and independent time-domain benchmarks and supports targeted spectral sampling that reduces the number of evaluated coordinates when the response is spectrally localized. A controlled hierarchy of finite-pulse, rotating-wave, short-pulse, and impulsive models separates the errors introduced by each approximation. For a coupled electronic dimer, the total impulsive-RWA error is nonmonotonic in pulse duration: an intermediate regime provides the highest accuracy, whereas ultrashort pulses expose coupling-enabled beyond-RWA pathways and longer pulses develop substantial finite-pulse corrections. These results show that the impulsive and rotating-wave approximations cannot be assumed to improve simultaneously and should be tested when quantitatively interpreting multidimensional spectra. PULSUS provides a direct frequency-domain framework for carrying out that comparison.

Explicitly correlated methods, which represent dominant short-range correlations by a diagonal Jastrow-type correlator, are designed to accurately describe systems of strongly correlated electrons, such as the fully periodic 2D Fermi--Hubbard model. However, as the reference state is compact in momentum space whereas the correlator acts naturally in real space, there is a fundamental mismatch of bases that classical algorithms resolve only by restricting the reference or the correlator. Here we propose a hybrid algorithm in which a quantum processor prepares a low-entanglement momentum-space matrix product state (MPS), precomputed classically by the transcorrelated method at the cost of a nonvariational energy, rotates it to real space, and measures in bases fixed by the Hamiltonian. Because the measurement bases are independent of the correlator, the correlator can be variationally optimized entirely in classical post-processing with no quantum-classical feedback loop. We demonstrate our algorithm on 32 qubits of Quantinuum's H2-2 with a bond-dimension-4 MPS for the half-filled $4 \times 4$ lattice and achieve a relative ground-state energy error of $16 \pm 4\%$ after postselection, reduced to $3.5 \pm 0.5\%$ by calibration using low-order moments from the MPS. Compared with other feedback-free hybrid algorithms, even under generous assumptions, our method requires fewer samples than quantum-selected configuration interaction and fewer two-qubit gates than quantum Krylov methods.

We propose a protocol to prepare and probe dark states in a single-molecule electron spin resonance based on atomic force microscopy (ESR-AFM), thus extending existing techniques developed to address Rabi oscillations. To this end, we simulate in analogy to atomic physics the coherent manipulation of a three-level system in the V-configuration using a multifrequency magnetic field. More specifically, we consider a neutral molecule with a zero-field-split (ZFS) first excited triplet and analyze within a pump-probe scheme the dynamics of the total triplet population. In the triplet subspace, the dark state is a coherent superposition formed by two ZFS states which does not evolve in time despite a continuous resonant driving towards the third one. We characterize the properties of this state comparing it to its fully incoherent counterpart. Within a density-matrix formalism for open systems, we then compute the expected dark state signatures both for ideal scenarios and for the realistic parameterization of ESR-AFM on pentacene.

We construct Clifford+$T$ circuits implementing arbitrary $n$-qubit unitaries with worst-case $T$-count $\widetilde{O}(N^{8/7})$ at constant operator-norm error, where $N=2^n$, improving the previous exponent $5/4$. The construction uses $\widetilde{O}(N^{6/7})$ clean ancillas. The main idea is to reduce the data addressed by each query to the block-encoding circuit for a sparse piece while controlling the additional simulation work needed to combine the pieces. We simulate a Hermitian logarithm of the target by flattening its traceless part with a two-layer random similarity transformation, randomly partitioning the transformed generator into block-sparse Hermitian pieces, and combining their evolutions using qDRIFT. For a target operator-norm error $ε\in(0,1/2)$, let $L=\log_2(N/ε)$, the qubit count plus the requested bits of accuracy. By successively correcting the approximation error, we obtain a circuit using $\widetilde{O}(N^{8/7}L^{3/7}+NL)$ $T$ gates and $\widetilde{O}(N)$ clean ancillas whenever $L\le N$. We also prove that, at constant precision, the exponent $8/7$ is optimal within a sequential block-SELECT model.

We investigate how unresolved quasistatic disorder in system bath coupling affects non-Markovian dynamics in spin environments. The coupling is fixed within each experimental shot but varies between shots, so repeated shot tomography reconstructs a disorder averaged dynamical map. For a single spin bath with pure dephasing Ising interaction, disorder can drive a transition to CP-divisible dynamics for fixed bath preparations, with a critical strength set by bath polarization along the interaction axis. However, when the bath state fluctuates physically between shots, the averaged dynamics remain CP indivisible at any finite disorder strength. We extend these results analytically to inhomogeneously coupled pure dephasing baths of any number \(N\) of non-interacting spins. At any finite disorder strength, one unpolarized bath spin suffices to retain CP-indivisible dynamics, whereas a fully polarized bath yields Markovian (CP-divisible) dynamics. Dynamics with physically fluctuating bath states likewise remain non-Markovian (CP indivisible) at finite disorder for arbitrary \(N\) in the pure dephasing case. For anisotropic Heisenberg interactions, any nonzero transverse exchange eliminates the disorder driven transition to CP divisibility in a single spin bath. Exact diagonalization of anisotropic models with inhomogeneous couplings up to \(N=12\) reveals persistent trace distance revivals for fixed bath preparations, sampled Haar random preparations, and physically fluctuating bath states, showing that this effect of transverse exchange extends beyond a single bath spin. Increasing disorder still suppresses experimentally accessible revivals and can make memory effects unresolvable at finite measurement resolution even as the dynamics remain CP indivisible. Thus, transverse exchange and physical bath state fluctuations preserve dynamical indivisibility against unresolved coupling disorder.

We consider a closed macroscopic quantum system in a pure state $ψ$ evolving unitarily with Hamiltonian $H$ in a finite-dimensional Hilbert space $\mathscr{H}$. Following von Neumann, we assume a decomposition of $\mathscr{H}$ into mutually orthogonal subspaces $\mathscr{H}_ν$, where each $ν$ represents a macro state, and $\mathscr{H}_ν$ contains the pure states compatible with $ν$. We define the quantum Boltzmann entropy for a macro state $ν$ as $S_\mathrm{qB}(ν) = k_{\mathrm{B}} \log \dim \mathscr{H}_ν$, where $k_\mathrm{B}$ is the Boltzmann constant. Goldstein et al. [http://arxiv.org/abs/1903.11870] have suggested, as a version of the second law of thermodynamics, that $S_\mathrm{qB}$ predominantly increases with time for realistic macroscopic systems. Here, we discuss precise versions of this statement and confirm them for several simple models of $H$ and $\mathscr{H}_ν$.

We investigate the rotational properties of a zero-temperature Bose-Einstein condensed gas, which is confined in a hard-wall potential. For weak interactions the gas carries its angular momentum via vortices of multiple quantization. As the coupling increases and for sufficiently slow rotational frequencies of the trap, the multiply-quantized vortex states become unstable against a mixed state. For stronger couplings, as the angular frequency of the trap increases, there is a transition from a vortex lattice, to a vortex lattice with a hole at the trap center, and finally to a giant vortex. For weak effective attractive interactions we still have vortices of multiple quantization. These states become unstable towards states which break the axial symmetry of the problem and resemble center-of-mass excitation, as the coupling becomes more negative. Finally, for even more attractive forces, the system becomes unstable against collapse.

In order to execute quantum algorithms on bosonic quantum computers, it is necessary to encode their inputs into a desired target quantum state, with a process called state preparation. In real settings, state preparation methods operate in stochastic scenarios, where the prepared state is represented as a mixed state, that is a probabilistic ensemble of pure states. Therefore, existing state preparation methods optimize a variational ansatz by averaging over all possible sequences of photon loss events contained in the prepared ensemble, yielding an output state which approximates the desired target with a certain average fidelity. Such an approach, however, does not take into account directly the distribution of fidelities across states in the ensemble. In this work, we aim to maximize the fidelity of only a subset of pure states sampled from the prepared ensemble, at the cost of reducing the average fidelity overall. This trade-off is relevant when the goal is to obtain high-fidelity states with a certain probability, rather than maximizing the average fidelity of the prepared ensemble. We borrow and adapt objective functions from risk-sensitive optimization, a framework that optimizes specific characteristics of a distribution rather than only its expectation, and that has been successfully applied in Reinforcement Learning. In the considered experimental settings, our results show that the infidelities of some pure states in the prepared ensemble can be reduced by up to four orders of magnitude when using risk-seeking objectives, compared to those achieved using the standard optimization of the average fidelity. Furthermore, we show that it is possible to control the trade-off between the probability of obtaining high-fidelity states and the lowest infidelity threshold reached, providing the flexibility to select the operating point that best suits a certain application.

Quantum computing promises new capabilities beyond classical computation. Mid-circuit measurements (MCMs) enable error correction and outcome-dependent control, but their reliability is limited by noise on superconducting hardware. These operations depend on accurate quantum state discrimination (QSD), which assigns measured signals to state labels. Neural network-based (NN-based) QSD improves this assignment, yet its error remains bounded below by the Bayes risk of the available readout distributions. A complementary challenge is state deterioration as successive measurements accumulate and circuit execution advances, making static calibration less representative of the workload. We present Lifting, a QSD framework that addresses both challenges through repetition encoding, neural decoding, and in situ calibration. Encoding supplies joint in-phase and quadrature (I-Q) readout signals from the target and auxiliary qubits, while contextual calibration trains the decoder for the conditions encountered during execution. Our theoretical analysis shows that retaining additional channels from a fixed joint distribution cannot increase Bayes risk and establishes sufficient conditions for contraction of an overlap-based upper bound. Experiments across three IBM processors evaluate the framework on repeated stabilizer measurement, parity-check, and teleportation workloads.

Fast entangling gates and low-interaction idling require distinct operating conditions in superconducting quantum processors. We experimentally realize a transmon-C-shunt-transmon (TCT) device in which a flux-tunable, three-junction capacitively shunted flux-qubit coupler connects two transmon data qubits. The C-shunt coupler provides a flux-tunable, positively anharmonic spectrum for tailoring the interactions between the data qubits. Conditional Ramsey and swap measurements identify an idle region with near-zero residual ZZ interaction strength and suppressed transverse exchange. At this bias, simultaneous single-qubit interleaved randomized benchmarking yields X-gate fldelities above 99.7%, consistent with individual operation. A 45 ns nonadiabatic controlled-Z (CZ) gate achieves an interleaved randomized benchmarking fldelity estimate of 99.23(15)%. Numerical simulations identify coupler energy relaxation as an important limitation on CZ-gate fldelity and indicate that extending the coupler lifetime can improve gate performance. These results demonstrate the experimental feasibility of C-shunt flux-qubit couplers for combining low-interaction idling with fast entangling operations between transmon qubits.

The ergotropy, or unitarily extractable work, of a quantum system naturally splits into incoherent and coherent contributions, respectively set by population inversion and coherences in the energy eigenbasis. We show that this split makes the coherent ergotropy of a Mach--Zehnder qubit sensitive to path predictability that the output interference fringes do not reveal. We send the path qubit, prepared as a thermal quantum battery, through two quantum-controlled interferometers built from the same elements, a fixed beam splitter and a beam splitter coherently controlled to be present or absent, differing only in the order in which these two act. The two arrangements share identical visibility, stored energy, and incoherent ergotropy at every point in the parameter space. Yet, for work extracted from the output battery alone, placing the controlled beam splitter first never yields less coherent ergotropy, and at fixed visibility and interferometric phase the difference is governed by the path predictability that this ordering creates. The same expression reappears as a purity deficit on the beam-splitter controller, so the work advantage comes with a Landauer bound on the cost of locally resetting the controller that is never larger at the same temperature. We further examine the effects of decoherence on the battery and consider a relativistic realization in which a Wigner rotation correlates the particle's spin with its path. Tracing out the spin decoheres the battery and allows the two arrangements to exhibit different coherent ergotropies even in regimes where their non-relativistic counterparts coincide. These results show that interference visibility is not a complete measure of the coherence available as work.

We analyze fork-grating generation of electron vortex beams beyond the ideal single-mode approximation. The incident beam is described as a paraxial Gaussian ensemble with finite transverse momentum spread and a first electromagnetic Hartree phase accumulated before the grating. Within Fresnel propagation we derive an analytical expression for each diffraction order and determine the corresponding orbital-angular-momentum statistics. The mean OAM of a selected order remains fixed by the topological rule, $\langle L_z\rangle_m=mp\hbar$, while its variance is set by the residual transverse momentum spread of the beam prepared at the grating. For the Gaussian mixture, the transverse purity is $\mathcal P_{\perp,m}=[1+2(ΔL_{z,m}/\hbar)^2]^{-1}$. The observed annular profile is governed by a separate propagation-dependent blurring scale, so a beam can retain well-defined mean OAM while having low transverse purity or a partially filled vortex minimum. Within the radial phase-screen approximation, the Hartree self-field modifies the propagated profile while preserving the full-plane OAM moments and transverse purity.

Polynomial excitations consisting of creation and annihilation operators are studied. Subsystem entanglement is proven produced and preserved by such manipulations. NPT entanglement already present between any two subsystems of a general pure or mixed multipartite Gaussian state is preserved under all polynomial excitations. Nevertheless, these excitations can create NPT entanglement between initially separable subsystems, implying that the number of NPT entangled pairs cannot decrease. Polynomial excitations of a wide class of initially separable pure states are considered. For these states, the method reduces the infinite-dimensional positivity problem to a finite-dimensional one: after partial transposition, NPT entanglement is equivalent to a corresponding bilinear representation matrix not being positive semi-definite. Furthermore, using symplectic diagonalization and spectral decomposition, an explicit transformation is constructed between the Fock-space and position representations. It is applied to quadratic excitations of a three-mode mixed Gaussian state. The behavior of the NPT entanglement is tracked between subsystems as a function of a parameter $κ$, which tunes the non-locality of the excitation, and quantum negativity is evaluated. Under a chosen quadratic Hamiltonian, the resulting unitary time evolution maintains NPT entanglement for long intervals, interrupted only by short periods of PPT states. Finally, a closed analytical expression is derived for the covariance matrix of a general quadratic operator for an arbitrary number of degrees of freedom in phase space. Our framework directly connects mathematical foundations, theoretical modeling, and experimentally feasible implementations.

Variance squeezing of a V-type atom interacting with a dissipative cavity is investigated. First, the influence of atomic initial state parameters on the variance squeezing is explored. The results show that the atomic variance squeezing switches alternately between Sx and Sy as the initial state parameter alpha sweeps from -pi to pi. The two squeezing intervals are symmetric about alpha = pi/4, each with a width of pi/2. For alpha = pi/14, only the Sx component can generate variance squeezing and will eventually disappear with time evolution due to unavoidable environmental noise. Then, the influence of system parameters on the variance squeezing is also studied. It is found that, the optical variance squeezing depth of Sx is determined solely by the atomic initial parameters and is independent of the system parameters. Both weak cavity-environment coupling and atom-cavity detuning can significantly enhance the robustness of the Sx variance squeezing. The SGI parameter has an extremely weak influence on variance squeezing. These results are beneficial for high-precision quantum communication applications.

Dissipation dilution has driven a revolution in the quality factors ($Q$) of top-down nanomechanical resonators. Yet it has not been leveraged for van der Waals (vdW) materials. Here we report quality factors up to $372{,}000\pm37{,}000$ in monolayer MoS$_2$ drums at 4 K, nearly an order of magnitude beyond the previous best for any vdW material at this temperature, enabled by a clean, polymer-free exfoliation technique. We develop a dissipation-dilution model for circular drums and analyze the contributing intrinsic and extrinsic dissipation mechanisms. The MoS$_2$ monolayer exhibits a dilution factor of order $1,000$, establishing sub-nanometer-thin resonators as ultimate dilution materials. The intrinsic quality factor, however, is limited by surface losses at atomic thickness. Conversely, multilayer drums show a lower dilution factor but a high intrinsic quality factor, on par with established top-down materials of similar dimensions, both resulting from the increased thickness. A two-level-system analysis of the temperature-dependent damping confirms this bulk-versus-surface picture and provides first insight into its microscopic origin. Our results identify dissipation dilution as the governing mechanism for high-$Q$ mechanical vdW resonators. Combined with strategies such as soft clamping or stress engineering, they establish atomically thin resonators as a platform for ultrahigh-$Q$ quantum transduction and sensing.

Photo-detection is a fundamental component of experimental photonics, yet theoretical models often treat detectors solely in the photon-number basis, neglecting other relevant degrees of freedom such as spectral characteristics. We present a complete quantum process model for physically realistic photodetection that incorporates both photon-number effects and frequency-dependent detector response, described through explicitly derived Kraus operators in the operator-sum representation. This formalism accommodates realistic inefficiencies, models detection within finite spectral windows, and can be directly substituted for idealized models in quantum optical analyses. The model leads to identifying the suitable detection window of the detectors relative to the spectral distribution of incident photons and conversely, in order to maximize the observability of quantum effects.

We report Zeus-256, a room-temperature nitrogen-vacancy (NV) diamond processor with 256 simultaneously active processor-level logical qubits arranged in a 16 x 16 array. Each logical qubit combines an NV electron-spin ensemble with nuclear-spin memory and ancillary resources. OpenQASM 2.0 circuits are transpiled into RFSoC-controlled microwave, radio-frequency, optical, timing, measurement and bus-configuration sequences. An optically programmable proprietary protein-chromophore layer with an internal metastable-triplet spin mediator provides a reconfigurable biomolecular quantum bus for local and long-range interactions. Benchmarks cover QFT, GHZ entanglement, Grover search, arithmetic, variational, neural-network, graph-state and Shor-family circuits. Factor recovery is reported for 11 integers of 8-84 bits, with 10 attempts per instance; the 84-bit endpoint uses 256 qubits and 40,250,342 reported gates, with a reported execution time of 551.694 ms. Bell-CHSH measurements yield S = 2.8008 +/- 0.0446. Three-qubit Grover search returns the marked state in 958 of 1,024 shots (93.55%), compared with an ideal reference of 94.53%. A separate 30,000-shot population-and-parity protocol yields fixed-phase GHZ+ fidelity of 99.8960%, an estimated standard error of 0.2885 percentage points and a conservative physical 95% interval of [98.2342%, 100%]. Timing metrics are partial and do not establish quantum advantage. Scaling to 9,984 processor-level logical qubits is an engineering target, distinct from the demonstrated register.

We present a fully autonomous model of a mechanical Maxwell demon engine that converts heat absorbed by a qubit into population inversion in an attached quantum battery. A damped mechanical oscillator acts as a pointer that incorporates the essential demon function of information acquisition about the qubit state and subsequent feedback into the system dynamics, replacing external measurements and control operations. This is achieved by means of a Holstein-type Hamiltonian, which makes the pointer's equilibrium position depend on the qubit state and thereby induces a state-dependent resonance shift. The mechanism enables a selective energy transfer to an attached spin system that acts as the quantum battery. We derive both local and global Lindblad master equations for the coupled system and identify the parameter regimes in which the engine operates efficiently. The figure of merit is the resulting steady-state population inversion of the battery, quantified in terms of ergotropy. Based on these results, we discuss the necessary conditions for practical implementations of the demon engine on realistic experimental platforms.

Quantum devices can lose the resource needed for a specified function without entering a fixed failure subspace. We propose a resource-based reliability framework for this situation, quantifying the remaining task-relevant resource relative to a stated ideal capacity. The resource measure is selected through its operational connection to the task and the allowed operations. We develop this approach for a trusted quantum random-number generator and a calibrated two-port interferometer. Relative-entropy coherence determines the optimal asymptotic yield of standard coherent qubits under incoherent operations for the former, while logarithmic $l_1$ coherence quantifies the fringe resource of the latter and determines its calibrated correct-port probability. An exactly solvable multi-spin spin-boson model illustrates how environmental records affect these resources at the same isolated-spin dephasing strength. Collective noise preserves coherence within magnetization sectors for product inputs, but enhances the decay of Greenberger-Horne-Zeilinger branch coherence. Finite-record simulations connect the resource definitions to measurement counts and show that increasing the sample size reduces statistical fluctuations without eliminating bias from an incorrect many-spin noise model. The resulting framework provides a task-specific route to reliability assessment when a fixed failure projector is insufficient, while keeping retained resource capacity distinct from a classical survival probability.

Quantum computers are approaching the early fault-tolerant regime. Verifying the next generation of quantum hardware requires joint emulation of the quantum processor, hardware noise, and classical control and decoding logic. We introduce the Programmable Pauli Virtual Machine (PPVM), an open-source framework for digital twins of quantum processors. PPVM unifies Pauli propagation and generalized tableau simulation under a common abstraction within a single virtual machine. Its bytecode supports arbitrary classical control flow, with measurement-conditioned feed-forward available in the generalized tableau backend. For neutral-atom hardware, we derive independent and correlated atom-loss channels and integrate them into both backends. We demonstrate loss-aware magic state distillation on over a thousand physical qubits and integration with classical decoding through Bloqade QEC Studio.

Quantum error-correction code and circuit construction is an active field of research, motivating automated methods for identifying equivalent designs. We develop and evaluate automated strategies for deciding whether two descriptions of quantum error-correction codes are equivalent under specified transformations. We formalize permutation equivalence for stabilizer and CSS codes and local-Clifford equivalence for stabilizer codes within a unified framework that separates physical from representation freedom. We develop three decision strategies (group-action search, isomorphism-based methods, and constraint solving), together with invariants and signatures for preprocessing. The empirical evaluation shows that no paradigm dominates across equivalence notions, code families, and parameter ranges. We therefore combine their complementary strengths in input-dependent hybrid checkers following a staged Refute-Refine-Decide architecture. Mean hybrid runtimes remain below 10 s for most evaluated structured-code cases with $n \leq 37$; for inequivalent code instances with $n=144$, they are about 310 s for permutation and 16 s for local-Clifford equivalence.

Spatiotemporal optical vortices (STOVs) are structured light featuring a phase singularity in the spatiotemporal domain, exhibiting unique topology that couples spatial and temporal dimensions. To date, amplification of STOVs remains unexplored, and their wavelength tunability is limited by available light sources. In this work, we present the theoretical analysis and experimental demonstration of optical parametric amplification (OPA) of STOVs. The pulse energy of the STOV signal is enhanced by a factor of 60, while its spatiotemporal structure is robustly preserved. The generated idler inherits the phase-conjugated STOV topology with the opposite topological charge, governed by simultaneous conservation of energy, linear momentum, and spatiotemporal orbital angular momentum. The intrinsic wavelength-conversion capability of OPA further provides a route towards spectrally tunable STOV generation, spanning from visible to near-infrared wavelength regimes. This work paves the way toward further development of multi-stage amplification architectures, facilitating applications of wavelength-tunable spatiotemporally structured light at ultrahigh intensities.

Trotterization is a widely used algorithm for simulating quantum evolutions and consists of approximating a target unitary through a local linear decomposition of its generator that is repeated over $N$ steps. We introduce {scheduled trotterization}, a variable-weight modification in which the coefficients of the local linear decomposition are allowed to change from step to step. Using the geometry of the Lie group of unitary operators, we express the global endpoint error as a product of transported local defects, whose leading terms are obtained by two applications of the Baker-Campbell-Hausdorff formula, one inside each local step and one between different transported defects, separating the internal Trotter error from the external accumulation error. While we recover recent tighter bounds on the global approximation error when the weights are held fixed, the new framework allows us to propose a weight-varying schedule that significantly decreases the global error. For exact infinitesimal synthesis, we prove that this improves the usual fixed-weight $O(N^{-1})$ behavior to $O(N^{-2})$, without changing the basic pulse skeleton. We also extend the framework to imperfect infinitesimal synthesis, as arises in quantum gate synthesis problems, where admissible coefficients may only approximate the desired local corrections. In this case, the error is controlled by a local covering parameter measuring the quality of the available coefficient set. Numerical experiments for random $\SU(2)$ targets further support the predicted theoretical improvements. The results suggest a novel perspective for the analysis of Trotter errors, which can be treated as schedulable quantities to be coherently canceled at the endpoint.

Quantum mechanics and general relativity are remarkably successful, yet their joint predictions remain beyond direct experimental reach. Photonic interferometers operating in a gravitational field offer a promising route to test this regime: gravitational redshift differentiates photon propagation between vertically separated arms, leading to a predicted phase shift and reduction in interference visibility. These effects are minute on laboratory scales, motivating existing proposals to consider large interferometer areas to accumulate them geometrically. Indeed, such schemes typically require kilometre-scale optical paths to produce appreciable interferometric signals. Here, we propose a strategy that replaces geometric accumulation with spectral enhancement by coupling the two interferometer arms to optical scatterers based on ultranarrow atomic transitions. These transitions serve as local spectral references: gravitational redshift changes the photon's detuning from each resonance, producing large differences in reflection amplitude and hence substantial visibility loss and interferometric phase shift already for centimetre-scale height differences. We quantify the experimental requirements and assess the feasibility of implementation with current or near-term technology. Our proposal thus opens a route to tabletop optical tests of the interplay between quantum mechanics and general relativity.

The distance of a quantum code is a fundamental metric that dictates its error-correction capability. While quantum low-density parity-check (qLDPC) families such as Bivariate Bicycle (BB) codes offer a promising pathway to low-overhead fault-tolerant quantum computing, computing their distance is challenging. Current exact solvers and even search heuristics that provide a distance upper bound suffer from severe computational bottlenecks, restricting the discovery of optimal codes. In this paper, we construct a dataset of BB codes with corresponding distance upper bounds obtained through high-budget heuristic searches. We introduce BB-Net, an attention-based neural network architecture for predicting the distance of BB codes. It achieves 96.39% accuracy on the reference distances in the test set, compared with 94.86% for state-of-the-art heuristics with a budget of up to $10^{4}$ times more computational runtime. On a subset with certified exact distances, BB-Net achieves 98.94%. By relieving the distance-calculation bottleneck, BB-Net enables faster screening of large code spaces, particularly in ML-driven search pipelines, and thereby can accelerate the discovery of novel quantum error-correcting codes, an important capability for advancing scalable fault-tolerant quantum computing. Our code is publicly available: https://github.com/NadavSc/BBNet

Discrete time crystals are non-equilibrium phases of matter with spatiotemporal order and a response that breaks the time-translation symmetry of a periodic external drive. Interactions, spatial disorder and correlated random driving can in theory stabilize this order. In experiments, however, coupling to the environment limits the time crystal lifetime. Here we use stochastic local bit-flip error correction to prolong the time-crystalline response of a driven, spatially disordered two-dimensional Ising model on a superconducting quantum processor, using a repetition code with distances three and five on a honeycomb lattice with up to 68 physical qubits. Even though ancilla qubits, midcircuit syndrome measurements and decoding increase the required quantum and classical resources, the stochastic drive increases the memory decay time by a factor of up to two. At late times we observe that recovery stabilizes spatial order across the lattice. The spin-configuration distributions explain this separation, as recovery suppresses disagreeing bonds while broadening occupies completely reversed states. Syndrome measurements without correction accelerate the memory decay, demonstrating the importance of conditional correction. Our results show that local bit-flip error correction can preserve time-crystalline memory over more drive cycles than the bare dynamics.

Scalable long-distance quantum gates are essential for distributed quantum computation and scalable quantum networks. We propose an efficient scheme for implementing an $n$-qubit fan-out gate $C^n$ (also known as a controlled-NOT-$\cdots$-NOT gate) across spatially separated parties. Our protocol requires only a pre-shared $n$-qubit Greenberger-Horne-Zeilinger state, $n$ local controlled-NOT (CNOT) gates, and feed-forward operations, thereby reducing both the CNOT and Hadamard gate counts by $(n-2)$ when compared with the standard decomposition-based approach. We further develop two optical architectures to implement the heralded and post-selected $n$-photon fan-out gates, respectively. These schemes require fewer single photons resources and achieve higher success probabilities than their decomposition-based counterparts, representing significant improvements. The results indicate that our approach is experimentally feasible and pave the way toward practical long-distance quantum computation.

We study coherent classical shadows protocols for an unknown $d$-dimensional quantum state of rank at most $r$, allowing an arbitrary joint measurement on all available copies. For observables with operator norm at most one and centered squared Frobenius norm at most $F$, we study the minumum number of copies $T$ needed for the protocol to successed with propbability $1 - δ$. We prove a lower bound on $T$, that depends both on $δ$ and the number $M$ of post-measurement observables. Denoting $\ell=\max\{\log(2M),\log(1/δ)\}$, we show that $T=Ω\left(\min\left\{\frac{\sqrt{rF\ell}}{\varepsilon},\frac{(F\ell)^{2/3}}{\varepsilon^{4/3}}\right\}+\frac{\ell}{\varepsilon^2}\right)$ under the mild assumption $\log(2M)\lesssim d\min\{r,F\}$. The lower bound nearly matches the known upper bound and matches the conjectural strengthening of the known upper bound. The proof is inspired by the framework of the proof of the lower bound for Boolean Hidden Matching. We develop a Gaussian-lift noise kernel that transfers forward and reverse Gaussian hypercontractivity to the Grassmannian, allowing us to bound the distinguishing advantage in an auxiliary game with a revealed query observable. We use Schur--Weyl structure and posterior moment bounds to control arbitrary coherent measurements on the source side.

Maximum compatibility provides a criterion for phylogenetic reconstruction in which the objective is to retain a maximum set of mutually compatible characters. For binary characters, pairwise compatibility can be represented by a weighted graph whose vertices correspond to characters and whose edges connect compatible pairs. A leading algorithm by Cherry [BMC Bioinformatics, 18(1):127, 2017] uses this representation to identify maximum compatible character sets as maximum weight cliques. We formulate the problem as maximum weight independent set enumeration on the complement graph and use deterministic postprocessing to map sampled bit strings to maximal feasible solutions. To explore the prospects of quantum computational advantage, we further construct bespoke correction-in-the-loop Quantum Approximate Optimisation Algorithm instances and find that traditional Lagrange multiplier choices may not be optimal for the enumeration problem on noisy devices. We also introduce lossless graph reductions with reconstruction rules that preserve the complete set of optimal solutions. Our results indicate that graph reduction and sampling can be effectively combined to address the enumeration bottleneck in maximum compatibility phylogeny, while retaining exact reconstruction when the residual optimum set is completely resolved. We enhance Cherry's approach to maximum compatibility by introducing graph reduction techniques and quantum sampling. Our classical benchmarks show a clear difference between finding one optimum and recovering the optimum set in practice. We demonstrate the utility of our methods on graphs constructed from SARS-CoV-2 sequences.

We investigate the ergotropy of tripartite Greenberger-Horne-Zeilinger (GHZ) and W states in the quantum atmosphere of a Schwarzschild black hole, focusing on how the extractable work is redistributed under Hawking-induced thermalization. We find that the two classes of multipartite entanglement exhibit qualitatively different ergotropy structures. For GHZ states, the ergotropies associated with different accessible subsystems organize into two degenerate families, whereas for W states they obey a linear averaging relation with no counterpart in the GHZ case. Under symmetric gravitational thermal corrections, the two GHZ families remain separated by a constant energy gap that is independent of the radial position. We further show that the Hartle-Hawking constant $D_{HH}$ and the normalized radial distance $r/r_h$ play competing roles in the evolution of extractable work: increasing $D_{HH}$ suppresses its recovery toward the asymptotic Hawking limit, while increasing $r/r_h$ enhances the ergotropy accessible to the observers. These results show that the redistribution of extractable work in a black-hole environment is governed not only by gravitationally induced thermalization but also by the structure of the underlying multipartite entanglement, providing a thermodynamic signature that distinguishes GHZ- and W-type quantum correlations in curved spacetime.

Noise characterisation not only enables error mitigation but also provides valuable information about the intrinsic performance of a quantum device, identifying dominant error contributions and bounding noise stability well beyond the aggregated calibration data. Deploying such methods on a specific hardware topology must combine efficiency and accuracy, assess noise stability, and validate the reconstructed noise model. Here we develop and implement these methods on a superconducting processor with square-lattice topology. First, we revise the cycle-benchmarking protocol and reduce the bias arising from unlearnable degrees of freedom via a regularised cost function. Second, we extend a previously developed tensor-network tomography method to match the device layout and show how its accuracy can be improved by repeated layer execution. Both methods allow approximate sublayer noise models to be extracted from parent ones. Using noise characterisation as a tool, we map the noise structure, track drift, and validate the adequacy of the learnt noise models against experimentally observed noisy estimations in benchmark physical and chemistry circuits. These results inform further improvements in the underlying technology and provide estimates of the size of noise-mitigated circuits that the device can support.

We present a Python-based program that combines maximally localized Wannier functions-based first-principles electronic structure with the nonequilibrium Green's function formalism to enable efficient simulations of scanning tunneling microscopy (STM). The workflow builds upon standard density functional theory packages to construct compact transport Hamiltonians that preserve the properties of realistic materials. Superconductivity is incorporated via an effective pairing potential within the Nambu-spinor formalism, while coupling to the STM tip and substrate electrodes is treated using the wide-band limit approximation. Within this formulation, transport quantities such as current-voltage characteristics and differential conductance are evaluated in a closed analytical form. This avoids explicit numerical energy integrations and enables rapid spectroscopic calculations over broad parameter spaces. The framework provides a unified and computationally efficient approach for modeling superconducting hybrid nanostructures with spin-orbit coupling, magnetic textures, and spin polarization. Representative applications in spin chains, two-dimensional and molecular magnets on a superconductor demonstrate its robust capabilities for both simple model systems and realistic ab initio molecular structures relevant to modern STM experiments.

The dynamical formation of a complete Bose-Einstein condensate and the asymptotic purification of trapped bosons coupled to a quantized radiation field are rigorously established. By tracking the macroscopic one-particle density matrix $κ_T$ through a nonlinear resonance cascade, it is demonstrated that radiative relaxation irreversibly depletes all excited trap modes, even when the initial macroscopic state $κ_0$ is genuinely mixed. Here $κ_T$ is an average, with respect to a de Finetti measure $μ_0$, over mean-field particle-field orbits, so that the mixedness of $κ_0$ reflects a statistical ensemble of orbits. Under the assumptions of a non-vanishing initial ground state component and strictly positive downward Fermi-Golden-Rule rates, strong trace-norm convergence to a pure condensate is proven, $$ \lim_{T\to\infty} \| κ_T-|χ_0\rangle\langleχ_0| \|_{\mathfrak{S}_1(\mathfrak{h})} = 0 \, . $$ Furthermore, the von Neumann entropy of the macroscopic one-particle density matrix is shown to vanish asymptotically, $$ \lim_{T\to\infty}S[κ_T]=0 \, , $$ without any claim of monotonicity in $T$. Thus, any initially mixed, positive-entropy state ($0<S[κ_0]<\infty$) is purified to the ground state $|χ_0\rangle\langleχ_0|$. For the proof, we derive the Hartree hierarchy of the coupled system of bosons and photons from the finite-$N$ BBGKY hierarchy of the microscopic quantum many-body system, establishing trace-norm convergence in the mean-field limit as $N\to\infty$. The limits are taken successively; first $N\to\infty$, then the weak-coupling limit, and finally $T\to\infty$. Although the global particle-field evolution remains unitary, the macroscopic one-particle state converges to a pure state as energy and correlations are continuously radiated into the dispersive field.

Spin wave theory plays a central role in the analysis of low-energy properties of the quantum ferromagnetic Heisenberg model. In this work, we present a first step towards a rigorous justification of this approximation in the context of quantum dynamics in one dimension. According to spin wave theory, the evolution of a spin wave state should be well approximated by its free evolution with the appropriate energy of free quasiparticles called magnons. Our main result establishes this idea rigorously for a class of spin wave packets. We focus on spin-$\frac{1}{2}$ systems, and consider wave packets composed of two magnons. We argue our result is optimal with respect to the timescales.

Non-Hermitian dynamics possesses distinct left and right eigenstates, but their normalization freedom obscures a direct probabilistic interpretation. Starting from a globally Hermitian system governed by the standard Born rule, we generalize dynamical quantum phase transitions (DQPTs) from a reference state to a physical subspace. This generalization provides a clear probabilistic interpretation of left and right states: when each state is normalized to itself, their mutual overlap determines a directly accessible dynamical transition rate. We discuss the new phenomena governed by this emergent non-biorthogonal Born rule and further identify a class of exceptional-point DQPTs (EP-DQPTs), at which the eigenstates of the critical propagator coalesce. Our theory places the probabilistic interpretation of non-Hermitian quantum mechanics on the firm footing of Hermitian quantum mechanics.

Amplitude embedding lets a variational quantum model read many classical features with few qubits, but the model output is then only a quadratic form in the normalized input. Data re-uploading, which encodes the input repeatedly between trainable blocks, can be used to enrich such a model. Because every additional upload of an amplitude embedding repeats a costly state preparation, the gain that an upload buys has to be known before the gates are spent. This tutorial thus addresses the problem of explaining what data re-uploading adds to an amplitude-embedded model and how large the gain is. We express sequential re-uploading and parallel re-uploading with two copies in one notation and show that each upload raises the reachable polynomial order by two. Under one trainable circuit family and one budget of trainable parameters, simulation results show that re-uploading raises the test coefficient of determination from 0.689 to between 0.883 and 0.975 on targets of order four and from 0.337 to between 0.642 and 0.783 on targets of order six, on all ten seeds. On a quadratic target and on handwritten digits, one upload remains the best choice, and every additional upload lowers the gate error that the classifier tolerates. These results help designers match the number of uploads to the polynomial order of the task at hand.

We theoretically investigate single-photon coherent transport through a finite waveguide quantum electrodynamics (QED) array with spatially modulated emitter-waveguide couplings. By combining exact scattering calculations with spectral factorization and a semiclassical WKB analysis, we identify how the coupling profile controls the reflection bandwidth and its finite-size dependence. A Gaussian transverse displacement produces an exponential-of-Gaussian decay-rate profile that broadens the high-reflectivity window and suppresses the boundary-induced Fabry-Perot oscillations compared with a uniform array. The transmission zeros remain exactly degenerate at the atomic resonance for arbitrary positive coupling profiles at non-Bragg spacings. In contrast, the collective poles reorganize under the spatial modulation, redistributing their radiative widths and preventing individual subradiant resonances from terminating the reflection window. We further derive an algebraic 1/N scaling law for the contraction of the bandwidth toward its bulk value. The bulk bandwidth is determined by the largest local decay rate, whereas the finite-size correction increases as the profile becomes sharper, leading to an optimal profile width. These results establish spatial coupling engineering as a practical tool for designing broadband atomic mirrors in atom-nanofiber and circuit-QED platforms.

Any pair of sufficiently generic Hamiltonians on $\mathbb{C}^d$ generates the full unitary group, i.e., any $W\in U(d)$ can be synthesized to arbitrary precision by alternating between the two evolutions for suitably chosen durations. For any given pair of Hamiltonians, the minimal number of switches required to cover the entire group is at least $d$ and unbounded in general. Despite this, we show that it scales linearly in $d$ in expectation. Assuming that the two spectra are sufficiently generic, we derive constructive upper bounds on the minimal switching number as a function of the change-of-basis matrix between the two eigenbases. In particular, if this matrix has a column whose entries all have equal moduli, as for a complex Hadamard matrix, then $9d$ switches suffice to reach every unitary. To obtain these results, we construct a short exact representation of any unitary as a product of unitaries that are alternately diagonal in two given bases. All bounds are extended to non-generic spectra and bounded evolution times.

Level crossings, where two quantum energy levels intersect, are ubiquitous in quantum systems and play a central role in controlling quantum dynamics. In this study, we establish a framework that connects these level crossing structures to the ultimate precision limits of quantum metrology. By analyzing a Hamiltonian with the level crossings structure, we identify the conditions under which multiple parameters can be estimated simultaneously with maximal sensitivity near the level crossing point. We then construct a resource efficient sensing protocol based on unitary quench dynamics and Bayesian estimation, enabling high precision, low cost parameter estimation without requiring entanglement or complex control. We present a protocol whose estimation precision saturates the Holevo Cramer Rao bound, the tightest achievable precision bound in multi parameter estimation. Using the two level model and the two spin Ising model as illustrative examples, we demonstrate how the protocol can be applied to a system with level crossing Hamiltonian structure. Our findings reveal that level crossings serve as universal operating points for precision quantum metrology, offering a simple and scalable path toward practical multi parameter sensing across diverse quantum platforms.

Boson sampling with array of on-demand single photons (discreet variable Fock states) as resource states provides distinct advantages in complexity scaling compared to single photon resource states mimicked by the states (continuous variable) generated in nonlinear photonics. Recent progress in realization of regular ordered array of mesa top single quantum dots (MTSQDs) enabling on-demand generation of many photon resource states with high single photon purity and indistinguishability [1,2] has opened the possibility of implementing chip-scale Boson sampling with single photons. An important question towards scale up of such circuits is how the dephasing and decay timescale of individual on-demand single photons affect the final probability distribution of the N-photon entangled state. In this work we report a framework that provides direct link between the physical sources of decoherence to the outcome of multiphoton correlation measurements. We explicitly incorporate the symmetrization of the N-photon states while accounting for the shape of the individual wave packets and dephasing. Using this framework, we show predictive estimates of the probability of generation of a 4-photon NOON state using an optical circuit initialized with 4 identical single photon wave packets, mimicking the emitted photons from MTSQD single photon sources reported in [2]. Specifically, we show how the probability of generating various 4-photon entangled states depend on the two-photon interference visibility which is determined by the pure dephasing timescale in relation to the radiative decay timescale. The results provide quantitative guidelines to measure 4 photon and higher number of entangled photon states generated in an optical circuit with on demand single photon sources and provide a link between physical processes such as temperature and the output state of the quantum optical circuits.

Variational quantum algorithms utilize parameterized circuits many times during training, at new parameter values, over batches of data, and with gradients. Pauli propagation approximates the expectation values of such circuits classically by evolving the observable in the Heisenberg picture as a truncated sum of Pauli strings. We present PADO-Pauli, a GPU engine for Pauli propagation that compiles a circuit and its observables once into sparse matrices in which each rotation angle contributes only a cosine and a sine factor, so every later evaluation reuses the compiled program. It evaluates batches of parameters and data inputs embedded as rotation angles. By default its gradients come from a vector-Jacobian product registered with PyTorch's automatic differentiation, so they flow through the angles to any classical layer that produces them. PADO-Pauli also provides truncation by Pauli weight and coefficient size, and noise channels. Zero-filtering removes terms that do not contribute to an expectation value in the all-zero reference state and makes the batched forward pass about 1.5 times faster. Compared to cuPauliProp on an NVIDIA A100, PADO-Pauli evaluates up to 10 times faster on 4 to 12 qubits and uses up to 3.1 times less memory on 16 qubits. We check its accuracy against exact statevector simulation up to 28 qubits. These features make PADO-Pauli a practical toolkit for training variational quantum algorithms, including quantum machine learning models.

Quantum Machine Learning (QML) has a theoretical advantage over classical algorithms for specific synthetic data that is computationally hard. However, it remains unclear whether such theoretical advantages play a meaningful role for realistic classical data, such as natural images. Quantum structural properties induced by unitary operations or entanglement introduce inductive biases that differ from those of classical models, potentially leading to distinct learning behavior on real-world data. In a fully quantum learning pipeline, classical real-world data are first encoded into quantum states via a quantum feature mapping, analogous to a classical feature extractor, and a quantum classifier then classifies the resulting states. Quantum feature mappings generate representations that are difficult to realize classically, while also inducing representation-level biases that do not necessarily match the structure of realistic data. To enable a fair comparison at the classifier level, we focus on the classifier and use classical feature extractors that already provide powerful representations for natural images. By controlling the data scale and supervision strength, we analyze how the unitary structure of quantum classifiers affects generalization, and show that their effectiveness depends strongly on the geometry of the input representations. These results indicate that quantum classifiers benefit from classical features that are aligned with quantum feature spaces. Our analysis shows that kernel alignment identifies representations compatible with quantum feature spaces, providing insights into translating classical models into quantum algorithms.

Practical quantum programs interleave quantum and classical computation: classical data shape the quantum operations that are performed, and measurement outcomes shape the classical computation that follows. Formal verification of such programs in a proof assistant requires mechanizing a program logic that handles this interplay consistently at every level, from the mathematics of quantum mechanics, through program syntax and semantics, to specifications and proof rules. Such mechanizations, along with the program proofs built on them, typically require substantial manual effort. We present QEDIA, a framework for verifying quantum programs with classical variables in Lean 4. At its foundation is an open library that formalizes the quantum Hoare logic QHL+ across all these levels and proves the logic sound for both partial and total correctness. We construct the library and the program proofs, under human supervision, using an LLM-based prover agent, whose general-purpose core we extend for quantum program verification. We illustrate QEDIA with verified programs including the quantum Fourier transform, phase estimation, repeat-until-success circuits, and Hamiltonian simulation.