In briefSequential Capacity of Quantum Processes with Finite Memory
SummaryThe paper studies how complex a quantum device's responses can become over longer runs when its internal memory is fixed. It defines sequential response capacity as the number of adaptive testing stages that can keep separating possible processes by a set probability gap. For fixed system and memory sizes, the capacity grows on the order of K log K in the number of time steps per run, with a tight matching bound. The authors achieve this with time-dependent phase rotations on a single qubit, whereas classical processes measuring in a fixed basis have only linear capacity.
In briefStark effect in hydrogenic ions to test an indefinite-metric spin-1/2 wave equation
SummaryThe paper examines the eight-component FV½ relativistic wave equation for spin-½ particles, which has a doubled solution space and an indefinite inner product. The authors compute first- and second-order Stark shifts of n=1–3 hydrogenic levels from H to U⁹¹⁺ in Schrödinger, Dirac and FV½ theories. FV½ and Dirac shifts agree level by level. The work also discusses the relativistic linear Stark effect and the weak/strong-field crossover.
Paulus C. Tjiang, Sylvia H. Sutanto, Vincentius E. W. Tjia
In briefTesting whether a quantum state is fermionic Gaussian, with sample complexity independent of mode count
SummaryThe paper studies how to decide whether an unknown pure n-mode quantum state is fermionic Gaussian or at least ε-far in trace distance from all Gaussian states. The authors introduce a new technique for upper bounding the acceptance probability of states far from a family, which bounds the sample complexity of such decision problems. They show that Θ(ε⁻²) copies suffice, which is optimal, and that the well-known Bell sampling procedure is optimal even against arbitrary collective and adaptive measurements. The same mode-independent sample complexity is also shown for deciding membership in the family of Slater determinant states.
WhyA general upper-bounding technique proves optimal Θ(ε^-2) sample complexity for fermionic Gaussianity testing and optimality of Bell sampling.
In briefComplexity of Finding the Nearest Stabilizer Product State
SummaryThis paper studies an optimization problem: given an n-qubit stabilizer state, find the single-qubit stabilizer product state that has the largest overlap with it. The authors show that solutions to this problem can tighten runtime bounds for certain classical simulation algorithms, serve as entanglement measures, and relate to low-rank matrix completion. They give a complete complexity classification, finding that after accounting for Clifford group symmetries there are 9 possible sets, and all but the two simplest are NP-complete.
WhyGives a complete complexity classification of the nearest stabilizer product state problem, with applications to simulation, entanglement measures, and matrix completion.
In briefNonlocality without entanglement in multipartite quantum measurements
SummaryThe paper studies when pairs of product measurements can be distinguished under different access conditions. Two-qubit product measurements that are perfectly distinguishable when accessed jointly cannot be perfectly distinguished when split between distant parties using LOCC. It also shows that adaptive LOCC protocols can outperform non-adaptive ones, that LOCC distinguishability can depend on which party starts, and it extends the results to n-qubit measurements.
WhyEstablishes measurement-level nonlocality without entanglement and shows adaptive LOCC strictly beats non-adaptive protocols, with fairly thorough constructions and proofs.
In briefAdaptive single-copy measurements enable optimal learning of stabilizer states
SummaryStabilizer states are central to quantum computing, but learning them with single-copy measurements was thought to need far more samples than two-copy Bell measurements. This paper gives a polynomial-time adaptive algorithm that learns any n-qubit stabilizer state from Θ(n) single-copy Clifford measurements. This matches the optimal sample complexity of Bell sampling without using multi-copy measurements.
WhyAdaptive single-copy measurements match optimal Bell-sampling complexity, closing a known gap with rigorous bounds and extensions to testing and near-stabilizer states.
In briefQuantum simulation of sparse Hamiltonians with optimal scaling in column norm
SummaryThis paper presents a quantum algorithm for simulating d-sparse Hermitian Hamiltonians, assuming a known upper bound on the maximum column Euclidean norm. The query complexity is O(tΛ√d + √d·log(2/ε)), removing the subpolynomial overhead of Low's earlier algorithm. For some parameter ranges the bound matches the worst-case lower bound. The authors also apply the result to sparse quantum linear systems and black-box unitary implementation.
WhyRemoves Low's subpolynomial overhead, matching the lower bound and resolving an open question of Berry and Childs via analytic results.
In briefA Variant of Clifford Circuit Synthesis Is NP-Complete
SummaryThe paper studies optimal Clifford circuit synthesis, which seeks the shortest-depth quantum circuit for a given operation using a fixed set of elementary gates. The authors show that a variant of this problem is NP-hard, by reducing 3-edge colorability of 3-regular graphs to a synthesis problem using only CZ gates. They further argue that adding Hadamard, phase, and CNOT gates does not reduce the optimal depth. Simulation and equivalence checking are in P, while deciding whether a Clifford unitary can be implemented within a given depth is NP-complete.
WhyReduces 3-edge colorability to CZ-only circuit synthesis and proves extra Clifford gates cannot lower depth, giving a complete NP-hardness proof with impact mainly within quantum circuit theory.
In briefOperational transformation rates for quantum states without the i.i.d. assumption
SummaryThe paper examines whether multiple copies of a quantum state can be treated as independent and identically distributed (iid). It relaxes this assumption by considering resource states that cannot be distinguished from a tensor power state. Using a de Finetti-type argument, the authors show that this set of states can asymptotically be represented by almost-iid states. They then introduce operational analogues of rates such as entanglement cost and distillation, and ask whether these coincide with their iid counterparts.
In briefGeometry of coefficients used to detect quantum errors exactly
SummaryThis paper studies the geometry of Knill-Laflamme coefficients, which characterize exact quantum error detection, and how operator representation, code dimension, and detection constraints shape the set of attainable coefficient vectors. The main theorem states that when each occupied block has multiplicity at least the code dimension times the rank of the active state, the coefficient range is the full active expectation body, which is convex and connected with a closed interval as its signature spectrum. The framework covers commuting Pauli families and subsystem stabilizer codes, and examples show how ranges can shrink, collapse, or become disconnected.
In briefMetastability of the Mean-Field Interchange Model for Local Dimension ≥3
SummaryThis paper studies how quantum systems thermalize at low temperatures. The authors show that the Davies dynamics of a mean-field interchange model with local dimension d≥3 and single-site generalized Pauli couplings has two distinguished inverse temperatures, with a static first-order phase transition between them. Between these temperatures, the spectral gap of the Davies generator vanishes exponentially in system size n, indicating metastability. Outside this interval, the gap is bounded below by an inverse polynomial in n, allowing polynomial-time thermalization.
In briefTesting whether a quantum state is near a product state, and learning the closest one
SummaryThe paper studies whether an unknown n-qudit quantum state is close to a product state or far from all product states, measured by state overlap. It gives a time-efficient algorithm that needs a number of state copies independent of n, and shows that a k-copy generalization of the Harrow and Montanaro product state test is an efficient tolerant tester. The same techniques yield an improved algorithm for learning the closest product state, which outputs an ε-approximately optimal product state.
WhyCombines random coloring with blockwise spectral projection to give a tolerant product-state tester and substantially improved closest-product-state learning with n-independent sample complexity.
In briefEfficient quantum ground-state preparation via imaginary-time Majorana evolution
SummaryThe paper introduces VIME, a classical pre-training method for preparing molecular ground states on quantum hardware, built on a compiled Majorana-propagation surrogate graph and a compressed tiled Unitary Product State circuit. For the ruthenium complex TLD-1411 with active spaces up to 52 qubits, it reports chemical precision against DMRG references, with energy errors about 400 times smaller than ADAPT-VMPE. Across acenes up to heptacene (60 qubits), it matches or improves the energy accuracy of the comparison points while using up to 26 times fewer CNOTs and 167 times lower two-qubit depth.
Federico Santona, Manuel G. Algaba, Aeishah Ameera Anuar et al.
In briefUniversal coding trades away reliability in classical-quantum channels
SummaryThis paper studies channel coding for classical-quantum channels, where universal codes work without full channel knowledge. For classical channels, universal codes can achieve both capacity and optimal high-rate reliability, but the authors show this fails in the quantum case because the unknown unitary rotation of the output prevents it. They exhibit a family of channels where no fixed scheme reaches the channel-aware optimal reliability, and derive a matching universal reliability bound for unitary-invariant decoders. The channel-aware and universal error exponents are governed by the Petz and sandwiched Rényi divergences, which coincide only when outputs commute.
WhyProves universal coding cannot reach channel-aware optimal reliability for classical-quantum channels, characterizing the universal exponent via sandwiched Rényi divergence.
Kaito Watanabe, Masahito Hayashi, Takaya Matsuura et al.
In briefProving optimal query complexity for fractional quantum evolution, confirming QSVT is asymptotically optimal
SummaryThis paper studies how many oracle queries are needed to implement a fractional power U^t of an unknown unitary U=e^{iH} with 0<t<1. Quantum singular value transformation gives an upper bound of O((1/δ)log(1/ε)). The authors prove a matching lower bound for arbitrary query algorithms, so the optimal complexity is Θ((1/δ)log(1/ε)) and the known construction is asymptotically optimal. They also give a second lower bound, Ω(log(1/ε)), that is uniform in the spectral gap δ.<br>
WhyProves a tight lower bound for fractional-power queries, showing the known QSVT construction is asymptotically optimal; strong theory, narrow application scope.
Anthony Yuezhang Liu, Adam Weso{\l}owski, Jayne Thompson et al.
In briefAvoiding Exponentially Large Groups with Open Quantum Systems: a study using small Lie groups and environment operations for quantum state preparation and channel universality.
SummaryThe paper proposes a new approach to quantum state preparation that avoids the full unitary group on n qubits by identifying a small Lie group G acting on n+3 qubits, whose Lie algebra has dimension polynomial in n. Using partial traces and state preparation in the environment together with group operations, any state can be approximated from a fixed input state. The authors also identify a single interaction Hamiltonian and show that all n-qubit channels can be approximated with a larger environment.
In briefLoss-tolerant distributed lattice surgery via fusion networks
SummaryThis paper studies how to perform distributed logical operations across photonic links connecting matter-based quantum processors. The authors use ZX calculus to build hybrid syndrome extraction protocols and apply them to distributed rotated surface code lattice surgery. Several protocols reach a 50% interface-erasure threshold when local noise is absent, and the hybrid ones increase interface distance. The paper also maps correctable regions under resource-state errors, circuit noise, and fusion erasure, and converts erasure thresholds into photon-loss thresholds.
WhyCombines ZX calculus and fusion networks to boost interface distance and reach a 50% erasure threshold, supported by numerical threshold and noise-mapping analysis.
In briefStreaming-setting exponential memory advantage for decoded quantum interferometry
SummaryThis paper examines whether decoded quantum interferometry (DQI), a quantum optimization algorithm, gives memory advantages in the streaming setting. It generalizes the optimal polynomial intersection problem using Hermite interpolation and Hasse derivatives. The authors report that a quantum adaptation satisfies 93% of constraints in one pass using polylogarithmic space, while any classical algorithm reaching 76% needs polynomial space.
WhyExtends DQI to streaming and proves unconditional memory advantage: quantum reaches 93% of constraints in polylog space versus classical needing polynomial space for 76%.
In briefSuperintegrability of a resonant ghostly three-Hamiltonian model and its transcendental completion
SummaryThis paper studies classical and quantum superintegrability of a resonant three-dimensional Hamiltonian with indefinite kinetic energy, described by three Poisson structures for the same flow. Beyond three commuting quadratic Hamiltonians, it identifies additional degree-four polynomial first integrals. The system is minimally superintegrable in the polynomial and rational classes, and maximally superintegrable on an invariant domain once transcendental integrals are admitted. Weyl quantisation yields exact higher-order differential symmetries.
In briefSymmetry analysis of chirality-induced spin selectivity
SummaryThis perspective paper examines chirality-induced spin selectivity (CISS), the coupling between structural chirality and electron spin polarization. It uses symmetry considerations common in fundamental particle physics to explain basic properties of the effect. The authors show that CISS does not violate fundamental symmetries such as parity and time-reversal, and argue that symmetry offers a conceptual foundation for interpreting experiments and guiding future work.
In briefFloquet-Universal Hamiltonian Simulation: a theory for building target Hamiltonians from periodically driven interactions
SummaryThis paper develops a theory of Floquet simulation, in which periodically driven Hamiltonians are used to synthesise time-independent ones. The authors show that a set of interactions S can Floquet-simulate every Hamiltonian in its Lie algebra Lie(S), and give a complete, constructive characterisation of Floquet-universal Hamiltonians. The construction needs only O(1) local interaction strengths and their ratios, with driving frequency ranges scaling polynomially with system size for k-local lattice Hamiltonians.
WhyGives a complete, constructive characterisation of Floquet-universal Hamiltonians with only O(1) interaction strengths, plus new BQP-completeness and QMA-hardness consequences.
Emilio Onorati, Harriet Apel, Michael M. Wolf et al.
In briefSymmetry-based Fourier method for geometric quantum machine learning
SummaryThis paper studies how symmetry affects the expressivity of quantum Fourier models, analyzing the variance of symmetrized Fourier coefficients. It proposes randomized encoding, which implements invariant models without ancilla qubits or extra circuit depth for twirling. Evaluated as quantum physics-informed neural networks on two-dimensional screened Poisson and stationary viscous Hamilton-Jacobi equations, the approaches achieve the lowest mean errors in the respective benchmarks.
Letao Wang, Abdel Lisser, Sreejith Sreekumar et al.
In briefAlgebraic methods for solving two magnetic quantum systems with hidden symmetries
SummaryThe paper studies two three-dimensional quantum superintegrable systems in nonvanishing axially symmetric magnetic fields. The integrals generate a quadratic algebra, and deformed-oscillator representations give algebraic spectra that match those from separation of variables. After separation the equations are reformulated as Sturm eigenvalue problems and algebraized into sl(2) and, before separation, sl(3) structures.
In briefCoherent release fronts in Krylov chains and thermal AdS2 response
SummaryThe paper studies coherent release from a finite serial Krylov sector into an exact conformal tail with asymptotically linear Lanczos coefficients. It derives the cumulative occupation behind a front that moves to greater Krylov depth over time. The tail sets the logarithmic transit scale while the finite sector shapes the distribution. The framework is illustrated in thermal AdS2, where weak coupling yields a two-site shallow sector coupled to the conformal tail.
In briefApproximation theorems for fermionic Gaussian states
SummaryThis paper shows that sufficiently distributed interactions or correlations in fermionic Gaussian states can be described approximately by mean-field or product states, working directly with Majorana covariance matrices. It uses a monogamy constraint on two-point correlations to obtain product-state approximations for quadratic Hamiltonians on high-degree graphs, a finite fermionic Gaussian de Finetti theorem, and recoverability estimates for spatial states with clustering mutual information.
WhyDerives quantitative product, de Finetti, and recoverability bounds from covariance monogamy for fermionic Gaussian states, a clear theoretical advance.
Amir-Reza Negari, Farzin Salek, Zolt\'an Zimbor\'as et al.
In briefQuantum optimal transport barycenters: existence, duality, and Gaussian rigidity
SummaryThis paper builds a quantum optimal transport (QOT) barycenter framework for quantum states, analogous to Wasserstein barycenters, and proves existence and duality results for a broad class of possibly unbounded costs on separable Hilbert spaces. It studies Gaussian input states and proves a rigidity theorem: if at least one Gaussian input is faithful, the 2-quantum Wasserstein barycenter is unique among all quantum states and is necessarily Gaussian. Faithfulness is sufficient but not necessary.
WhyProves existence, duality, and a Gaussian rigidity theorem for quantum Wasserstein barycenters, a substantive theoretical advance with limited practical scope.
In briefDiagram-based rules for fermionic quantum computing circuits
SummaryThis paper studies fermionic quantum computation based on local fermionic modes, whose pure state spaces match qubit state spaces via the Jordan-Wigner representation but whose parallel composition differs. The authors show that LFM processes form a symmetric premonoidal category whose centre is the even, parity-preserving subcategory, and introduce pronaps for diagrammatic reasoning in the fermionic ZW calculus. They provide normal forms and completeness proofs for the EoW, FoW, EW and FW fragments, with the FW presentation giving a new normal form for the matchgate fragment.
In briefBallistic speed and recurrence in homogeneous open quantum random walks
SummaryThe paper links root-mean-square ballistic transport to potential-theoretic recurrence for finite-range open quantum random walks. Under stated spectral assumptions, it proves a periodic uniform local limit theorem and exponential finite-set return bounds for nonzero drift, and gives Green-function and potential-kernel asymptotics for centered walks. For reducible walks, an explicit harmonic h-transform decomposes absorption components, and a centered noncommuting family verifies the assumptions with explicit constants.
Ameur Dhahri, Chul Ki Ko, Farrukh Mukhamedov et al.
In briefNear-optimal circuit depth for simulating local quantum systems on a lattice
SummaryThe paper studies digital simulation of time evolution for geometrically local quantum Hamiltonians. It builds a nearest-neighbor circuit with depth O(T log(nT/ε)), reducing the polylogarithmic overhead of prior work to a single logarithm. For uniform XXZ Hamiltonians, it proves a depth lower bound of Ω(log n/log log n), matching the upper bound up to a doubly logarithmic factor.
WhyReduces polylogarithmic overhead to a single logarithm and proves a near-matching depth lower bound for XXZ.
In briefA wave-particle test of Wheeler's delayed-choice experiment using two controlled beam splitters.
SummaryThis paper reports an experiment that realizes Wheeler's delayed-choice experiment using entangled photons. Both beam splitters in a Mach-Zehnder interferometer are controlled, with the presence or absence of the second one set through path encoding. The results show the wave-particle behavior of single photons under different two-beam-splitter configurations. The authors also discuss how photons would be in a wave-particle quantum superposition if the beam splitters are in a superposition of being present and absent.
