In briefNew Problems for Decoded Quantum Interferometry Screened by Soundness Rules
SummaryDecoded quantum interferometry (DQI) solves optimization problems using classical error correction, but it is unclear which problems could show a quantum advantage. The paper proposes soundness rules that screen candidate problems by code parameters, decoding guarantees and classical baselines. It proves that for counting satisfied constraints under worst-case Hamming decoding, DQI's guarantee exceeds Prange completion by at most (√2−1)/2, a cap that optimal polynomial intersection asymptotically attains. An AI-agent search guided by these rules proposed two candidate applications, and on the larger instances tested, the authors report DQI's expected quality exceeded their classical solvers' results within fixed budgets.
In briefFast parallel logic operations on ultra-high-rate quantum codes to reduce fault-tolerance overhead
SummaryThis paper develops fast, parallel logical computation methods for ultra-high-rate quantum LDPC codes. The authors use the codes' group symmetries to partition logical qubits into orbits and apply parallel surgery to implement group-invariant Pauli-product measurements, with a chain-map convolution technique to boost distances efficiently. Case studies on specific codes report distance-preserving measurement gadgets with about 2.5× space overhead and 3 to 4 syndrome-extraction rounds.
In briefMinimal quantum description length for density matrices with known spectrum
SummaryThe paper studies a variant of Schumacher compression that asks for the minimal memory needed to compress many copies of a density matrix with known spectrum and unknown eigenbasis, without preserving its purification. For fixed dimension and distinct positive eigenvalues, the cost is determined through its additive constant. Achievability generalizes Werner's cloning map to GL(d,C) irreducible representations with finite trace-distance bounds, and the converse uses a quantitative Koashi–Imoto incompressibility result under a spectral-gap assumption. A Lean certificate for the proofs is provided.
Patrick Hayden, Alexander Maloney, Jinzhao Wang et al.
In briefFree entropy and quantum minimum description length: a physical measure of the minimal quantum memory for programming state copies
SummaryThe paper defines a finite-dimensional physical free entropy at finite resolution, derived from Voiculescu's free entropy in free probability. It shows that this quantity characterizes, up to an explicit constant, the minimal quantum memory needed to program many copies of a state with known eigenvalues and unknown eigenbasis. The optimal cost of this task is called the quantum minimum description length.
Patrick Hayden, Alexander Maloney, Jinzhao Wang et al.
In briefSeparating clonable QMA and QCMA with a classical oracle
SummaryThis paper shows that even clonable quantum proofs can be more powerful than classical proofs relative to a classical oracle. The authors construct a classical oracle O for which QCMA^O differs from ClonableQMA^O, answering an open question of Nehoran and Zhandry (ITCS '24). The paper also gives a classical-oracle separation between BQP/clonableqpoly and BQP/poly and discusses applications to quantum cryptography.
WhySeparates QCMA from ClonableQMA with a classical oracle, resolving an open question and showing unclonability is not necessary for quantum proof advantage.
Alper Cakan, Kai-Min Chung, Wei-Hsiang Hung et al.
In briefAnti-symmetrization Is Cheap and Useful: A method for preparing anti-symmetric quantum states from mixed-state copies
SummaryThe paper studies anti-symmetrizing an unknown mixed quantum state: given copies of a rank-r state, prepare a copy of the state proportional to the anti-symmetric projection of its eigenvectors. A simple algorithm uses about r over the minimum nonzero eigenvalue copies and works in a streaming setting with small memory. A second, Schur-Weyl-based procedure uses O(r over λ_min) copies and supports weak and unitary Schur sampling and optimal purity amplification.
Adam Bene Watts, John Bostanci, Matthias C. Caro et al.
In briefCharacterizing Partial Photon Distinguishability via Gram Matrix Tomography
SummaryThis paper introduces Gram-matrix tomography to characterize how partially distinguishable independently prepared photons are, a property that affects multiphoton interference. The method reconstructs the Gram matrix from a quadratic number of Bargmann invariants, measured using Fourier interferometers or photon-number correlations in a single random interferometer. The authors derive error bounds controlling the total-variation distance between predicted and actual outcomes, and show the total sample complexity is independent of the internal Hilbert-space dimension.
WhyIntroduces Gram-matrix tomography for partial distinguishability with dimension-independent sample complexity and explicit total-variation error bounds, a substantive advance.
Marcin Kotowski, Marco Robbio, Oliver Reardon-Smith et al.
In briefStreaming Regev's Quantum Factoring Algorithm: A method to make Regev's quantum factoring algorithm use fewer qubits.
SummaryA major practical problem with Regev's factoring algorithm is its large space usage, and it was previously thought to be incompatible with qubit recycling, which streams control qubits in phase estimation. The paper builds on Ragavan and Vaikuntanathan's Fibonacci accumulator construction, using superposition masking to avoid uncomputation and phase estimation with Fibonacci powers of a unitary. These changes let phase-estimation qubits be used only once and streamed. The space usage becomes n+M(n)+O(√n), and with the in-place multiplier of Luo et al. (2026), an n-bit integer can be factored with about 4n+O(√n) qubits.
In briefQubit CSS codes with universal transversal gates
SummaryThe Eastin-Knill theorem forbids a universal set of transversal logical gates on codes that detect single-qubit errors. This paper shows that depth-one layers of few-qubit gates, each respecting its own qubit partition, can together generate a universal logical gate set on an error-correcting code. The authors construct 47 such codes by applying entangling circuits to lower-distance seed codes, including a [[37,1,7]] and a [[59,1,9]] code.
In briefRandom-order quantum streaming: replenishment and robust lower bounds
SummaryThis paper studies how random input order changes the value of quantum memory in streaming, showing that later classical input can make a consumed quantum state useful again, a effect called replenishment. The authors build a Hidden Matching-based problem that a one-pass quantum algorithm solves in polylogarithmic space under uniformly random order, while classical random-order and quantum settings with all updates first need polynomial space. They prove that quantum encodings supporting multiple matching requests require Omega(r) qubits, and extend Kallaugher's triangle-counting algorithm and the Noisy Gap Cycle framework to quantum streaming.
WhyIntroduces replenishment under random order, with a constructed problem and strengthened quantum lower bounds; a solid theoretical contribution with moderate impact.
In briefCertifying measurement incompatibility when classical messages can be sent
SummaryThe paper studies how to certify that measurements are incompatible when a classical message can influence the receiver's outcome. It introduces union maximal leakage, computed from observed probabilities by a linear program. If the message has at most k bits, compatible measurements give union maximal leakage at most k, and in quantum theory a violation implies the shared state is entangled.
WhyIntroduces union maximal leakage via a linear program and proves a k-bit message bound for certifying measurement incompatibility, a clear theoretical advance with limited scope beyond quantum theory.
In briefApproximate cloning of structured quantum states: copying special families of pure states with far fewer samples
SummaryThe no-cloning theorem forbids copying arbitrary unknown quantum states. This paper studies how many copies are needed to approximately clone pure states drawn from structured families, such as fermionic Gaussian and Slater states, bosonic Gaussian states, and qudit phase states. For fermionic states the authors construct optimal cloning channels, and for bosonic Gaussian states they give an explicit cloner, both with polynomial rather than exponential complexity in the number of modes.
Yaroslav Herasymenko, Junqiao Lin, Philip Verduyn Lunel et al.
In briefLearning a quantum system's Hamiltonian from its dynamics using only very limited control, such as uniform or computational-basis measurements.
SummaryThe paper studies how to learn the Hamiltonian of a many-body quantum system from its dynamics under minimal experimental access, motivated by near-term analog simulators. It considers two constrained settings: uniform state preparation and measurement in the same basis on every qubit, and computational-basis-only preparation and measurement. The authors report that generic 2-local Hamiltonians on any interaction graph can be reconstructed in the uniform setting, and that nearest-neighbor Hamiltonians with Pauli X/Z interactions on 1D and 2D rectangular lattices can be reconstructed in the computational-basis setting, up to unavoidable gauges.
WhyShows Hamiltonian reconstruction under severely restricted uniform and computational-basis access, with new techniques for structured polynomial systems and solid theoretical support.
In briefOptimal Data Compression with Quantum Retrieval: how to shrink a sparse bit string so any bit can be read back exactly using a few quantum queries.
SummaryThe paper studies compressing a binary string of length m and Hamming weight at most n into a shorter string, such that any original bit can be retrieved error-free using at most t quantum queries to the standard oracle encoding. With adaptive queries, the authors achieve optimal compression up to a logarithmic factor. With non-adaptive queries, their schemes are optimal in the dependence on m up to a logarithmic factor and are at most quadratically worse in the dependence on n.
Shyam Dhamapurkar, Mohit Garg, Manaswi Paraashar et al.
In briefRandom-Oracle Unitary Synthesis Is Impossible: proves that efficiently implementing Haar-random unitaries is impossible given only random Boolean function access.
SummaryThe paper studies unitary synthesis, asking whether any unitary can be efficiently implemented given the ability to evaluate classical functions in superposition. It proposes an average-case version: efficiently implementing a Haar-random unitary given access to a random Boolean function. The authors prove a superpolynomial query lower bound, showing this is impossible in this model. They also show that in the ROM-PRU model no Ω(N^{1+γ}) unitary design is efficiently achievable for any γ>0, while constructing an O(N)-design with polynomially many queries, improving on the previous O(√N) results.
In briefA cohomological description of the Clifford hierarchy, a structure of quantum gates
SummaryThe paper studies the higher levels of the Clifford hierarchy, which matter for fault-tolerant quantum computation but are poorly understood. It shows that the quantum derivatives of a unitary operator form a non-abelian 1-cocycle, and that every such cocycle arises from a unitary, giving a recursive cohomological characterization. For the third level, the cocycle data is split into symplectic, affine and phase parts. The authors use this to prove that every two-qudit and every three-qudit third-level gate is semi-Clifford.
WhyCharacterizes Clifford hierarchy via non-abelian 1-cocycles and proves three-qudit third-level gates are semi-Clifford for the first time, a substantive theoretical advance.
In briefMeasurement-free surface-code state preparation using digital-analog counterdiabatic driving
SummaryThe paper proposes a digital-analog method to prepare surface-code ground states on superconducting qubit hardware without measurements. It maps stabilizer-local counterdiabatic terms, derived from the adiabatic gauge potential, onto fixed-angle XY gates, single-qubit rotations, and analog exchange evolutions. Benchmarks on checkerboard plaquette grids up to 4 x 4 show better ground-state preparation than bare adiabatic evolution at short times, and the authors report that the synthesis can reduce entangling depth by an order of magnitude.
Shubham Kumar, Balaganchi A. Bhargava, Paolo A. Erdman et al.
In briefClimbing the Fusion Tree: Center Ordering and Decoding Hierarchy in Non-Abelian Mixed States
SummaryThis paper studies strong-to-weak spontaneous symmetry breaking for non-Abelian symmetry groups by framing it as decoding two strongly symmetric states after strongly symmetric decoherence. The authors derive a hierarchy of statistical mechanics models describing optimal decoding from fusion outcomes on nested regions. Tensor-network calculations for S3 and SU(2) show that the only transition at nonzero error rate is center ordering, with S3 showing no transition at the first level and SU(2) exhibiting a Z2 transition in the Nishimori-Ising class.
In briefQuantum critical point with U(1) symmetry breaking in 1D chains
SummaryThe paper reports spontaneous breaking of continuous U(1) spin-rotation symmetry and an interacting quantum critical point in one-dimensional spin-1/2 and spin-1 chains, contrary to the usual expectation. Using subsystem Binder scaling, the authors find a correlation-length exponent of ν = 0.60 ± 0.02. They estimate the dynamical exponent z at about 1.96 to 1.99, and argue that z < 2 rules out frustration-free models as microscopic realizations.]
In briefPreparing quantum Gibbs states by relative decoding to broader Hamiltonian classes
SummaryThis paper studies provably efficient preparation of quantum Gibbs states. The authors use relative decoding, a generalization of DQI and HDQI, to transfer a preparation guarantee from a source Hamiltonian H_A to a target H_B. If the relative distance is linear and decoding is efficient at linear radius, a constant inverse temperature is certified. Starting from a nearest-neighbor spin chain, they construct bounded-degree, geometrically nonlocal, noncommuting targets, and state this gives a new class of efficiently preparable thermofield double states.
Zhong-Xia Shang, Yufei Wang, Daniel Stilck Fran\c{c}a
In briefKramers' theorem leaves a topological imprint in classical records
SummaryThe paper notes that time reversal squares to -1 on half-integer spin, a sign usually read only from quantum objects. The authors show that for a detector resolving handedness, the probabilities linking one record stretch to the time reverse of another reflect the cohomology class of time reversal, with the sign appearing in the matrix signature as a topological integer that survives equal emission and absorption losses. They report that a programmed emitter on quantum processors reads this integer in about 10^3 shots.
Chon-Fai Kam (1, 2), Kai-Wen Wong (3) ((1) Universit\`a degli Studi di Palermo et al.
In briefHow quantum channels can destroy or keep measurement incompatibility
SummaryThis paper studies two kinds of quantum channels: those that always destroy the incompatibility of quantum measurements, and those that never do. Using the mathematical tools of zonotopes and zonoids, the authors give necessary and sufficient conditions for when a qubit unital channel is incompatibility-breaking. They show that two such channels can lose this property when used in parallel, and that a channel with matching input and output dimensions preserves general incompatibility only if it is unitary.</summary>
WhyUses zonoid theory to characterize incompatibility-breaking and preserving channels, proving superactivation for qubit channels, a notable theoretical advance.
In briefLLM-guided search for weight-five bivariate bicycle quantum codes
SummaryThe paper extends an earlier LLM-guided program-evolution workflow to weight-five bivariate bicycle (BB) and perturbed BB quantum error-correcting codes. It reports a catalogue of 1,142 code proposals, most from LLM-generated programs, and certifies several connected CSS parameter sets with exact distance evidence. Among CSS proposals with a recorded positive distance, 87.18% reach distance at least 5, exceeding the 72.50–74.26% rate of three random-search controls, though the random controls cover more connected classes.
In briefGPU-Driven Discrete Simulated Bifurcation for Fast Requests and Dense Models
SummaryThe paper presents a discrete simulated bifurcation (dSB) system built on NVIDIA DOCA GPUNetIO to reduce communication bottlenecks in GPU-based optimization. For models that fit in GPU memory, a persistent service handles receiving, solving, and replying entirely on the device, and its median latency rises only 6% as load grows from 400 to 800 thousand requests per second. For dense models larger than GPU memory, a streaming solver processes ten-million-variable matrices at about 307 Gb/s, and results are verified through ground-state recovery on planted instances and agreement with reference runs.
In briefQuantum Krylov Linear Solver Beyond Global Conditioning Using Spectral Compression
SummaryThe paper studies time-evolution quantum Krylov linear solving when a vanishing eigenvalue remains relevant to the solution and must be kept. It argues that normalized-state complexity need not inherit the divergence of the global condition number, and depends instead on whether inverse amplification changes the solution direction. Under these conditions the solution-relevant spectrum compresses into a compact reduced space, yielding an end-to-end complexity bound with no inverse dependence on the retained small eigenvalue.
In briefQuantum codes as quantized codes: stabilizer codes from quantization over finite fields
SummaryThe paper presents a discrete analogue of geometric quantization over finite fields. When applied to certain classical error-correcting codes, it produces quantum error-correcting codes. This offers a physical interpretation of a previously known quantum-classical correspondence in coding theory.
In brief"Staying Sober": A Method That Predicts Logical Error Rates of Concatenated Quantum Codes Without Sampling
SummaryEstimating the logical error rate of quantum error-correcting codes usually requires large Monte Carlo sampling, which becomes very costly at large code distances and low physical error rates, especially for concatenated codes. The paper proposes a predictor that computes the leading term of the logical error rate directly from stabilizers and minimum-weight logical operators, handling each concatenation level without sampling. The prediction is proven exact for unconcatenated stabilizer codes and approximates concatenated codes, matching exact enumeration at level 1 in the evaluated cases. The authors report comparing 37 code configurations in 48 core-hours.
WhyProposes sampling-free LER prediction with exact leading terms for concatenated codes, verified against exact enumeration and sizable comparisons, offering notable value to the subfield.
In briefInformation causality does not uniquely determine the set of quantum correlations
SummaryInformation causality (IC) is a physical principle limiting non-local correlations between two parties in a Bell scenario, requiring that the information Bob gains about Alice's database be bounded by what she communicates. The paper shows that for any finite database length n ≥ 2, there exists a set of correlations satisfying IC that displays post-quantum behaviour. It further constructs a set satisfying IC for all database sizes that contains post-quantum points in the three-input, two-output scenario. Therefore, all known formulations of IC fail to fully characterize the quantum correlation set.
WhyShows information causality fails to uniquely characterize quantum correlations, constructing post-quantum examples for all n with an entropic proof.
In briefControlling double descent in quantum extreme learning through model design
SummaryThis paper studies double descent, where generalization first worsens as model capacity grows, then improves after the model passes the interpolation threshold. The authors analytically characterize the full risk curve for classical linear regression using the condition number of the feature covariance and a spectral measure of correlation. They then apply this theory to quantum extreme learning machines (QELMs), showing that encoding strength, input reuploads, and measurement shots each regularize the output covariance and can keep the interpolation threshold stable.
In briefCT-bMPS: Approximate tensor network contraction using boundary MPS on contraction trees
SummaryThis paper introduces CT-bMPS, a scalable method for approximately contracting general closed tensor networks. It represents the boundary tensor and its environment on each edge of a contraction tree as matrix product states, and compresses them locally using a reduced transition matrix. Benchmarks on Ising partition functions, random tensor networks, kicked Ising dynamics, and quantum error correction decoding show better accuracy and efficiency than existing general-purpose methods.
In briefMid-circuit measurements with feedforward achieve exact unitary synthesis in constant quantum depth
SummaryThis paper shows that mid-circuit measurements combined with feedforward, where later operations depend on earlier measurement outcomes, lower the worst-case depth needed for exact n-qubit unitary synthesis from Θ(n) to O(1). The deterministic construction uses single-qubit measurements, O(1) rounds of parity feedforward, and O(n4^n log(n+2)) qubits. The authors also analyze depth-width trade-offs and show they nearly match a lower bound for generic targets.
WhyReduces exact unitary synthesis depth from Θ(n) to O(1) via feedforward, with matching width lower bounds; a strong theoretical result with rigorous construction but no experiments.
In briefUnitary products as continuous evolutions at finite precision
SummaryThe paper presents a short method for discretizing continuous unitary evolution, giving a two-way correspondence between continuous evolutions and products of unitaries in finite dimensions. It uses this to reduce discrete adiabatic theorems to continuous ones, with an explicit additive O(1/T) operator-norm error bound. For positive definite quantum linear systems, the approach yields a rescaled qubitized walk with O(κ/δ) steps, matching a previously known scaling without requiring a discrete adiabatic theorem.
In briefSymmetry and AI-assisted search for magic-state factories
SummaryThis paper studies magic-state distillation, a major resource cost in fault-tolerant quantum computing, and proposes symmetry- and AI-assisted methods to search for factories of distance three and above. The searches yield 699 factory classes, 564 of them new, including pure-T and entangled-output factories. The authors also release methods, data, and search briefs for an open-source repository of distillation protocols.
WhyUnified symmetry and AI-assisted search finds 564 new factories with lower overhead exponents, backed by extensive computational verification and comparisons.
In briefMermin-Peres magic square game extended to three or more players, where quantum advantage disappears
SummaryThis paper generalizes the Mermin-Peres magic square game to N players, replacing the square with an N-dimensional hypercube. The optimal classical strategy's winning probability stays at 8/9 for all N. For N ≥ 3, a generalized version of the quantum strategy achieves a winning probability between 1/3 and 3/4. The authors attribute the loss of quantum advantage for N ≥ 3 to monogamy.
In briefExplicit quantum channels with arbitrarily large Rényi entropy non-additivity
SummaryThe paper gives a closed-form, finite-dimensional construction of quantum channels with real algebraic entries. These channels show arbitrarily large violations of minimum-output Rényi entropy additivity for every Rényi order above a chosen positive cutoff. The construction uses direct products of free groups and fixed-field high-girth graphs. For any target gap, the authors give a channel and Bell input whose additivity gap exceeds it for all orders at once.
In briefClassical simulation of lossy Gaussian boson sampling beyond the square-root limit
SummaryPhoton loss makes Gaussian boson sampling easier to simulate classically, and a standard method replaces the lossy input with classical light. That method stays accurate only while the mean surviving photon number grows no faster than the square root of the number N of squeezed inputs. The paper proves this scale is a limit of classical-light replacement. It then approximates the detection process instead, giving a polynomial-cost sampler with error O(Nη³), which allows the mean surviving photon number to grow as N^(2/3); a separate pair construction reaches N^(3/4) when all inputs are equally squeezed.
WhyProves a fundamental limit of classical-light replacement and gives a detection-approximating sampler beyond the square-root scale, with rigorous error analysis.
In briefCausal memory and structure of correlated quantum sequences: how much memory a quantum process needs to generate its outputs, measured by entanglement.
SummaryThis paper extends computational mechanics to the quantum setting, studying correlated sequences of quantum outputs that do not interact again with their generator. For stationary, memoryful sequences, the authors show that a memory-minimal generator can be chosen to produce outputs isometrically, represented by a canonical matrix product state. The minimum memory entropy equals the entanglement entropy across the past-future split, and the minimum memory dimension is set by the Schmidt rank. The authors further show that the fundamental entropy rate vanishes, causal generation is time-reversal symmetric, and all memoryful processes have infinite quantum Markov order for arbitrary sharp measurements.
WhyExtends computational mechanics to quantum sequences, proving minimum memory entropy equals past-future entanglement entropy with rigorous structural results.
In briefEntanglement needed for perfect nonlocal play and zero-error communication
SummaryThe paper builds a Flagged Magic-Square game by adding a flag outcome and extra questions to the standard Magic-Square game. It shows that perfect play requires a specific non-maximally entangled state with Schmidt coefficients proportional to (1,√2,√2,√2,√2), and that the game self-tests this state. The authors also prove that maximally entangled strategies win with probability bounded away from one regardless of dimension. A game-to-channel reduction then shows entanglement can zero-error transmit ten messages in one use over a classical channel, while maximally entangled resources manage at most nine.
WhyConstructs a flagged Magic-Square game requiring a specific non-maximally entangled state, self-tests it, and shows separation for zero-error communication.
