In briefQuantum decoding sampler for hard spin-glass Gibbs distributions
SummaryThis paper applies Decoded Quantum Interferometry (DQI) to sample from Gibbs measures of classical Ising spin Hamiltonians, reducing the task to a quantum decoding problem. For Ising k-spin glasses on random hypergraphs, shattering and disorder chaos create a topological barrier that blocks many stable algorithms, including Glauber dynamics, near the dynamical phase transition. The authors prove that both a classical Prange-based algorithm and DQI with a quantum decoder can break this barrier and sample at lower temperatures for large k.
WhyApplies DQI to Gibbs sampling of Ising spin glasses, proving it breaks shattering barriers that block stable algorithms; novel theory with concrete proofs but no experiments.
In briefQuantum de Finetti theorems for states and channels under any distance measure
SummaryThe paper proves standard and Renner's exponential quantum de Finetti theorems in the stronger form of operator inequalities, which yield bounds in every Schatten norm and for every quantum Rényi divergence satisfying data processing. For permutation-covariant channels, it shows that the k-system reduced channel is dominated in CP order by a mixture of tensor-power channels with error O(k/√n). Under the no-signalling condition, it also gives an exponential channel de Finetti theorem using Choi-almost-iid channels.
WhyStrengthens quantum de Finetti theorems to operator inequalities, improving the k/n bound and extending to channels with rigorous proofs.
In briefThe Single-Copy Quantum Bandit Is Classical: An Exact Spectral Collapse
SummaryThis paper studies multi-armed bandits in which each arm supplies an unknown quantum state and mean rewards are defined by a known effect F. The authors show that spectral measurement of F followed by classical KL-UCB is asymptotically instance-optimal among single-copy policies, and adaptive or randomized measurement cannot improve the leading logarithmic regret coefficient. For consistent policies with quantum memory, a converse is derived using the Umegaki half-space divergence, and the two regret floors coincide only when the arm commutes with F. Whether the Umegaki floor is attainable is posed as an open problem.
In briefLocal relaxation methods for estimating quantum ground state energies
SummaryThe paper proposes local convex relaxation hierarchies and parallelisable message passing algorithms for estimating lower bounds on quantum many-body ground state energies. It shows the first hierarchy level is exact for commuting Hamiltonians on trees, and that a consistent-interval hierarchy converges exponentially in interval size for weakly perturbed separable Hamiltonians on a chain. Two message passing variants run in O(n/ε²) and O(n/ε) time on bounded-degree graphs, assuming optimal messages have O(1) norm.
WhyProves exactness of local relaxation on trees and exponential convergence on chains, with complexity guarantees and benchmark experiments validating message passing algorithms.
In briefA noise-operator method for quantum query and time-space lower bounds
SummaryThis paper introduces a new noise-operator-based technique for proving lower bounds on quantum query complexity and time-space tradeoffs. Using it, the authors prove the first fully general quantum time-space tradeoff lower bound for sorting, showing that quantum algorithms with at most S qubits of memory need Ω(n^{4/3}(log log n)/(S^{1/3} log n)) queries to sort n numbers from [n^2]. They also show that for strongly universal hash families, almost all hash functions require Ω(nm/S) quantum queries to compute.
WhyIntroduces a noise operator method yielding the first fully general quantum time-space lower bound for sorting, extended to hash functions with rigorous proofs and substantial subfield impact.
In briefLearning Local Fermionic Lindbladians Under Parity Superselection
SummaryThis paper studies how to learn the generator of a Lindblad evolution for fermionic systems when parity superselection forbids measuring odd Majorana observables. The authors use even-parity preparations and measurements, internal marker modes, and pairwise calibration, then recover coefficients via signed Fierz inversion and semidefinite fitting. They give sample-complexity bounds for finite-range models on bounded-degree graphs, extend the results to settings without a known graph, and discuss geometric and finite-volume cases.
Tim M\"{o}bus, Daniel Stilck Fran\c{c}a, Cambyse Rouz\'e
In briefTight Universal Bounds on Quantum Data Hiding with Multipartite Werner States
SummaryThis paper studies quantum data hiding, where two states are highly distinguishable under global measurements but nearly indistinguishable under local operations and classical communication. The authors show that the distinguishing bias of any pair of n-qudit Werner states is O(n²/d) for measurements that stay positive under partial transposition across every bipartition. An explicit pair achieves this scaling using only nonadaptive local measurements, establishing worst-case optimality.
WhyProves optimal O(n^2/d) hiding bias scaling for multipartite Werner states with matching construction, extending results to quantum property testing.
In briefQuantum algorithms that learn linear threshold functions faster
SummaryThe paper studies quantum algorithms for learning linear threshold functions, which compute the sign of a weighted sum of inputs compared with a threshold. It presents three results: with real-domain membership queries, a quantum algorithm uses fewer queries than classical methods require; for homogeneous functions whose weight vector has k equal nonzero entries on the Boolean cube, it achieves an exponential query improvement over prior quantum work; and it gives a learner for homogeneous functions under Gaussian quantum examples.
Aleksandrs Krivcenko, Tuyen Nguyen, Ronald de Wolf
In briefCooling a mixed quantum state to its ground state using one bath contact, without resetting the bath
SummaryThe paper asks whether a single coherent bath contact can cool any mixed quantum state to a pure ground state without repeated bath resets. The proposed mechanism moves the input information into bath degrees of freedom that later decouple, while the system and remaining bath follow a ground-state path. The authors rigorously realize it for a class of weakly interacting, gapped local fermionic systems, claiming polylogarithmic total physical time.
WhyProposes single-contact bath cooling without resets, with rigorous polylogarithmic time guarantees for gapped fermionic systems; novel and rigorous but restricted to a class of models.
In briefQuantum-enhanced deep RL for power distribution network reconfiguration
SummaryThis paper proposes a deep reinforcement learning framework for static distribution network reconfiguration, which adjusts switch settings to optimize grid topology. The authors vary only the Q-network architecture to isolate its effect on solution quality and learning. They report that quantum-enhanced Q-networks reach higher rewards than their classical counterpart while using fewer parameters.
Daniel Germain, Mason Blanchard, Audrey Versteegen et al.
In briefComputational Work Extraction: How Catalysts Affect Extractable Work
SummaryThe paper proves that n-qubit systems can have Θ(n) ergotropy while every efficient process extracts negligible work, even for Hamiltonians made of single-qubit terms. It links ergotropy to catalytic computation, where auxiliary qubits must be restored, and shows catalysts enable efficient extraction of the full Θ(n) ergotropy. The authors also introduce pseudoergotropy, analogous to pseudorandomness.
WhyLinks computational ergotropy to catalytic computation, proving maximal separations and query lower bounds for quantum-space bounded algorithms.
Atul Singh Arora, Shantanav Chakraborty, Alexandru Cojocaru et al.
In briefLocal automorphism-aware syndrome scheduling for general quantum LDPC codes
SummaryThe paper formulates low-depth syndrome extraction for CSS quantum LDPC codes as an ordered edge-coloring problem under quantum parity constraints. It introduces LocalASC, which solves the constraints on edge orbits under a subgroup of Tanner graph automorphisms and lifts feasible solutions to the full graph. The method finds depth-optimal schedules for several two-block CSS codes with odd component weights and lower-bound-saturating schedules for some quantum Tanner codes.
Eugenio Durazo Rocha, Olai \AA. Mostad, Hsuan-Yin Lin et al.
In briefQuantum algorithm for sampling random spanning trees with amortized data structures
SummaryThis paper presents a quantum algorithm that creates a uniform superposition over the spanning trees of a graph, called a q-sample, using a sub-linear number of graph queries. For an n-vertex, m-edge graph, preprocessing costs Õ(√(mn)+m^{1-δ}) and each q-sample then costs Õ(n^{1+2δ}). The authors prove a matching lower bound up to logarithmic factors, showing the algorithm is essentially optimal.
WhyGives the first sublinear-query quantum algorithm for uniform spanning tree superpositions with a matching lower bound, a substantial theoretical improvement with mainly theoretical scope.
Yassine Hamoudi, Adrian Tanasa, Shrinidhi Teganahally Sridhara
In briefExplicit quantum LDPC codes that reach list-decoding capacity and decode in near-linear time
SummaryThe paper presents what the authors believe are the first explicit quantum LDPC codes that achieve list-decoding capacity, with list-decoding radius approaching the quantum Singleton bound and constant list sizes. The construction uses expander graphs through a quantum analogue of Alon-Edmonds-Luby amplification, which provides the LDPC property. The authors also generalize classical expander-based list-decoding algorithms to these codes, obtaining near-capacity decoders that run in near-linear time in the block length.
William Gay, Fernando Granha Jeronimo, Abhi Shukul
In briefPaper on constructing more mutually unbiased bases for quantum measurements
SummaryThis paper studies mutually unbiased bases (MUBs), quantum measurement bases where certainty in one basis yields uniform outcomes in the others. The authors introduce a construction that applies a diagonal phase matrix to a fixed unitary built from tensor products of Fourier matrices and optionally a real Hadamard matrix. It yields more MUBs than previously known in many dimensions, and in some cases exceeds the tensor product bound.
In briefPlanted Clique Detection with Quantum Symmetry-Adapted Measurements: Examines whether quantum encodings and symmetry-based measurements can retain detection information from one graph, and whether they can be done efficiently.
SummaryThe paper studies detecting a planted clique in a single classical graph, where detection is statistically possible but conjectured hard for polynomial-time classical algorithms. For a compact binary phase encoding, the authors prove that constant-advantage detection requires Ω(n^{1+2ε} ln² n) copies of the phase state, even under arbitrary joint measurements. They show the optimal rule is not an efficient detector and explore symmetry-guided measurements such as the Schur transform and subgroup isotypic measurements, whose efficiency remains open. They also show that a single coherent quantum sample permits efficient detection.
In briefDecoupling QAOA into independent spin-boson systems and high-depth tests on spin glasses
SummaryThis paper shows that when computing QAOA energy for any mixed dense spin glass, the spins approximately decouple into independent spin-boson systems, with the decoupling becoming exact in the infinite-size limit. The authors derive a recursive method that uses tensor networks at modest cost and apply it to optimize QAOA on pure and mixed spin glasses at depths previously intractable. The work notes that it does not enable strong simulation of QAOA, since a quantum computer is still needed to sample the corresponding bitstrings.
Sami Boulebnane, Abid Khan, Pragna Subrahmanya et al.
In briefA fully Gaussian quantum Stein's lemma: asymptotic state discrimination under Gaussian measurements
SummaryThe paper studies asymptotic asymmetric hypothesis testing for multi-mode bosonic Gaussian states under arbitrary collective Gaussian measurements. It derives a single-letter formula for the Stein exponent for many pairs of states, with separate contributions from first and second moments. For centred Gaussian states, the authors show that collective Gaussian measurements offer no advantage.
WhyDerives a single-letter Stein exponent for Gaussian states under collective Gaussian measurements via novel determinant inequalities, with proofs; applicability limited to certain state classes.
In briefA classical sublinear-time SDP solver inspired by the quantum OR lemma
SummaryThis paper presents the first classical sublinear-time solver for sparse semidefinite programs in the bounded-radius regime, without low-rank or Frobenius norm assumptions. It combines randomized Lanczos filtering with a sampling-based estimator to estimate many Gibbs-state expectation values at once, mirroring the sample-reuse mechanism of the quantum OR lemma. The runtime is Õ(ns·γ^4.5 + ms·γ²) when γ² ≤ min{m, n/s}, and Õ((n+m)s) for constant γ. The authors conclude that, in terms of dimensions m and n, there is no super-quadratic quantum advantage for generic sparse SDP solving.
WhyGives the first classical sublinear sparse SDP solver, realizing quantum OR-lemma sample reuse and matching lower bounds in dimensions.
Fernando G.S.L. Brand\~ao, Alexander M. Dalzell, Andr\'as Gily\'en et al.
In briefHow much quantum computing constant-depth circuits can do when size is unlimited
SummaryThe paper asks whether quantum circuits of constant depth, built from single-qubit gates and generalised Toffoli gates with no limit on size or ancillary qubits, can implement every unitary. It gives exact constant-depth constructions for permutations of basis states, diagonal unitaries, and arbitrary pure-state preparation. Implementing arbitrary unitaries in constant depth remains open, and the authors use port-based teleportation to obtain approximate constructions.
WhyGives constant-depth constructions for permutations, diagonal unitaries and state preparation, linking quantum state preparation to reversible computation, with a new port-based teleportation fidelity
In briefQuantum lower bounds for set disjointness via sub-linear reductions from 3SUM
SummaryThis paper studies fine-grained complexity in the quantum setting. The authors give the first sub-linear time quantum reductions from 3SUM to online SetDisjointness. Assuming the quantum 3SUM conjecture, they derive a tradeoff bound p + 2q ≥ 1 for quantum SetDisjointness algorithms with O(N^p) preprocessing and O(N^q) query time. An analogous reduction from 3XOR is also presented.
WhyGives the first sublinear quantum reduction from 3SUM to online SetDisjointness, yielding a p+2q≥1 tradeoff lower bound.
In briefTelling Coherent Crosstalk Apart from Calibration Drift Using Pauli-Transfer Signatures and Quantum Edge Detection
SummaryThe paper addresses how coherent crosstalk on multi-tenant quantum processors can mimic benign calibration drift at matched gate infidelity. It proposes a verification and detection framework based on the residual Pauli transfer matrix, proving that local unital, trace-preserving channels cannot mix weight-1 and weight-2 Pauli operators. Simulations with 16,384 randomized settings give a detection threshold of about 0.13 at a 5% calibrated false-positive target, and further experiments examine detection under several noise conditions.
In briefDetecting memory dimension in open quantum dynamics using pseudo-control, a method for measuring how much environmental memory affects a quantum system.
SummaryThe paper proposes a pseudo-control protocol that encodes memory dimension information into an experimentally accessible interference matrix. Its rank provides a lower bound on the memory dimension without direct environment access or full process-tensor tomography. The authors show how interaction and interval times affect the detectable memory in quantum many-body environments.
In briefClassical simulation of coherent crosstalk errors in surface codes
SummaryThe paper presents a polynomial-time classical algorithm that samples syndrome distributions of surface code states corrupted by coherent nearest-neighbor ZZ crosstalk. This complements known efficient simulation methods for coherent single-qubit errors. When single-qubit coherent noise and crosstalk coexist, the authors show that, unless the polynomial hierarchy collapses, no efficient classical sampling algorithm exists, even up to a constant multiplicative error. The result connects syndrome distributions under coherent noise to output distributions of IQP circuits associated with a non-planar graph.
WhyGives a polynomial-time classical sampler for syndrome distributions under coherent crosstalk, and a hardness result when combined with single-qubit noise via IQP circuits.
Andrew S. Darmawan, Yelyzaveta Kolesnyk, Robert Koenig
In briefComputational Lower Bounds for f-Routing Attacks
SummaryThe paper studies f-routing, a leading protocol for quantum position verification. It proves unconditional lower bounds on the resources needed by uniform attackers and derives computational complexity bounds on the function f under several restricted attack models. These results imply explicit functions secure against polynomial and quasipolynomial numbers of qubits within those restrictions.
WhyNew techniques bypass communication-complexity limits, linking f-routing security to computational classes with lower bounds across several attacker models.
In briefQuantum algorithm for non-uniform Chebyshev and Fourier transforms without conditioning
SummaryThis paper presents an efficient quantum algorithm for the non-uniform Chebyshev transform, which projects a function onto Chebyshev polynomials sampled at nodes uniform in x but non-uniform in the angle. The authors improve an existing non-uniform quantum Fourier transform by removing the conditioning from non-uniform node sampling, so error bounds no longer depend on the geometry-dependent parameter κ. The resulting ε-accurate block encoding has O(1) normalization, uses O(L) qubits and Õ(L²) gates, where L=log N+log(1/ε).
In briefExponential quantum advantage in three-party Numbers-on-Forehead communication
SummaryThe paper shows the first exponential quantum advantage for a decision problem in the general interactive three-party Numbers-on-Forehead model. It constructs an explicit partial Boolean function, the Interleaved Unitary Product problem, which needs only O(log n) quantum communication but Ω~(n^{1/32}) randomized communication. The randomized lower bound relies on a regularity-based argument.
WhyGives the first exponential quantum advantage for a decision problem in general interactive NOF, with a new randomized lower-bound argument.
In briefFiner sample complexities via the tomographic rate function
SummaryThis paper studies quantum state tomography protocols using two measures: sample complexity and the tomographic rate function, which governs large deviations of error estimates. The authors build an analysis framework for covariant protocols and derive rate functions for several, including random purification-based protocols and the sample-optimal protocol of Haah et al. Although each protocol's sample complexity is order optimal, their rate functions obey a strict ordering. Analogous strict inequalities hold for a Wasserstein-distance-based sample complexity, so the rate function is a more fine-grained performance indicator than ordinary sample complexity.
Arick Grootveld, Alexander Maloney, Jason Pollack et al.
In briefTesting whether quantum states are Gaussian using a constant number of samples
SummaryThis paper studies how to efficiently test whether a quantum state is Gaussian, a structure important in quantum optics and many-body physics. The authors give optimal, robust algorithms for fermionic and bosonic Gaussian states. The sample complexity is independent of system size, particle number, and energy. They also introduce a unified analysis approach called the gradient-flow method.
WhyGives the first optimal Gaussianity testers with size-independent sample complexity, plus a unified gradient-flow analysis technique.
Mahtab Yaghubi Rad, Ricard Puig, Saksham Hassanandani et al.
In briefLong-lived departures from equilibrium of electrons, nuclear spins and lattice in a low-temperature solid-state ion trap
SummaryThe paper uses optical methods to study how electron and nuclear spin energy levels cross and equilibrate in holmium ions within a LiYF₄ crystal. At low temperatures, very different non-equilibrium states appear depending on the experimental protocol. The authors report evidence that nuclear spin excitations equilibrate without phonon assistance and reach higher effective temperatures than electronic spins and the lattice.
In briefCompatibility of quantum instruments: whether several quantum measurements can be simulated from one parent measurement plus classical processing, with a d-dimensional limit.
SummaryThe paper studies measurement compatibility, asking whether a family of quantum measurements can be simulated by one parent measurement followed by classical post-processing. It introduces d-compatibility, where the parent passes only a d-dimensional quantum system plus unlimited classical information, and characterizes it via common linear factorizations of operator spaces. A compatibility functional is defined to certify d-incompatibility, and links are drawn to Schmidt numbers and one-way LOCC implementability.
In briefA two-stage quantum-classical method for reconfiguring distribution networks using cycle-edge encoding
SummaryThe paper proposes a two-stage method combining quantum and classical computing to reconfigure electrical distribution networks for lower losses. A quantum search, using an iterative linear-ramp QAOA over subspaces built with a cycle-edge encoding that guarantees spanning-tree configurations, produces samples that guide a mixed-integer second-order-cone solver. It is tested on six networks of 33 to 417 buses using simulation and trapped-ion quantum hardware. For the 417-bus network, hardware sampling finds a configuration within about 1.4% of the literature reference loss.
Nowar Alashkar, Cade Kennedy, Phillip C. Lotshaw et al.
In briefLower bounds on quantum queries needed to detect a subgraph
SummaryThe paper studies how many quantum queries to an adjacency matrix are needed to decide whether an n-vertex graph contains a fixed subgraph H with bounded error. It proves the first unconditional superlinear lower bounds for this problem, such as n^{λ_r-o(1)} queries for detecting the clique K_r, with λ_4 = 19/18. Similar bounds are given for complete bipartite graphs K_{r,r}, and the main technical result combines Zhandry's compressed oracle with conditioning on a planted certificate.
WhyProves first superlinear quantum query lower bounds for subgraph detection, resolving a long-open question with technically substantial arguments.
In briefQuantum List Recovery and Decoding: Achievability and Limits of Short Candidate Correction Lists
SummaryThis paper studies quantum list recovery and quantum list decoding, which seek short lists of logically distinct Pauli corrections consistent with a syndrome and error constraints. It gives combinatorial upper and lower bounds for balanced folded quantum Reed-Solomon codes and balanced random CSS codes. The authors also state an asymptotically exact tradeoff for the QLD radius.
In briefQuantum algorithms for finding minimal generating sets of black-box groups
SummaryThis paper presents a polynomial-time quantum algorithm that computes a minimum-sized generating set for solvable black-box groups. It also treats the class Γ_d, whose non-abelian composition factors are isomorphic to subgroups of S_d, developing polynomial-time quantum methods for direct product decomposition of abelian factor groups and constructive membership in factor groups. These tools yield a chief series computation and, from it, minimum generating sets for Γ_d. The paper further shows that the minimum generating set problem for general black-box groups lies in NP ∩ coAM.
In briefVerifying the toric code's quantum state even if untrusted devices can secretly talk
SummaryThis paper studies device-independent self-testing in a quantum network, where honest parties never communicate but untrusted devices may secretly exchange classical messages within bounded distances. The authors show that the code space of the toric code, laid out on a torus-shaped network, can be self-tested in a noise-robust way against communication up to distances proportional to the network diameter. They also present an algorithmic method for constructing such protocols and extend the results to the surface code and cluster states.
WhyExtends self-testing of the toric code to a relaxed network setting tolerating classical communication, with noise-robust rigorous results and algorithmic construction.
Gustavo Fr\'oes, Amanda Wei, Carlos de Gois et al.
In briefFlexible rigidity: compiling general trusted-preparation protocols into sequential device-independent ones
SummaryThe paper presents a generic compiler that converts a broad class of device-dependent protocols with trusted state preparation into sequential device-independent protocols. It is applied to uncloneable encryption, copy-protection of point functions, and blind randomness expansion. The key technical tool is a new set of rigidity theorems based on Rényi divergences, which allow a constant rate while tolerating constant noise per device use.
WhyIntroduces a generic compiler and new Rényi-divergence rigidity theorems achieving constant rate, overcoming prior trace-distance scaling limits, with rigorous proofs.
In briefA general theory for combining finite-group asymmetry with other quantum resource theories
SummaryThis paper develops a unified framework for combining finite-group asymmetry with resource theories such as entanglement, magic, and athermality. The key finding is that if symmetry information can be extracted with asymptotically vanishing error, the combined conversion rate equals the smaller of the two constituent rates, so combining them adds no extra cost. The authors also examine compatibility conditions for thermal operations and analyze symmetry imposed on elementary operations.
WhyUnifies finite-group asymmetry with many resource theories, proving conversion-rate results via symmetry-information accessibility; novel theory, impact mainly within quantum resource theory.
In briefQuantum oblique eigenprojection: decomposing a space into non-orthogonal eigen-subspaces on a quantum computer
SummaryThe paper shows that a quantum computer can perform an oblique (non-orthogonal) eigenprojection of a matrix, given block-encoding access to the matrix. Under a spectral-set condition, the query complexity is nearly linear in the inverse eigenvalue gap, with a normalization factor close to the projector's norm. Applications include preparing eigenstates of complex-spectrum matrices, solving continuous-time algebraic Riccati equations, and solving Sylvester equations, with speedups over prior methods claimed.
WhyGives a quantum algorithm for oblique eigenprojections with near-linear gap dependence and improvements over prior Riccati and Sylvester solvers.
In briefExplicit qLDPC Codes from Random Quantum Codes Using Local Properties
SummaryThe paper extends the local coordinate-wise linear (LCL) framework to quantum CSS codes on nested spaces, separating physical rank from logical rank in the quotient. It proves a threshold theorem for random CSS codes, showing the per-sector rate threshold equals the classical one. The authors also give explicit constructions for folded quantum LCL properties, yielding qLDPC codes with optimal list sizes for list-decoding and list-recovery, and explicit quantum subspace designs.
WhyExtends the LCL framework to quantum CSS codes, yielding the first explicit optimal-list quantum list-decodable and list-recoverable codes; theoretical, with no experiments.
Fernando Granha Jeronimo, Xiaojuan Ma, Nikhil Shagrithaya
In briefRobust classical and quantum communication over channels that are nearly iid
SummaryThe paper asks whether the asymptotic communication capacities of a quantum channel still hold for sequences of channels that are only almost independent and identically distributed along that channel. It shows that for the class of Choi-almost-iid channels, the unassisted classical and quantum capacities equal those of the original channel. The result is universal within this class: for each rate below capacity, one code sequence depending only on the channel and rate achieves vanishing error for every channel sequence in the class.
WhyExtends exponential de Finetti almost-iid framework to channels, rigorously proving universal classical and quantum capacities match the iid channel within the class.
In briefA nearly efficient classical algorithm for sampling typical Gibbs states of the quantum p-spin model
SummaryThe paper presents a classical algorithm that samples from the Gibbs state of the quantum p-spin model to any polynomially small error in total variation distance. It is built on algorithmic stochastic localization (ASL) and relies on a generalized convergence theorem for ASL. The authors argue this gives strong evidence against an exponential quantum advantage for Gibbs sampling in this model, though their claim that the method works down to the spin glass transition temperature is a non-rigorous physics argument.
In briefOptimal purity estimation using incoherent measurements
SummaryThe paper studies how many copies of an unknown quantum state are needed to estimate its purity to within multiplicative error ε. With general collective measurements, the known requirement is Θ(√d/ε² + d/ε) copies. For incoherent measurements, the authors give a non-adaptive algorithm using O(d/ε² + d^{3/2}/ε) copies and show this is optimal among non-adaptive methods. They also present an adaptive estimator that improves the high-precision regime, and combining both yields the optimal complexity for incoherent purity estimation.
WhyImproves known incoherent purity estimation complexity, giving matching upper and lower bounds for non-adaptive measurements plus a new adaptive estimator.
In briefClassical communication over a quantum erasure channel at finite blocklength, with and without feedback
SummaryThe paper determines the optimal success probability for sending a fixed number of classical messages through a finite number of uses of a quantum erasure channel, with noiseless classical feedback and no shared entanglement. The optimum is E[min{1, d^K/M}], where K is binomial with parameters n and 1-p. A classical protocol attains this bound, and the paper also compares the case without feedback, including a strict gap at small parameters.
WhyGives exact optimal success probability for finite-blocklength feedback-assisted classical communication over the erasure channel, with a rigorous converse and new feedback-versus-no-feedback separati
In briefA quantum algorithm for transporting states between connected vertices on flat connection graphs
SummaryThe paper generalizes undirected st-connectivity to graphs whose edges carry unitary operations, with path-independent products (a flat connection). It defines the st-transport problem: decide whether s and t are connected and estimate the overlap of the transported state with the target state. The authors give a bounded-error quantum algorithm running in Õ(n/ε) time and O(log n+log k+log(1/ε)) space. They also prove an Ω(n) quantum query lower bound, even when s and t are promised to be connected.
In briefProof that perfect non-local quantum computation is impossible for most operations
SummaryNon-local quantum computation lets two parties apply a joint operation to their quantum inputs using an entangled resource and one round of simultaneous communication. The paper shows that even for two qubits, almost every unitary (in the Haar sense) has no exact protocol with finite-dimensional resources. It also states that a controlled phase gate with a transcendental phase has no such exact protocol, and extends the result to localizable measurements.
WhyProves almost all two-qubit unitaries lack exact finite-dimensional NLQC protocols, resolving an open problem with rigorous proofs and explicit counterexamples.
Marten Folkertsma, Dmitry Grinko, Gina Muuss et al.
In briefRandomness of exact unitary designs under symmetry
SummaryThe paper defines unitary design strength and symmetric design strength for finite unitary ensembles and compares them when physical symmetry is present. It shows that in sufficiently high dimension, for a broad family of symmetries including global on-site U(1) and SU(d), there exist ensembles whose symmetric design strength is strictly higher than their unitary design strength. It also derives bounds for ensembles forming finite groups, including a proof that such groups have symmetric design strength at most two under U(1) and SU(d) symmetries.
In briefA physically grounded, universal model of bosonic quantum computing with a Solovay-Kitaev theorem
SummaryThis paper introduces Bosonic Energy-Preserving Quantum Computation (BEQC), a model that treats energy as a computational resource. Energy enters only through input coherent states, and all gates come from energy-preserving Hamiltonians, so unbounded energy growth is impossible. The authors show BEQC efficiently simulates polynomial-energy computations from existing models and exactly recovers BQP in that regime. They also provide universal gate sets based on linear optics and Kerr interactions, a Solovay-Kitaev theorem, and applications such as GKP state preparation and Fock state preparation.
WhyProposes an energy-preserving bosonic quantum computation model with a Solovay-Kitaev theorem that circumvents prior no-go results, with rigorous theoretical guarantees and applications.
Dorian Rudolph, Arsalan Motamedi, Dhruva Sambrani et al.
In briefCausal inequality violations as witnesses of nonstabilizerness
SummaryThis paper studies nonstabilizerness, a resource needed for universal quantum computation, by comparing two frameworks of free operations for magic states. It gives a criterion for deciding whether a stabilizer basis can be perfectly discriminated using stabilizer operations alone. For stabilizer product bases, it proves that perfect discrimination requires nonstabilizerness exactly when the corresponding process function violates a causal inequality.
WhyProves necessary and sufficient conditions linking causal inequality violations to nonstabilizerness, a new operational meaning; rigorous but limited to product stabilizer bases.
In briefNLTM Hamiltonians from gauged sheaf quantum locally testable codes: proves a conjecture that low-energy states need deep circuits to prepare.
SummaryThe paper proves the no low-energy trivial magic (NLTM) conjecture by constructing local Hamiltonians. Every state in a positive energy density window needs circuit depth Ω(log n) to prepare from an arbitrary stabilizer state. The result holds for qudit stabilizer inputs of any bounded local dimension. It strengthens NLTS and advances understanding of low-energy complexity relevant to quantum PCP.
WhyProves the NLTM conjecture via gauged sheaf codes, showing low-energy states need Ω(log n) depth; a strong NLTS strengthening with rigorous but intricate proofs.
In briefPurification enables unbounded query separation in sequential channel discrimination
SummaryThis paper studies whether purifications of quantum channels, including their correlations with an environment, can serve as an operational resource in sequential channel discrimination, even when the environmental reference frame is unknown or averaged. Unlike parallel discrimination, sequential access to purified resources gives a strict advantage in success probability. The authors construct qubit channel families with a strict separation at two queries, and a pair whose purifications are perfectly distinguishable with three queries while no finite number of bare queries suffices.
Zoe G. del Toro, Marco T\'ulio Quintino, Jessica Bavaresco
In briefFaster quantum algorithm for estimating convex body volume using amortized quantum walks
SummaryThis paper studies volume estimation, a classic problem in computational geometry. The authors quantize the randomized algorithm of Cousins and Vempala, achieving a quantum query complexity of Õ(d^3.5 + d^1.75/ε), which improves on the previous Õ(d^3.5 + d^2.25/ε). The key contribution is a framework for amortizing the cost of quantum walks, built on the transducer toolkit of Belovs, Jeffery, and Yolcu, which allows the amortized analysis of the ball walk to be used in a quantum implementation.
In briefNo-signaling-in-time condition for three-flavor neutrino oscillations
SummaryThis paper studies macrorealism, a basic concept in quantum foundations, and the Leggett-Garg inequalities that test it, which have already been used in neutrino oscillation experiments. The authors examine the no-signaling-in-time condition required for strong macrorealism. They extend earlier work on this condition to three-flavor neutrino oscillations, including the CP-violating phase of the PMNS matrix.
Massimo Blasone, Fabrizio Illuminati, Luciano Petruzziello et al.
In briefQuantum log-determinant methods for detecting torsion in topological data analysis
SummaryBetti numbers in topological data analysis cannot capture torsion in integral homology, which can distinguish structures with identical Betti numbers. This paper proposes quantum spectral methods using log pseudodeterminants of boundary-Laplacian eigenvalues to access torsion information. It presents a quantum algorithm for estimating torsion subgroup order with explicit query, accuracy, and spectral-gap dependence.
Dimitrios Thanos, Caesnan Leditto, Adam Wesolowski et al.
In briefUniversal distillation of quantum entanglement: a protocol that reaches the optimal entanglement distillation rate without knowing the input state
SummaryThis paper studies entanglement distillation, the maximum rate at which Bell states can be extracted from noisy entangled states using local operations and classical communication (LOCC). Previous results assumed both parties knew the input state and could tailor their protocol to it. The authors present a universal LOCC protocol that does not depend on the input state and achieves the distillable entanglement for any arbitrary unknown input. The protocol is based on state merging for compound states and the uniform convergence of finite-block quantities.
WhyShows a universal LOCC protocol achieves distillable entanglement for unknown inputs, removing a long-standing assumption; rigorous theory with broad conceptual significance.
Ryuji Takagi, Kaito Watanabe, Takaya Matsuura et al.
In briefQuantum Markov state models for slow dynamics in open systems
SummaryThe paper introduces quantum Markov state models (QMSMs) that describe the few slow degrees of freedom governing long-time dynamics of open quantum systems. The models live on a small state space combining classical sectors and quantum matrix blocks, so they can keep coherence between metastable states. Under an assumption that the evolution channel changes little when applied twice, the authors build compression and reconstruction channels and prove diamond-norm error bounds of O(η^{1/3}) for all inputs and O(η^{1/2}) for metastable states.
WhyExtends classical Markov state models to open quantum systems with coherence, giving exact reconstruction channels and provable diamond-norm error bounds.
In briefSubmodularity of entropy under quantum convolution: a noncommutative entropy inequality framework
SummaryThe paper builds a submodular framework for the von Neumann entropy of discrete quantum convolutions, a noncommutative analogue of entropic additive combinatorics. It shows that entropy growth has a polymatroidal structure, yielding convolutional strong subadditivity, a quantum Ruzsa triangle inequality, and quantum entropic Plünnecke–Ruzsa inequalities. For repeated inputs, the quantum doubling constant controls higher convolution entropies.
WhyExtends submodular methods to quantum convolution entropy, yielding noncommutative additive-combinatorics inequalities with sharp exponents; strong theory but purely analytical.
In briefGeneralized Reimpell-Werner Iteration: a numerical method for optimizing quantum measurements and channels
SummaryOptimizing quantum measurements and channels often requires numerical methods that stay practical as Hilbert space dimensions grow. This paper generalizes the Reimpell-Werner iteration to linear objectives with arbitrary Hermitian cost matrices. The authors prove that the iterates converge to a global optimum when the initialization satisfies suitable support overlap conditions. For a fixed problem, iteration parameters, and admissible initialization, they show that asymptotically O(1/ε) iterations suffice to bring the objective within ε of the optimum.
In briefFast classical simulation algorithms for free-fermion dynamics with non-Gaussian inputs
SummaryThis paper develops classical algorithms for simulating free-fermion circuits when the input states are non-Gaussian ("magic" states). It gives exact sampling algorithms for inputs made of n four-mode magic states, covering passive and active dynamics. It also extends additive-error estimation of observables from passive to active dynamics and gives an exact polynomial-time method for expectation values of logarithmic-weight Majorana monomials. The algorithms serve as classical benchmarks for fermionic quantum simulations.
WhyExtends classical free-fermion simulation to non-Gaussian inputs, with exact sampling and polynomial-time Majorana expectation values improving prior methods.
Jiwon Heo, Oliver Reardon-Smith, Micha{\l} Oszmaniec et al.
In briefA general framework for higher-order quantum resources, applied to coherence
SummaryThe paper develops a unified framework for the resourcefulness of quantum states, channels, and supermaps. It introduces supermap resource monotones, distillation, and dilution, and studies free networks, compatible supermaps, and maximally free superchannels. For dynamical coherence, it shows that largest compatible supermap sets exist and characterizes them with semidefinite constraints, finding they are strictly larger than free networks but do not contain all maximally free superchannels. The authors also analyze their operational differences in one-shot channel distillation and dilution.
In brief"More is Less": A Study of Optimal Security for Haar Quantum Money
SummaryThis paper studies a quantum money construction based on an n-qubit Haar-random state and a reflection oracle. The authors show that unless a user holds Ω(2^n) banknotes, their existing notes cannot asymptotically speed up counterfeiting, so the best attack matches that of a user with no banknotes. The work uses the compressed-oracle technique, proves a tight lower bound for generating r additional copies with a matching attack, and applies the results to quantum copy-protection.
WhyProves Haar quantum money keeps optimal query security below Ω(2^n) banknotes, with tight lower bound and matching attack.
In briefA mixing-time method for estimating quantum state discrimination sample complexity
SummaryThe paper proposes a mixing-time method to estimate the sample complexity of quantum state discrimination. For minimum-error discrimination of geometrically uniform pure state ensembles, it shows the complexity has a tight estimate via a quantum homogeneous mixing time and a generalized Dobrushin coefficient. The framework reduces to classical mixing time problems in Gelfand pair cases and is applied to phase states and hypergraph state ensembles, with extensions to mixed state ensembles.
WhyLinks quantum state discrimination sample complexity to classical mixing times, giving tight estimates and resolving open problems, a notable theoretical advance with narrower application scope.
In briefImproved quantum query bounds for checking Boolean matrix products
SummaryThis paper gives the first non-trivial quantum query upper bound for Boolean Matrix Product Verification, Õ(n^{17/12}), improving on the standard Grover-based O(n^{3/2}) bound. It also shows an Ω(n^{5/4}) lower bound, improving the previous best known lower bound. The results rely on a connection with the Orthogonal Vectors problem, and a tight Õ(n^{3/2}) bound is proven for a variant of the problem.
WhyGives the first nontrivial quantum query upper bound for BMPV, n^{17/12}, plus an improved lower bound via OV reductions, with rigorous theoretical support.
Amin Shiraz Gilani, Fran\c{c}ois Le Gall, Xingyu Zhou
In briefA paper on reducing query costs for estimating quantum entropy measures.
SummaryThis paper studies estimation of quantum entropies, including von Neumann, Tsallis, and Rényi entropies, and proposes multi-level algorithms that use local normalization and precision allocation to reduce query overhead. It improves the query bound for von Neumann entropy from Õ(R/ε²) to Õ(R/ε) and gives bounds for Tsallis and Rényi entropies at various orders. The framework is extended to a broader class of density-matrix functionals.
WhyReplaces global product with a sum of local costs, improving query bounds for von Neumann and Tsallis entropy estimation.
In briefNoise makes open quantum system simulation easier, on both quantum and classical computers
SummaryThe paper shows that Pauli noise, including depolarization, exponentially suppresses high-weight components of Heisenberg-evolved observables, which can ease simulation of open quantum systems. It gives circuit depth bounds for estimating local observables that do not depend on system size, and shows sparse Pauli propagation runs in polynomial time for any fixed dissipation rate. The gap between quantum and classical bounds suggests a polynomial quantum advantage as dissipation weakens, which numerical results support.
Armando Angrisani, Ricard Puig, Yanting Teng et al.
In briefImproved sample-complexity bounds make fermionic shadow methods more practical
SummaryThis paper studies fermionic (matchgate) shadow tomography, a method for estimating observables of quantum systems from randomized measurements. The authors improve the known sample-complexity bound from O(n^{2k}||O||²) to O(n^k||O||²) for observables of Majorana degree 2k, and state that this bound is asymptotically tight. For an open 50-site Hubbard chain, they report that the required number of shots drops from about 10^9 to about 10^5 for the stated precision.
In briefUsing non-Markovian dissipation to boost quantum reservoir computing memory
SummaryThe paper introduces a quantum reservoir computing framework that models and controls non-Markovian effects with fractional derivatives. Fractional time subordination produces tunable, heavy-tailed relaxation that governs information backflow between system and environment. In an optimal regime, this improves short-delay linear memory capacity and nonlinear prediction accuracy, at the cost of long-range temporal retention.
In briefShadow QSVT: Estimating Observables with Shallower Quantum Circuits
SummaryThe paper introduces Shadow QSVT, which estimates expectation values of a set of observables on a state transformed by a polynomial of a Hermitian matrix, without building the full unitary block-encoding. It presents three algorithms: a state-aware QSVT, an observable-aware version using a new Krylov subspace and history states, and Classical Shadow QSVT, which allows observables to be specified after the quantum computation. Together they aim to reduce circuit depth for QSVT-based computations.
In briefSpectral gaps and slow modes of random Pauli rotations and quantum circuits
SummaryThe paper determines which representation sectors control the slowest convergence of random Pauli rotations and several local random quantum circuits. It gives exact all-representation spectral gaps for the continuous Pauli walk, for both the special unitary and projective cases. It also analyzes the fourth-tensor gap of real complete-graph models and its asymptotic expansion.
In briefClassical and quantum simulation of all-to-all spin dynamics in logarithmic space
SummaryThe paper studies the classical and quantum complexity of estimating disorder-averaged quench dynamics for all-to-all spin models such as quantum Hopfield, Sherrington–Kirkpatrick, and Dicke-type models. The authors give a quantum algorithm for permutation-invariant k-local dynamics that runs in polynomial time using O(log N) quantum and classical space. They show that a classical algorithm matching these resources would imply BQL ⊆ SC, while classical algorithms are provided for short times.
In briefMinimal quantum dimension needed for binary words to uniquely synchronize
SummaryThe paper defines the quantum Černý complexity of a binary word as the least dimension of quantum channels for which that word is the unique shortest synchronizing word. It shows the complexity is at most about the square root of the word length, a quadratic saving over the classical case, with constant words extremal. The authors also study a variant requiring pure target states, with explicit results in dimensions two and three.
Pui Hang Lee, Pui-Yee Lee, and Bj{\o}rn Kjos-Hanssen
In briefQuLoC: Photonic quantum-assisted compression for low-rank LLMs
SummaryThis paper proposes QuLoC, a photonic quantum-assisted algorithm for compressing large language models. It uses quantum circuit outputs to gate retained low-rank components during training, recovering performance through local reconstruction and end-to-end distillation. After training, the gating is absorbed into the low-rank factors so the compressed model runs on classical hardware. On Qwen3.5-4B it reports a 9.73% relative gain in average accuracy over state-of-the-art baselines, and on LLaMA-7B comparable or higher accuracy at different compression ratios.
In briefFast quantum Clifford circuits using dirty qubits as catalytic workspace
SummaryThis paper studies whether "dirty" qubits, whose state is unknown, can serve as catalytic workspace for quantum circuits, provided their joint state is exactly restored at the end of the computation. The authors show that any n-qubit Clifford circuit can be implemented with depth O(log n) using O(n²/log²n) catalytic qubits and no clean qubits, matching the asymptotic depth achievable with clean workspace. The approach is extended to diagonal elements of any fixed level C_k of the Clifford hierarchy and to semi-Clifford gates.
WhyExtends logarithmic-depth Clifford implementations to catalytic dirty-qubit settings and the Clifford hierarchy, with rigorous construction and resource analysis, though impact stays within quantum ci
Marten Folkertsma, Ian Mertz, Sergii Strelchuk et al.
In briefSmite: A Python tool for quasiclassical trajectory simulations of molecular collisions and reactions
SummaryThis paper presents Smite, a Python toolkit for quasiclassical trajectory (QCT) simulations of reactive and inelastic bimolecular collisions, unimolecular dynamics, and collisions with surfaces. It offers explicit control over reactant preparation, such as harmonic normal modes, thermal populations, and Wigner sampling. The same propagators work with on-the-fly electronic-structure calculations or user-supplied analytical and machine-learned potential energy surfaces. Analysis tools cover product energy partitioning, stereodynamics, and related properties.
P\'eter Szab\'o, Jenne van Veerdeghem, J\'er\^ome Loreau et al.
In briefOptimal shot allocation for early fault-tolerant iterative phase estimation under cost-error tradeoffs
SummaryThe paper studies how many repeated measurements (shots) each iteration of iterative quantum phase estimation should use so that all phase bits are correct under a total resource budget. The authors derive closed-form optimal shot counts using surrogate problems and concentration bounds. They also give simple rules of thumb for resource allocation in practical systems.
In briefQuantum advantage for symmetric functions in communication complexity
SummaryThis paper studies how symmetry under coordinate permutations affects quantum advantage in two-party communication complexity. It proves that public-coin randomized communication complexity of such permutation-invariant partial functions is bounded by a logarithmic expression in the entanglement-assisted quantum communication complexity, and that this bound is tight for set disjointness. The authors also show exponential separations for growing alphabets and graph symmetries, with all separating protocols requiring no prior entanglement.
WhyProves tight bounds and exponential quantum-randomized separations for symmetric functions, a substantial theoretical advance with impact mostly within communication complexity theory.
In briefMachine learning method solving the full electron-nuclear Schrödinger equation with a quantum-chemistry-inspired wavefunction
SummaryThe paper proposes an orbital-based neural network wavefunction with explicit many-body electron-electron correlation terms, whose parameters depend on the full electron-nuclear configuration. A hybrid optimization combining variational Monte Carlo with local-energy constraints is developed to reduce sampling bias and statistical error. These components are integrated into a unified framework called Schrödinger, which the authors report can determine potential energy surfaces for strongly correlated diatomics, triatomic reactions with conical intersections, and polyatomic multi-reference molecules.
In briefComplete natural rewrite rules for multi-qudit Clifford circuits in odd prime dimensions
SummaryThe paper gives 16 rewrite rules for multi-qudit Clifford circuits in all odd prime dimensions and proves they are complete, so any two circuits implementing the same linear map can be transformed into each other. Each rule involves at most three qudits and has an intuitive interpretation. Completeness is first established at the symplectic level via a circuit normal form, then lifted to Clifford relations using Pauli corrections. The completeness result is also formally verified in the Agda proof assistant.
WhyGives a complete, natural rewrite rule set for odd-prime-dimensional Clifford circuits, formally verified in Agda, a substantive advance over prior work.
In briefVerification Complexity and Extension of Classical Shadows: Studies whether classical data can be verified as coming from a real quantum state and whether shadows predicting higher-order properties can be faked.
SummaryThis paper studies two questions about classical shadows, a framework that compresses copies of a quantum state into classical data. The first asks when one can efficiently verify that given data came from a genuine n-qubit state, known as the Classical Shadow Validity problem, with results varying by shadow type and observable family. The second asks whether a shadow capturing 2-local properties can be faked to predict 3-local properties, and shows this estimation is intractable unless QCMA is contained in BPP.
WhySystematically classifies verification and spoofing complexity of classical shadows, with a new qc-Σ2 ⊆ P^PP upper bound and rigorous complexity proofs.
Georgios Karaiskos, Asad Raza, Dorian Rudolph et al.
In briefUsing problem structure to keep quantum speed-ups after full encoding costs
SummaryThe paper introduces a framework that compiles compact recursive descriptions of problem structure into efficient state-preparation circuits for quantum data encoding. For the uncapacitated facility-location problem, structure-agnostic encoding allows classical dequantization that removes the quadratic speed-up, while exploiting structure keeps the advantage even including state-preparation costs. The framework also prepares structured quantum states for combinatorial optimization problems with constraint relations such as group balance, conflicts and synergistic rewards.
In briefLogarithmic-depth fermion sampling: proof that anticoncentration and hardness need not require linear depth
SummaryThis paper studies Fermion Sampling, where passive linear optics acts on a non-Gaussian input. The authors show that random pairings of Haar two-mode gates reach the anticoncentration of global Haar randomness at about 0.855 log2 n layers, a logarithmic depth rather than linear. At larger logarithmic depth, they prove average-case #P-hardness for estimating output probabilities.
WhyShows logarithmic depth suffices for anticoncentration and average-case hardness, with a sharp threshold, matching lower bound, and rigorous proofs.
In briefFinding gflow on graphs with unspecified measurements
SummaryThe one-way model of quantum computing performs computations through successive adaptive single-qubit measurements on a resource graph state. Gflow is a necessary and sufficient condition for deterministically implementing certain one-way computations and is used in translating them to quantum circuits. This paper addresses open graphs whose measurements are not yet fixed, presenting an O(n³) algorithm that finds a measurement labelling together with a compatible gflow, and can respect constraints on measurement order.
Miriam Backens, Victor Gasse, Piotr Mitosek et al.
In briefLimit Theorems for Disordered Quantum Trajectories: Long-run averages and statistical laws of repeatedly measured quantum systems in random environments
SummaryThe paper studies discrete-time quantum trajectories of a finite-dimensional system in a disordered environment, where each step's instrument is set by an invertible measure-preserving dynamical system. Under a quenched Doeblin condition, it establishes existence and uniqueness of random posterior laws and identifies their barycenter as the unique dynamically stationary state. For ergodic environments it proves a pathwise ergodic theorem, a central limit theorem with Berry–Esseen bounds, and that the annealed joint process inherits the instrument process's α-mixing.
In briefClassical shadows using selective GHZ measurements for estimating quantum state properties
SummaryThe paper introduces selective GHZ measurement (SGM) shadows, which apply GHZ-basis measurements to random qubit subsets and computational-basis measurements to the rest. Its circuits need a number of CNOT gates that scales linearly with qubit count, unlike generally hard-to-implement global Clifford circuits. Simulations up to 50 qubits show advantages over local Pauli and global Clifford shadows for nonlocal observables and long-range systems.
Nicolas Faro{\ss}, Marc Wanner, Pingal Pratyush Nath et al.
In briefFaster quantum simulation of accumulated observables using locality
SummaryThis paper studies how to estimate time-integrated observables, called dense outputs, in quantum simulations. For lattice Hamiltonians, the authors propose a locality-based truncation framework and use Lieb-Robinson bounds to tighten the truncation error, so a local simulation can recover the dense output. The analysis covers free and interacting fermionic and bosonic systems as well as open systems governed by Lindbladians. Numerical experiments are included to support the findings.
In briefQuantum Tilted Walks Achieving Super-Quadratic Speedups for Combinatorial Optimization
SummaryThis paper introduces quantum tilted walks, a quantum algorithm framework for exact combinatorial optimization that biases a base Markov chain with the objective function through a tilted Hamiltonian. The authors note that existing quantum short-path algorithms do not give super-quadratic speedups over a recent classical conditioning-and-search algorithm under the same assumptions. For maximization problems, the framework is shown to increase amplitude on high-value target states under stated conditions, yielding super-quadratic speedups over that classical baseline. The advantage is demonstrated on a synthetic optimization problem where short-path algorithms do not achieve such a speedup.]
In briefUniversal Entanglement Distillation: Reaching Optimal Rates Without Knowing the State
SummaryThis paper presents a universal entanglement distillation protocol that asymptotically achieves the distillable entanglement of any unknown bipartite state in a fixed finite dimension. The approach combines tomography via local operations and classical communication with an adaptive distillation routine, using a local robustness lemma to control finite-sample errors. The results show that not knowing the state does not incur an asymptotic rate penalty.
WhyGives a universal protocol matching distillable entanglement for unknown bipartite states, plus a worst-case characterization; rigorous theory with limited empirical validation.
Salvatore Tirone, Francesco Anna Mele, Vittorio Giovannetti et al.
In briefBasic building blocks for simulating molecular quantum dynamics on oscillator-qubit processors.
SummaryThis paper develops quantum primitives for simulating molecular dynamics, representing electrons with qubits and nuclear vibrations with oscillators. The authors synthesize nonlinear multimode bosonic phase gates using generalized Jacobi-Anger expansions within quantum signal processing. Their benchmark circuits are about one-third shorter than those from the previous direct QSP approach. A short simulation of a simplified carbon dioxide model with circuit-QED noise narrowly misses the accuracy criteria at qubit and oscillator lifetimes near 2 ms and 5 ms.
In briefTransducer-based linear combination of unitaries: a method for cheaper quantum algorithms
SummaryThis paper proposes a transducer-based framework for linear combinations of unitaries (LCU), a basic building block in quantum algorithms. It reduces the query cost from being set by the most expensive unitary to a weighted average over the constituent unitaries. The authors apply the method to block-encodings of sparse matrices, yielding algorithms for sparse Hamiltonian simulation and quantum linear systems.
WhyProposes a transducer-based LCU framework replacing worst-case cost with weighted average query complexity and improving precision dependence from polynomial to logarithmic.
In briefWhen the Bosonic Quantum Entropy Power Inequality Becomes an Equality
SummaryThis paper studies when the bosonic quantum entropy power inequality, which bounds beam-splitter output entropy in terms of input entropies, holds with equality. For independent inputs of finite mean photon number, equality in either form holds exactly when the inputs are Gaussian with the same covariance matrix, with arbitrary displacements allowed. The result applies for any number of modes and any transmissivity strictly between zero and one.
WhyCompletely characterizes equality in the bosonic quantum entropy power inequality via a rigorous chain linking mutual-information preservation to Gaussianity.
In briefTransmitting Algebras Through Quantum Channels: A theory of exactly sending finite-dimensional algebras through quantum channels, unifying zero-error information theory and operator-algebraic error correction.
SummaryThe paper studies how to exactly transmit finite-dimensional C*-algebras through quantum channels, describing hybrid classical-quantum information whose quantum dimension may depend on the classical message. The authors show that a dominating algebra may fail to exist even in small dimensions, so one channel can have several incomparable optimal uses. They introduce hybrid capacities and a finite characterization of domination via minimal forbidden algebra types. The work also covers joint coding under tensor products and a channel whose tensor powers have rapidly growing numbers of maximal algebra types.
WhyIntroduces a new framework for algebra transmission over channels, proving domination can fail, giving finite characterization and doubly exponential growth; strong theory, limited direct practical im
In briefUnconditional quantum advantage using noisy planar quantum circuits
SummaryThe paper studies quantum devices limited to local operations in two dimensions and subject to local stochastic noise below a constant threshold. The authors construct a problem that such noisy 2D-local quantum circuits solve correctly with high probability, while polynomial-size AC0 circuits fail on certain instances with constant probability. Because the separation does not rely on complexity-theoretic assumptions, it is presented as the first unconditional separation that applies to planar, noise-resilient quantum devices.
WhyProves unconditional separation of noisy planar quantum circuits from AC0, a novel and rigorous result, though its impact is mainly theoretical.
In briefProtecting a three-level quantum heat engine from parasitic heat leaks with a finite-bandwidth filter
SummaryThis paper studies a continuously operating three-level quantum heat engine whose hot environment parasitically couples to the cold transition. The authors solve the three-state rate network exactly, showing that the parasitic transition creates a hot-to-cold thermodynamic short circuit and a threshold beyond which positive-power operation is lost. They then model a damped auxiliary mode as a physical spectral filter, finding that its Lorentzian response suppresses the detuned parasitic transition while overly narrow filtering limits useful energy throughput.
Gilberto Aparecido Prataviera, Marcos C\'esar de Oliveira
In briefCycle Codes and Decoded Quantum Interferometry: a study of how well a quantum optimization method performs when reduced to decoding cycle codes.
SummaryThe paper studies Decoded Quantum Interferometry (DQI), which reduces optimization problems with two-variable constraints to decoding cycle codes, with MaxCut as a main example. The authors derive DQI satisfaction guarantees under imperfect decoding and show that minimum-weight decoding of homological cycle codes is NP-hard over every field of size greater than two. On the Linial–Simkin ensemble of regular graphs, they prove maximum-likelihood recovery bounds, a strong converse, and polynomial-time recovery using LP decoders. These results give upper and lower bounds on approximate optima reachable by DQI with classical decoders, ruling out quantum advantage in the analyzed regimes while identifying regular Max-k-Cut instances where DQI efficiently achieves a nontrivial satisfaction fraction.
WhyProves minimum-weight decoding of cycle codes over larger fields is NP-hard and derives recovery bounds, sharpening DQI theory within a specialized subfield.
In briefExperimental demonstration of a tradeoff between local and global quantum resources
SummaryThe paper proposes and experimentally demonstrates a tradeoff between local and global quantum resources, measured by local maximum coherence and quantum mutual information. The experiments show that their sum is bounded by a definite upper limit. The authors argue that in quantum networks, local resources at individual nodes and global network resources are mutually exclusive, so enhancing one limits the other.
In briefPauli instability in arbitrary states: a way to detect quantum “magic” from physical correlators
SummaryThis paper shows how to measure the “magic” (non-stabilizerness) of a quantum evolution using out-of-time-order correlators evaluated in an arbitrary state, including Gibbs states. For every full-rank state, the quantity vanishes if and only if the evolution is Clifford. The authors establish its basic properties, relate it to the stabilizer entropy of the Choi state, and prove it lower-bounds the number of T gates needed for the dynamics in any circuit architecture.
In briefParticles on a one-dimensional lattice whose motion is shaped by continuous measurement
SummaryThis paper studies particles tunneling between sites of a one-dimensional lattice. The authors examine how weak continuous measurement of the occupation of a single lattice site creates entanglement and fixes properties such as wave function parity and permutation symmetry. Simulations show that continuous measurement can steer two- and three-particle systems, which initially lack permutation symmetry, into stable bosonic, fermionic and parastatistical symmetry sectors.
In briefCSS codes for quantum metrology with discrete-time error correction
SummaryThis paper studies a quantum metrology protocol based on Calderbank-Shor-Steane (CSS) codes, aiming to keep Heisenberg-like precision under noise. For noise perpendicular to the sensing Hamiltonian, discrete-time error correction preserves Heisenberg-like temporal scaling over a finite interrogation-time window whose length depends on the correction frequency. Applying recovery only after the sensing evolution gives no metrological advantage over the uncorrected noisy protocol. The Steane and Shor codes are analysed numerically, determining the corrected dynamics, the crossover to standard-quantum-limit-like scaling, and the optimal interrogation time.
Ugn\.e Liaubait\.e, Debora Ramacciotti, Robert Rau{\ss}endorf
In briefTechnical analysis of a resource-efficient quantum-walker-based quantum RAM
SummaryThis paper is a technical follow-up to an earlier quantum random access memory (qRAM) model, providing full derivations, protocol details and resource analysis. The architecture uses a number of quantum walkers that grows linearly with address and message sizes, avoiding the exponential active nodes of the Bucket Brigade design. A short-range variant decomposes interactions into 2- and 3-body local gates and is reported to reach optimal O(n+m) circuit depth.
Giuseppe De Riso, Giuseppe Catalano, Seth Lloyd et al.
In briefMany-body topology in parity-preserving tensor networks
SummaryThis paper studies planar parity-preserving tensor networks, whose contraction can be viewed as an interacting fermionic partition function, a loop gas, a deformed toric-code norm, or a quartic Ising model. Using a minimal two-parameter model, the authors apply many-body methods to analyze the same phase diagram from complementary angles. Fermionic perturbation theory predicts the phase boundaries, tensor-network numerics establish their critical behavior, and the dual descriptions reveal a self-dual line and a c=1 four-state Potts multicritical point.
Maksimilian Usoltcev, Nguyen Hanh Dung, Carolin Wille et al.
