Papers

We show two unconditional quantum space advantages in the random-order streaming model. First, we show the Yamakawa–Zhandry Code Intersection problem admits exponential quantum advantage in the streaming model when its inputs are streamed in random order. This means quantum computers exhibit exponential space advantage even when simply receiving $(x,f(x))$ pairs for a uniformly random function $f$ in a uniformly random order. Our lower bound is shown using density-restoring partitions as in the work of Göös, Gur, Jain, and Li (STOC 2025) combined with a convex potential, similar to the work of Raz (J.ACM 2018) on parity learning and its generalization by Garg, Raz, and Tal (STOC 2018). Second, we use our framework to show quantum space advantage for the Optimal Polynomial Intersection (OPI) problem in certain regimes via a streaming version of the Decoded Quantum Interferometry algorithm (Nature 2025; arXiv:2510.10967). In particular, we show that for degree $d$ and $n$ evaluation points, attaining $1/2 + \Omega(\sqrt{d/n})$ fraction of satisfied OPI constraints via streaming requires $\Omega(n)$ classical bits of memory but only $O(d\log n)$ qubits. This yields provable quantum advantage in a "low-rate" regime when the number of evaluation points is much larger than the degree, with a space advantage that can be as large as exponential in certain parameter settings.

In our previous paper on the matter, we proved that real quantum theory (RQT) cannot be experimentally falsified without the experiment falsifying quantum theory (QT) as well. Our result is in direct contradiction to the central claim of an article by Renou et al., published in Nature [600, 625–629 (2021)], reporting a bilocal network experiment that could falsify real quantum theory without falsifying quantum theory. The purpose of this note is to address several seemingly natural attempts to recover the experimental conclusion of Renou et al. We first explain how these results, although based on nonlocality experiments, are far from a Bell-like level of proof. Then we explain why the proposed experiment requires an experimentally untestable premise about independent preparations necessarily being represented as product states. Finally, we discuss some concerns that lie outside the scope of both results.

We study a multilinear optimization problem for tensors with bounded Frobenius norm, where each of the $k$ local factors of dimension $d$ is chosen from a convex set. We give a deterministic algorithm running in time $d^{O(k)}$ for constant additive approximations. As applications, we obtain the first polynomial-time algorithms at constant accuracy for weak membership in the nuclear-norm unit ball of high-order tensors and for multipartite quantum separability in Frobenius norm. Our approach views tensor optimization as a cooperative multiprover game and combines this perspective with a recursive spectral compression procedure. We then show that related ideas admit a quantum implementation when the input state is given through copies, rather than an explicit classical description. In these settings we obtain an algorithm to solve Frobenius-norm separability testing using $\text{poly}(k)$ copies and $\text{poly}(k\log d)$ time.

We prove that the von Neumann entanglement of purification is nonadditive. For two-qubit Werner states $W(f)$ with singlet weight $1/64\le f\le1/4$, we show that canonical purification is globally optimal: its entanglement, also known as reflected entropy, gives the exact entanglement of purification. In contrast, the regularized entanglement of purification lies strictly below the reflected entropy for $0<f<f_\ast$, where $f_\ast\approx0.017$. Together, these results establish nonadditivity throughout $1/64\le f<f_\ast$. Our canonical-optimality proof generalizes the proof in [1], which established Rényi nonadditivity for $0\le\alpha<1$ using classical two-qubit states. We thus resolve the additivity question at $\alpha=1$. Remarkably, nonadditivity is again witnessed by separable states and no entanglement in the underlying states is required.

The fundamental task of quantum hypothesis testing, which consists in discriminating quantum objects, has been extensively studied for quantum states and channels. Here, we investigate the fundamental limits of discriminating an arbitrary pair of quantum Markovian dynamics generated by Lindbladians, focusing on the roles of total exposure time and temporal resolution. We allow adaptive choices of evolution durations and arbitrary instantaneous controls between them. We characterise the optimal type-II error exponent (Stein exponent) as the largest instantaneous increase of quantum relative entropy, and give an algebraic criterion for its finiteness in terms of the Lindbladians. Remarkably, an infinite exponent is equivalent to a vanishing type-II error probability at sufficiently large finite total time, for every positive type-I tolerance. While some dynamics admit a finite protocol with zero type-II error, others require increasingly fine temporal control. For the latter, the error vanishes as the minimum allowed evolution duration, or resolution time, tends to zero at fixed sufficiently large total time, but remains bounded away from zero at every fixed positive resolution time. We achieve this using quantum Zeno protocols, establishing temporal resolution as a resource for discrimination. When the null hypothesis is the identity semigroup, an infinite asymptotic error exponent has a stronger consequence: at a fixed finite total exposure time, the type-II error can be made arbitrarily small while keeping the type-I error exactly zero. This is impossible in the corresponding classical setting. Discriminating the identity semigroup from generalised amplitude damping on a qubit provides examples of all three regimes: a finite asymptotic error exponent, zero type-II error attainable at positive resolution time, and vanishing type-II error requiring the resolution time to tend to zero.

Fault-tolerant quantum simulation requires compiling symmetry-preserving time evolutions into discrete gate sets. Standard Clifford+T synthesis can break continuous symmetries even when the target evolution preserves them, causing compiled simulations to lose essential features of the original system. We develop a fault-tolerant compilation framework that preserves SU(2) symmetry exactly. We characterize the number-theoretic obstruction preventing symmetry-preserving unitary Clifford+T circuits from approximating arbitrary SU(2)-symmetric evolutions and circumvent it using measurement and feed-forward. The resulting synthesis confines compilation errors to the symmetry-preserving operator algebra rather than introducing symmetry-breaking perturbations. We demonstrate the algorithm by simulating transport in the one-dimensional Heisenberg model. At a lower matched T-count, for instance, 54 T gates per two-site Trotter step, standard synthesis yields an incorrect transport exponent, whereas our symmetry-preserving compilation reproduces the expected exponent for the same expected T-count. If instead each approach is allocated whatever resources are necessary to estimate this exponent to the same accuracy, our construction reduces the T-count by approximately a factor of five. We further extend the framework to gauge symmetries in lattice gauge theories and to particle-number and spin symmetries in fermionic models relevant to quantum chemistry and the Fermi-Hubbard model. These results show that symmetry-preserving fault-tolerant compilation can qualitatively change the effects of synthesis error while substantially reducing the resources required for quantum simulation.

We study anyon decoherence in 2D topological order, with the fermion decoherence in Kitaev's sixteenfold way as explicit examples. The sixteenfold way includes chiral topological phases, which are believed to admit no commuting projector Hamiltonian, making it challenging to study their decoherence directly. We further conjecture the density matrix produced by this decoherence induced phase transition can be obtained by a three-step procedure: first lift the topological order to its Walker-Wang model, followed by a transition to another Walker-Wang model, and finally trace over the bulk degrees of freedom. This establishes a connection between the decoherence of a topological order and a pure state phase transition in its 3D counterpart. Many examples are given. In particular, we show that decohering the fermion in each of the sixteen states always yields an intrinsically mixed-state topological order, a consequence of the fact the corresponding 3D bulk always transits into the 3D fermionic toric code (fTC). Our result suggests a systematic method for studying anyon decoherence in chiral topological orders at the level of commuting projector Hamiltonians.

The QICK (Quantum Instrumentation Control Kit), first introduced in 2022, is a standalone open source control system for quantum information science. Since then, QICK has been migrated to new hardware platforms, expanded its functionality for applications with different types of qubits (superconducting, atomic, ion-trapped, and spin defects), as well as quantum sensors, and quantum networks. QICK is a highly optimized control kit, with a library of functions that can be used for more than one application. In particular, the software and firmware are customized to minimize latency and maximize control performance and throughput. In this white paper, we describe hardware details and performance of the QICK Box. The QICK Box features up to 16 outputs, up to 8 inputs, and 8 20-bit DC biases. Modular output and input daughtercards give the choice of signal chains optimized for fast DC-coupled signals or RF signals up to 10 GHz. Power levels, step attenuation, and bandpass filtering are controlled by software. We demonstrate the system's performance through single-shot readout measurements of a six-transmon device at the Quantum Underground Instrumentation Experimental Testbed (QUIET) at Fermilab, achieving (91.7 +/- 0.4)% readout fidelity limited by T1 decay during the readout. The single shot readout signal-to-noise ratio (SNR) is 4.4 +/- 0.1 without a quantum amplifier, confirming that the QICK Box is suitable for high-fidelity quantum control and measurement applications. Advances in firmware and software will be described in a separate paper.

Non-Clifford gates are essential for avoiding classical simulability under the Gottesman-Knill theorem. An error-corrected circuit with non-Clifford gates will therefore be an important element for realizing useful fault-tolerant quantum algorithms. However, accurately understanding the fault-tolerant performance of such circuits faces challenges due to the classical hardness of simulating these circuits. We avoid simulating logical measurements and develop exact and efficient classical methods for benchmarking circuits composed of X, CNOT, and diagonal gates in the Clifford hierarchy, including state and gate teleportation gadgets with feedforward. For circuits with third-level diagonal gates, our benchmarking algorithm efficiently samples syndrome statistics and estimates the output logical fidelity and expectation values of certain Clifford observables, including all Pauli observables. The evaluation of syndrome expectation values also extends to circuits with fourth-level diagonal gates. Our algorithm scales polynomially in the number of physical qubits n and circuit depth T, independent of the number of logical qubits. The benchmarking applications include IQP sampling and magic state preparation/cultivation. We demonstrate the practical utility of our simulation algorithms by using them to optimize high-rate magic state distillation factories based on three copies of a [[27,3,3]] tricycle code.

The minimal sampling overhead of the quadratic collective phase $e^{-i\gamma K^2}$ over one layer of single-qubit rotations is decided by the continued fraction of $\gamma/\pi$. Here $K$ is a collective observable with spectrum $\{0,\dots,n\}$, such as the permutation-symmetric Hamming weight. This gate is the cardinality-penalty layer of constrained optimization, the one-axis-twisting gate of spin squeezing and the Kerr phase of a bosonic mode. Instead of compiling it to two-qubit gates, we sample it as an LCU over such layers at overhead $\Gamma$. Our results give an optimality theory for this overhead. Ancilla-free sampling reproduces the target's outcome probabilities up to the minimal $\Gamma$, and no smaller factor works for every input; for permutation-symmetric $K$, independent per-qubit angles or one layer of arbitrary single-qubit gates give no further reduction. Rational angles $\pi p/q$ in lowest terms cost exactly $q$ once $n\ge2q-2$, attained uniquely by a uniform $q$-point sampler; the cost is $\Theta(n)$ if and only if $\gamma/\pi$ is badly approximable, and bounded in $n$ if and only if it is rational. A second result shows what the symmetry buys: without it, the squaring phase of Fourier arithmetic on $m$ qubits costs at least $2^{0.557m-O(1)}$ over single-qubit gates, beyond the $2^{m/2}$ of every cut bound, by a new certificate-lifting argument. For constructions known only through upper bounds, it gives the optimum: the Fourier-based LCU of Carrera Vazquez, Egger and Woerner is, at fixed $n$, optimal up to a constant at typical angles and beaten by $(n+1)/q$ at rational ones with an $n$-independent sampler; the Kerr decomposition of Upreti, Quesada and Chabaud is the unique optimum over phase shifters at rational parameters without photon-number cutoff; and it identifies the rational couplings where one-axis twisting admits optimal cat decompositions.

For quantum low-density parity check (qLDPC) codes, the ability to manipulate individual logical units of information, i.e. the use of addressable gates, enables maximal utility of their efficient encoding. We introduce explicit low-depth unitary circuits that realize fully addressable and fault-tolerant two-qubit Clifford gates for a subset of two-dimensional translationally invariant qLDPC codes. Our transversal unitaries are created by applying a geometrically structured sparsification procedure to round-robin circuits. We verify the general applicability of our protocol by proposing and numerically simulating a range of addressable CZs between toric, cyclic hypergraph-product, color, gross, and directional codes, demonstrating fault-tolerant memory-like logical error rate scaling.

Quantum fire is a recently introduced cryptographic primitive consisting of efficiently preparable quantum states, called flames, that admit efficient cloning but resist efficient telegraphing, namely reconstruction via classical communication without preshared entanglement. In all prior constructions of quantum fire, cloning is a public operation that requires no separate key and every holder of a flame state can clone it. For applications to access control, however, an issuer may wish to delegate cloning to designated quantum servers while withholding this capability from other flame holders. To address this, we introduce delegatable quantum fire, in which cloning requires a separate key. We give two constructions in the classical-oracle model. Our first construction uses a classical secret key which enables cloning, and any user with the entire key may clone successfully. Our second construction, which we call torch-fire, uses quantum cloning keys, called torches, which enable cloning while remaining unaffected in the process but cannot otherwise be split or delegated to enable additional cloning. An efficient adversary given $m$ torches cannot, except with negligible probability, enable more than $m$ noncommunicating parties to each clone a fresh, independently issued challenge flame. The adversary may jointly process its resources before separating the parties and distribute arbitrarily entangled registers among them. Both constructions are in the oracle model, relying on public classical oracles that allow queries in quantum superposition.

We present a unified framework for upgrading a broad class of cryptographic primitives to support constant-rate certified deletion. Previous constructions require a linear number of qubits per encrypted bit of certified-deletable plaintext. In contrast, we obtain the first constant-rate constructions in the plain model that achieve certified deletion while preserving everlasting security. Our approach applies to a wide range of "all-or-nothing"-type primitives based on BB84-style encodings, including commitment schemes, public-key encryption, attribute-based encryption, and fully homomorphic encryption. Beyond this class, we also obtain constant-rate certified deletion for primitives built from subspace coset states, such as blind delegation, secure software leasing, functional encryption, and differing-inputs iO, and CCA-PKE. Importantly, our framework does not introduce any additional assumptions beyond those required by the underlying certified deletion primitives. Finally, under the hardness of SIS, we show that public verifiability can be incorporated into BB84- and coset-based certified deletion. In combination with our constant-rate constructions, this yields publicly verifiable certified deletion schemes with constant rate.

Randomized benchmarking comprises a suite of standard techniques for assessing the operational fidelity of quantum processors. These techniques can be reliably applied to groups with process matrix representations that are free of multiplicity. However, many groups that are naturally formed from native gates do have multiplicity, and it is difficult to draw robust conclusions from the resulting data. In this work, we present a new and intrinsic solution to the problem of multiplicity that completely eliminates the need to fit multi-exponential decays while still remaining robust to errors in state preparation and measurement. Our procedure, which we call lifted randomized benchmarking, generalizes key elements of both character and synthetic randomized benchmarking to benchmark a target group of quantum gates with respect to an enlarged group. We illustrate in numerical examples that our method can efficiently and reliably estimate the fidelity of two-qubit gates relevant to experimental trapped-ion systems. These techniques may find applications beyond randomized benchmarking to quantum tomography and learning, as well as the characterization of error-correcting codes.

The computational complexity of simplicial homology has been studied since the question was raised by Kaibel and Pfetsch, and clique homology was later shown to be $\mathsf{QMA}_1$-hard by Crichigno and Kohler. King and Kohler subsequently introduced the weighted, spectrally gapped version considered here and developed a reduction intended to establish the same hardness result in this setting. We give a complete proof of the hard direction. The earlier King-Kohler argument contains a gap in the analysis of the nontrivially folded local gadgets, so the required topological and spectral properties have to be re-established on the clique complexes actually produced by the reduction. This is not a local repair of the published proof: the argument requires a new analysis of the local topology, the filtered cochain complexes, and the interaction of many overlapping gadgets. Our proof uses exact finite certificates for the local combinatorial data and relative homology to determine the effect of each gadget on the encoded qubit space. We then prove the finite-dimensional filtered-Hodge statement needed to recover the corresponding rank-one low-energy penalty and derive a quantitative global estimate that transfers the source-Hamiltonian promise gap to the final weighted Hodge Laplacian. Consequently, for fixed efficiently computable $k(n)$ and inverse-polynomial $\gamma(n)$, weighted gapped clique homology is $\mathsf{QMA}_1(\mathcal G)$-hard. The previously known $\mathsf{QMA}$-containment argument is logically independent of the gap and remains unaffected.

We initiate the study of weak Schur sampling (WSS) under noisy inputs. Many optimal quantum learning algorithms rely on this measurement, for instance in quantum spectrum estimation (QSE) and quantum state tomography (QST). The standard analysis of WSS, QSE and QST assumes that the $n$ input copies of the target state $\rho$ are identical, i.e. $\rho^{\otimes n}$. We study what happens when they are not, a more realistic noisy scenario that breaks the very permutation symmetry on which WSS is built. In the simplest model the input is a noisy product state: the copies are independent but not necessarily identical and each is $\epsilon$-close in trace distance to the $d$-dimensional target state $\rho$. A naive argument via the data-processing inequality allows the per-copy errors to accumulate to $n\epsilon$ on the measurement outcome. We show that for QSE via WSS this does not happen: the expected estimation error in total variation is at most $\epsilon+\eta(n,d)$, where $\eta(n,d)=O(d/\sqrt n)$ is the noiseless error, and the additive noise term $\epsilon$ is optimal. The output error does not grow with $n$ even though the input error does; in this sense WSS is robust. Beyond noisy product states, for arbitrary input $\omega$ we show that the error is at most $\eta(n,d)+\frac{1}{n}\|\omega-\rho^{\otimes n}\|_{W_1}$, where $W_1$ is the quantum Wasserstein distance of De Palma et al. In particular, our results imply, for the first time, noise-robustness of Keyl and Werner's seminal algorithm for QSE, more than two decades after its introduction. Finally, we show that the noise cannot be too bad: within our model of robustness the promise on the input cannot be weakened to closeness of single-copy marginals or to a global trace-distance budget alone, as in both cases some inputs defeat every measurement and estimator.

A quantum orthogonal polynomial transform (QOPT) is an algorithmic primitive that maps a superposition of standard basis states $\sum_k \alpha_{k} \ket{k}$ coherently to a basis of normalized univariate polynomials orthogonal with respect to a probability measure $\mu(x)$. We provide new discrete and continuous QOPTs for polynomial families in the Askey scheme extending the results for the quantum Hermite transform (Jain et al., STOC'26). Our efficient QOPT algorithms require time $O(\text{polylog}(N, 1/\epsilon))$, where $N$ is the grid size and $\epsilon$ is the error, for the discrete Charlier, Meixner and Krawtchouk transforms and for the integer-order Laguerre transform in the continuous setting. The efficient QOPTs are obtained by uncovering the links between Askey scheme polynomials and Gaussian quantum optical gates and developing a compilation framework for $SU(2)$ and $SU(1,1)$ optical gates on Cartesian grids extending the framework developed by Iyer et al. (arXiv:2602.15180). Further, we reduce the continuous Jacobi transform to the discrete Hahn transform and provide an $O\!\left(N\operatorname{polylog}((N+\alpha+\beta+1)/\epsilon)\right)$-time Hahn transform, a quadratic speedup over the naive implementation. This is based on a more efficient compilation of the Clebsch–Gordan transform for coupling $\mathrm{SU}(2)$ representations with spins $(j_{1}, j_{2})$. Finally, we develop a new framework for Laguerre transforms for all orders $\nu>0$ by fast-forwarding the corresponding radial oscillator using a 3-term chirp decomposition and an efficient algorithm for the Quantum Hankel Transform on a logarithmic grid.

For classical–quantum wiretap channels with a transitive covariant input action, both output ensembles admit a description as unitary group orbits of fixed seed states. We use this structure to construct finite-block preprocessing schemes whose private information is an entropy difference evaluated at two distributions related by group convolution. Applying the construction to product groups allows correlations across any fixed number of channel uses. We give a sufficient condition for the associated uniform-input bound to equal the single-use private information. Constant-composition channel codes and universal$_2$ hashing achieve the resulting rates, with trace-distance leakage controlled by sandwiched Rényi information. For uniform outer randomization, the representation structure reduces the comparison-state optimization to Eve's invariant states. For the hybrid binary channel considered by Tikku, Berta and Renes, numerical optimization at three and four uses gives rates above our numerical estimate of the optimized noisy-repetition benchmark wherever that estimate is positive on the tested grid. The improvement comes from noise distributions beyond the family of independent physical flips and a symmetric logical flip. We also prove nonadditivity at an explicit channel parameter using a two-use encoder, an analytic single-use converse, and certified entropy bounds. Finally, we relate the hybrid model to binary phase-shift keying with a fixed receiver measurement.

Classical Dobrushin–Shlosman theory uses heat-bath block updates to identify sharp temperature thresholds for establishing the rapid mixing of Gibbs samplers. In particular, these mixing guarantees often hold even when stricter single-site conditions fail. We extend this approach to noncommuting quantum lattice systems through a quantum Dobrushin–Shlosman condition for finite-block dynamics, which we call smoothed heat-bath dynamics. We establish this condition in two regimes. For finite-range quantum spin chains at every fixed finite temperature, we prove logarithmic trace-norm mixing in system size, with normalized bounds uniform in on-site fields and single exponential in inverse temperature. We also prove stability under small local perturbations of interacting, possibly noncommuting reference Hamiltonians on graphs of polynomial volume growth. For classical references with bounded local interactions, uniform strong spatial mixing implies our quantum condition. With bounded local terms and fixed physical, geometric and block parameters, the resulting samplers prepare Gibbs states to trace-norm error $\varepsilon$ using $N\operatorname{polylog}(N/\varepsilon)$ gates and classical operations. Our block updates combine a local Gibbs reset with quantum belief propagation to incorporate interactions across the block boundary, yielding exactly Gibbs-preserving, KMS-reversible channels. Two independently tunable parameters control contraction: an internal evolution time suppresses the influence of sites inside a block, while the block size allows interior contraction to dominate boundary influence. This finite-time relaxation has no counterpart in a classical heat-bath block update.

We propose a Gibbs state preparation algorithm that exploits algebraic structure in the Hamiltonian. Our starting point is Hamiltonian Decoded Quantum Interferometry (HDQI), a recent algorithm that reduces Gibbs state preparation for Pauli Hamiltonians to decoding error-correcting codes. We introduce quantum decoding HDQI (QD-HDQI), replacing HDQI's coherent classical decoder by a quantum decoder that can exploit interference between different errors. For commuting Pauli Hamiltonians, our reduction is efficient and the associated quantum decoding problem corresponds to transmitting the associated symplectic code over i.i.d. pure-state classical-quantum channels. For uniformly random Hamiltonian signs, the vanishing-error threshold of an efficient decoder directly determines the lowest temperature that our algorithm can reach. Even using only classical decoders, this improves upon HDQI's achievable inverse temperature from linear to square-root in the correctable error fraction; quantum decoders can improve further by tolerating still stronger noise. A similar picture extends to the noncommuting regime previously handled by HDQI, where now the noise is correlated within small, independent blocks. We study two such quantum decoders in our QD-HDQI Gibbs sampling framework. The first, based on unambiguous state discrimination, works efficiently for arbitrary binary linear codes. However, we "dequantize" this strategy for commuting Hamiltonians, contributing a classical rejection sampler that matches its temperature threshold. The second is belief propagation with quantum messages (BPQM), a quantum generalization of classical belief propagation. We show that for certain dilute spin glasses, BPQM's decoding threshold exceeds the Shannon limit for classical decoding, reaching temperatures inaccessible to any classical decoder within our framework.

Exactly solvable models are often identified from structural features of their interactions. For quantum spin Hamiltonians, these are captured by the frustration graph of anticommuting Pauli terms. The frustration graph characterizes broad families of spin models that map to free fermions for arbitrary, or generic, values of their coupling strengths. Nevertheless, there exist non-generically solvable models that admit free-fermion solutions only at finely tuned couplings. In this work, we characterize a family of such models in terms of graph structures. Given an arbitrary instance of Fendley's free-fermions-in-disguise (FFD) chain, we construct a set of operators, called Krylov currents, that are exactly quadratic in its effective fermionic modes and thus extend it to a linear family of free-fermion solvable Hamiltonians. As the Krylov currents are nonlinear in the FFD Hamiltonian terms, the elements of this generated family are non-generically solvable, and they accordingly fail the known conditions for generic solvability. We prove that every Krylov current admits an expansion in terms of induced paths of the frustration graph and that they generate the full special-orthogonal algebra of Gaussian transformations. Our results identify path support as a signature of non-generic solvability, and they provide a systematic route to finding exactly solvable many-body Hamiltonians.

What must a quantum error-correction decoder know about temporally correlated noise, and what does it cost to learn? We study this question for fixed stabilizer memory experiments with known system-environment interactions. We formulate calibration in terms of the fidelity differences that select a Pauli recovery and relate missing information to the resulting fidelity loss. Our main example uses weak coherent $X$ rotations in a class of CSS codes including Shor, Steane, and odd-distance rotated surface codes. All physical qubits share a sign either fixed throughout a run or independently redrawn each interval. The two models have identical syndrome statistics and the same spatiotemporal Pauli process (SPP), obtained by Pauli-twirling every noise interval. Yet at suitable storage times, they require different logical corrections. In the weak-noise limit, each model is almost perfectly correctable when known. Without model information, even the best final recovery has a worst-case fidelity loss approaching $1/2$ relative to the noise-aware optimum, despite access to the full syndrome record. For this pair of models, at fixed code and fixed positive target loss below $1/2$, we prove matching calibration bounds. With logical preparation and final readout, complete QEC cycles require a number of noise intervals scaling as the inverse rotation angle raised to the code's $X$ distance. Allowing two uninterrupted intervals before one extraction reduces the optimal cost to inverse-square scaling. Physical Pauli twirling of every noise interval changes both recovery performance and its information requirements. Discarding the record of applied random Pauli operations makes the SPP sufficient for optimal recovery. Keeping this record can improve the attainable fidelity, but reaching that optimum may require additional noise information.

Loading data into quantum computers is a key bottleneck that threatens end-to-end quantum advantage. Quantum-circuit compilers for structured states like matrix product states (MPS) are a critical enabler to manage this in quantum chemistry, finance, and many-body quantum simulation. Approximate preparation of MPS typically relies on layered sequential staircases of nearest-neighbour gates. We present Adaptive State Preparation by Iterative Removal of Entanglement (ASPIRE), an algorithm that approximately compiles state-preparation circuits by selecting gates based on the state's underlying entanglement geometry and the available connectivity of the target quantum processor. Our protocol scores candidate qubit pairs on the removability of their entanglement and identifies layers of parallelised long-ranged gates that remove the most entanglement. We demonstrate our protocol empirically across a range of settings, illustrating its success for preparing Hamiltonian ground states and multivariate amplitude-encoded functions, and accounting for qubit connectivity, hardware noise, and both NISQ and early fault-tolerant settings. Throughout, ASPIRE typically achieves higher fidelities and shallower circuits than existing methods for states with long-ranged entanglement, even when classical optimisation is accounted for. Our investigation positions ASPIRE as a competitive, resource-frugal state-preparation protocol, with particular promise for applications tolerant to imperfect fidelity such as preparation of guide states for quantum phase estimation.

We investigate dynamical relaxation to the Born rule in a semiclassical gravity model described by the Schrödinger-Newton equations. Using a Gaussian variational solution for the self-gravitating wave packet, combined with Nelson's stochastic representation of quantum dynamics, we track the evolution of particle ensembles whose initial probability distribution differs from $|\Psi|^2$. Relaxation to the Born rule ("quantum equilibrium") occurs when the wave packet remains bounded, or grows sufficiently slowly in time; in contrast, for rapidly expanding solutions of the Schrödinger-Newton equations, deviations from the Born rule can persist indefinitely. Numerical simulations confirm this analytical picture. These results show that semiclassical self-gravity can either enable or inhibit relaxation towards the Born rule, providing a minimal model relevant to proposals of primordial quantum non-equilibrium, as suggested by Underwood and Valentini [Phys. Rev. D 92, 063531 (2015)].

Frequency-bin encoding provides a scalable platform for photonic quantum information processing by enabling high-dimensional qudit states compatible with the telecommunications infrastructure. However, characterizing these systems remains challenging, as conventional quantum state tomography requires measurement resources that increase rapidly with dimensionality, compounded by the difficulty of implementing controllable measurements across many frequency modes at once. Here, we address these challenges and demonstrate threshold quantum state tomography of entangled frequency-bin qudits using adaptive measurements that exploit the sparsity of highly entangled biphoton frequency combs. Combined with Bayesian inference, we experimentally demonstrate full state estimation of biphoton frequency combs with Hilbert space dimensions up to $d^2=100$—a 56% increase over the previous record—all while performing a mere 1.9% of the measurements required by conventional tomographically complete approaches. This work confirms the promise of measurement-aware approaches for characterizing high-dimensional photonic quantum systems, unlocking new tools for full tomography that are hardware-efficient, state-aware, and free from a priori assumptions about state structure.

Multicore optical fibers (MCFs), developed to scale classical telecommunications, are gaining traction as a quantum platform for high-dimensional key distribution, entanglement, and photonic quantum walks. So far, quantum light has occupied these fibers only as single-mode path channels; the spatial-mode structure within each core has remained untouched. Here we operate a telecom-grade 39-core fiber far from its design wavelength, where each core supports exactly two LP mode groups (LP01, LP11), and measure heralded photon-number states |1> and |2>, resolving the photon number simultaneously with the intra-core spatial mode or with the core index. Displacing the launch prepares a coherent LP01-LP11 superposition whose single-sided intensity pattern shows that the intermodal phase is preserved over the fiber: a drift-resolved joint fit gives a pixel asymmetry (0.4% vs 47%) incompatible with an incoherent mode mixture. Because the two modes couple to neighboring cores at different rates (kappa_LP11/kappa_LP01 = 2.4), the launched mode content acts as a state-selectable coupling knob: the effective inter-core coupling of the passive fiber is set by the launch alone (3.9-13.1%), a tunability that otherwise requires electro-optic, thermo-optic, or mechanical reconfiguration. The propagation is photon-number independent: the per-photon crosstalk of heralded |2> states equals that of |1>, bounding any Fock-state dependence to |dx/x| < 6.1% (95% CL), and the imaged mode distributions of |1> and |2> agree to better than 1%. This measured linear-optics null, validated against exact Fock-space simulation, is the baseline against which genuine multiphoton interference in fiber quantum walks must be certified; we also show how coincidence-based event selection produces spurious photon-number-dependent crosstalk if accidentals are not subtracted.

Fermionic non-Gaussianity is a key resource for universal quantum computation, and its behavior in quantum many-body systems has attracted growing interest. Recently, a convolution-based measure, which we call the magic Rényi entropy (MRE), has been proposed as a resource measure of non-Gaussianity, but its evaluation is limited to small systems due to the computational cost growing exponentially with system size. In this work, we develop a perfect-sampling method to calculate the second-order MRE from matrix product states (MPSs). Our method uses a bounded estimator to control sampling fluctuations and a recursive sweep to draw the samples directly from the input MPS, which allows us to generate each sample with $\mathcal O(nD^3)$ time, where $n$ and $D$ denote the number of modes and MPS bond dimension, respectively. We benchmark our method on the XXZ chain with up to $128$ sites, demonstrating that the MRE captures intricate higher-order correlations at large scales, which are inaccessible to covariance-based measures. These results provide a computational tool that quantitatively evaluates many-body fermionic non-Gaussianity by accounting for higher-order correlations.

Neural quantum states based on modern deep learning architectures have emerged as powerful representations for quantum many-body systems. In particular, Transformer-based neural quantum states provide expressive models capable of capturing long-range correlations, and their empirical generalization performance has recently been demonstrated. However, a theoretical understanding of their generalization behavior remains largely unexplored. In this paper, we develop a theoretical framework to analyze the generalization properties of Transformer-based neural quantum states under in-context learning. We establish a rigorous inference-time generalization error bound in terms of mean squared error (MSE), showing that the pointwise prediction error decreases inversely with both the number of in-context examples and the depth of the Transformer. We further show that the Transformer depth required to achieve this guarantee scales only linearly with the system size–namely, the number of particles in continuous systems or the number of qudits in discrete systems. Building on this result, we extend our analysis to full quantum states formulated as rank-one density operators, and derive MSE-based generalization bounds over both continuous and discrete domains under physical constraints. Finally, numerical simulations corroborate our theoretical analysis.

Quantum entanglement is a fundamental resource in quantum information theory, yet its general characterization and quantification remain challenging, especially in multipartite systems. In this work we investigate entanglement from a geometric perspective, focusing on the Riemannian structure induced by the Fubini–Study metric on the projective Hilbert space of multi-qubit quantum states. By exploiting the local-unitary invariance of this metric, we derive the entanglement distance (ED), a geometric measure that quantifies entanglement as an obstruction to locally minimizing the sum of squared Fubini–Study distances generated by local operations. We analyze the properties of ED for pure multi-qubit states and discuss its behavior under local operations and classical communication. In particular, we show that ED reproduces established entanglement measures in well-defined and restricted settings. For pure states of two qubits, ED reduces to an exact monotone function of the concurrence and, independently, to an explicit monotone function of the entropy of entanglement. These results provide a clear geometric interpretation of standard bipartite entanglement measures within the present framework, while highlighting the limitations of such correspondences beyond the two-qubit case.

Bell correlations have been detected in atomic ensembles ranging from hundreds to hundreds of thousands of particles, witnessed by the permutationally invariant (PI) Bell operators. For all the operators realized so far, the maximally violating state can be brought, in a suitable basis, into a nonnegative-amplitude form. In that basis, the Bell operator is stoquastic. The coefficients parametrising these operators that at the same time lead to stoquasticity form a convex cone, the so-called stoquasticity cone. Its characterization had remained open beyond two-body operators, as for many-body operators the number of inequalities grows with the system size $n$. In this work we show that, in the thermodynamic limit, the stoquasticity cone admits an exact semidefinite characterization, valid at any operator order. The key observation is that, along each off-diagonal, the matrix elements are the values of a single univariate polynomial. Being univariate, this condition is equivalent to a linear matrix inequality, with no relaxation hierarchy. Therefore, deciding stoquasticity becomes a single semidefinite feasibility problem. As its lowest-degree instances, this description recovers the known three-hyperplane characterization for two-body operators and yields, for three-body operators, a curved boundary.