Papers

Discovering properties of many-body quantum systems is challenging because of the large number of parameters to determine. Here, we show that correlations among quantum observables help reduce the complexity of quantum learning. A polynomial number of selected measurements can bound the values of exponentially many dependent yet unmeasured quantities, enabling efficient estimation of general functions of quantum states. We leverage this result to design correlation-informed learning algorithms that estimate key quantum resources, such as entanglement and magic, in systems of 100 qubits. They achieve a lower relative error than shadow tomography and neural-state methods by using information about a polynomial number of measured Pauli strings. These protocols are readily testable with today's quantum computers, as they do not require premeasurement entangling gates. Quantum constraints themselves are therefore a resource for exploring large quantum systems.

Montanaro and Zhou proved that depth-one Quantum Approximate Optimization Algorithm (QAOA) finds the planted solution of certain near-symmetric constraint satisfaction problems with probability $\Omega(1)$, and observed exponential runtimes for general-purpose classical solvers on explicit realizations, providing strong evidence of an empirical exponential speedup of low-depth QAOA. We ask what such a circuit costs fault-tolerantly. Although the cost Hamiltonian carries $\Theta(n^\ell)$ clauses, the rotation angle at which QAOA succeeds shrinks as $n^{1-\ell}$, and we show that small-angle Clifford$+T$ rotation synthesis reduces the non-Clifford cost per circuit to $\widetilde O(n^2)$ for every clause locality $\ell$. Compiling the circuit, however, requires the explicit clause list. We find that the mechanism underlying constant QAOA success fixes the degree-one Fourier coefficients of the cost, whose signs reveal the planted solution. However, this leakage need not reveal the solution: we design families in which the quadratic non-Clifford scaling and hard exact optimization coexist.

A central question in the theory of quantum advantage is whether there are quantum advantage protocols with similar resource requirements as random circuit sampling that are also verifiable just from the classical outputs of the quantum computation. Here, we develop the idea of simulation secrets for verifiable advantage. A verifier can use a simulation secret to evaluate a cross-entropy test faster than it would take a classical adversary to pass the test. We instantiate this idea using IQP circuits described by cubic polynomials with planted independent spaces. These correspond to the largest independent set in the orbit of a polynomial under the general linear group and yield a low-rank stabilizer decomposition of the corresponding state. We conjecture that large independent spaces are invisible to a computationally bounded adversary, and therefore they cannot exploit them to pass the protocol. A second conjecture regards the fine-grained complexity of producing samples that pass the cross-entropy test for uniformly random polynomials. Under these conjectures, our scheme results in a polynomial gap between the verification time and the time a classical adversary would need to pass the protocol—both are exponential. It has a potential application to generating classically certifiable randomness, since the output distributions have high min-entropy. We estimate that the planted polynomial scheme is implementable using 100 logical qubits at logical error rates around $10^{-6}$.

We introduce an entanglement distillation protocol that utilizes an arbitrary $[[n,k,d]]$ stabilizer code to convert $n$ raw copies of an $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state into $k$ logical copies in the presence of Pauli noise. Our explicit formulation of the scheme on a star network topology is efficiently scalable to arbitrary $N$, requires only local operations, and minimizes the impact of errors on idle physical qubits, enabling the distribution of high-fidelity entangled logical states between any number of quantum processors. We report the results of numerical experiments using the 5-qubit code, toric code, and $[[144,12,12]]$ bivariate bicyle code to protect against independent single-qubit depolarizing noise on all qubits. Our encoding scheme improves the final GHZ state fidelity relative to a single bare GHZ state sent over the same noisy channel for depolarizing rates up to or above $6 \%$ for all codes tested. Additionally, we use the stabilizer formalism to prove that our protocol can be applied to any $N$-qubit Calderbank-Shor-Steane (CSS) stabilizer state, from which the GHZ state emerges as a special case. This result explicitly establishes the working principle of previous stabilizer-based Bell pair and GHZ state distillation schemes, and generalizes such protocols beyond the traditionally considered states. We also show that some stabilizer codes can distill any stabilizer state with our protocol.

We introduce the notion of stochastically evolving Hamiltonians (SEHs), which are local Hamiltonians whose coefficients are governed by stochastic differential equations (SDEs). After developing some theoretical aspects of these objects, we consider the task of Hamiltonian learning for SEHs. We reanalyse and make necessary extensions to the Huang-Tong-Fang-Su protocol, which first achieved the Heisenberg limit for Hamiltonian coefficient learning, under these circumstances. We delineate theoretically the regimes where the Heisenberg limit can and cannot be retained. Along the way we develop a few tools in quantum sensing and Hamiltonian simulation that may be of independent interest under similar settings in quantum information processing. The broad aim is to encourage the exploration of various settings in quantum information processing in which the control parameters are governed by SDEs.

Routing unknown quantum information across distributed communication networks requires autonomous, measurement-free mechanisms to prevent wave-function collapse. Szegedy quantum walks provide a mechanism for spatial state transport. The conventional walks on unweighted graphs suffer from severe back-reflection, spatial dispersion, and channel crosstalk. In this paper, we introduce a deterministic topological quantum routing architecture based on coined Szegedy quantum walks on edge-duplicated signed graphs. By treating edge signs as localized phase shifts within a balanced coin reflection, we enforce an exact zero back-scattering condition across routing nodes. We demonstrate deterministic Perfect State Transfer (PST) with unit fidelity at exact arrival times across fundamental archetypes, including the signed dumbbell switch $D_{2m,0,2n}$ and scalable glued binary trees. Furthermore, we analyse routing performance under realistic open-system amplitude and phase damping noise channels.

We introduce a classification of quantum phases of mixed states based on the ability to preserve and fault tolerantly transfer information. We formulate phase equivalence between sets of states that encode logical quantum information and are connected by shallow local channel circuits assisted by local measurements and global classical communication of measurement outcomes, where all quantum operations, including measurements, must be robust to noise. We show that the existence of a recovery threshold for local noise is a property of an entire phase. We prove that any two sets of states with nonzero thresholds that are related by finite-depth local channel circuits belong to the same fault tolerant phase. Our approach leads to a classification of subsystem codes without favoring any state of the gauge subsystem, and we demonstrate phase equivalence between 2D and 3D color codes using dimensional jumps within the 3D gauge color code. Lastly, we study how syndrome structure affects fault tolerance in circuits with measurements. We show that qudit stabilizer codes with extended syndromes permit single-shot state preparation, whereas a broad class of shallow circuits measuring point-like syndromes, including state preparation for 2D topological codes and non-Abelian topological orders with solvable anyon theories, is not fault tolerant.

Reconfigurable atom arrays provide a promising platform for high-rate quantum low-density parity-check codes, but their computational advantage depends on whether logical operations can be implemented without incurring prohibitive shuttling and space overheads. We introduce algebraic surgery for lifted product codes, co-designing the logical measurements, auxiliary codes, and atom shuttling to enable hardware-efficient Pauli-product measurements. These protocols provide flexible logical addressability subject to the cyclic-symmetry constraint, enabling a broad class of parallel logical measurements, including canonical logical operators with heavily overlapping physical supports and joint measurements within or between code blocks even with different lift sizes, while achieving constant shuttling depth on neutral-atom processors under explicit layout assumptions. In a representative hardware-model benchmark, a cycle supporting 33 parallel canonical logical measurements is about $2\times$ faster than the compared single-observable graph-based surgery schedules, with competitive qubit overhead. These shuttling and circuit-level simulations confirm that the algebraic structure of quantum low-density parity-check codes can be used not only to reduce space overhead, but also to simplify physical implementation and expand the set of efficiently accessible logical operations on neutral-atom processors.

Distributed quantum computation connects multiple quantum processing units (QPUs) through quantum communication to jointly perform large-scale quantum computations. Since the number of qubits available at each QPU is limited, it is important to reduce quantum communication while keeping the qubit overhead small. To this end, we study an entanglement-assisted model, in which entanglement consumption serves as a measure of quantum communication cost. For exact deterministic implementations in this model, the operator Schmidt rank of the target bipartite unitary provides a general lower bound on entanglement cost when qubit overhead is unrestricted. However, it has remained unclear how closely this bound can be approached with constant qubit overhead. In this work, we show that this lower bound is attainable for every bipartite Clifford unitary using at most two auxiliary qubits per QPU. In addition, for non-Clifford unitaries specified by exact Clifford+$T$ decompositions with $T$-count $t$, we construct implementations with the same qubit overhead whose entanglement cost is at most $2t$ Bell pairs above this lower bound.

Quantum state diffusion unravels a Lindblad master equation into stochastic trajectories of pure states. The ensemble of trajectories is described by a probability density on the manifold of pure states, which contains much more information than the density matrix, its first moment. We derive the time reversal of this diffusion. Writing the reversal of a general diffusion on a manifold in Stratonovich form, and passing through the manifold of pure states, we obtain a backward stochastic differential equation for the state vector, valid for any Hilbert space dimension and any Lindbladian. The backward stochastic equation provides a physical, nonlinear unravelling of the inverse Lindbladian that holds only for the ensemble from which it was constructed. Following score-based generative models, we then use the backward equation to generate a new ensemble close to the original. For the depolarizing channel the unravelling is a Brownian motion on complex projective space, so the uniform distribution of pure states is its stationary law in any dimension. Starting the backward equation from that prior, we bound the error of the resulting distribution compared to the original one in different settings: exact and learned scores, continuous and discrete time.

Inspired by results in quantum information, we report the development of a formalism for optical sensing which abstracts the details of specific optical systems and allows us to form general bounds on measurement based only on the quantity to be measured. We find a universal bound that controls the performance of any passive optical system regardless of the technology used to construct it and that this bound is attained by a unique measurement scheme for each quantity of interest. Shockingly, our optical formalism is nearly identical to the quantum formalism, with essentially the same notions of the state to be measured and the operation of the measurement, along with an accompanying uncertainty principle.

EPR-pair consumption is commonly used as a communication-cost objective in distributed quantum computing, but minimizing EPR cost does not necessarily minimize distributed execution time. Despite its widespread use, the reliability of EPR count as a runtime surrogate has received limited direct characterization across different workloads and communication conditions. This work addresses this gap by systematically evaluating the relationship between EPR cost and runtime over all balanced two-QPU mappings of QFT, QAOA, and CDKM circuits. The results show that mappings with identical EPR cost can have substantially different execution times, lower-EPR mappings can be slower, and minimum-EPR mappings can be runtime-suboptimal. The reliability of EPR count is strongly workload dependent and also changes with the communication operating regime: increasing EPR-generation latency amplifies runtime differences hidden by equal EPR cost, while increased communication concurrency can reduce the ability of EPR count to preserve runtime ordering. These results show that EPR count and execution time are related but distinct optimization objectives, and identify regimes in which explicit communication-aware runtime modeling is necessary.

Encrypted key exchange (EKE), introduced by Bellovin and Merritt (IEEE S&P 1992), and Masny-Rindal OT, introduced by Masny and Rindal (ACM CCS 2019), are highly-efficient methods for compiling essentially any KEM into advanced cryptographic protocols, namely password-authenticated key exchange (PAKE) and oblivious transfer (OT), by relying only on idealized symmetric-key primitives. They have become leading candidates for practically-implementable PAKE and OT due to (1) their simplicity, (2) their plug-and-play nature, allowing for flexibility in the choice of KEM, and (3) existing proofs of UC-security (in the classical adversarial model). Due to point (2) above, these compilers yield attractive candidates for efficient post-quantum PAKE and OT, especially given the recent post-quantum KEM standardization efforts. This motivates the question of whether the (UC-)security of these compilers translates to the quantum adversarial model. In this work, we show that it does not. In particular, we prove that a general family of (O)EKE protocols, as well as Masny-Rindal OT, are not UC-secure against quantum polynomial-time adversaries, even when instantiated with a post-quantum KEM. To establish UC-insecurity, we devise an adversarial strategy that provably thwarts any attempt by the simulator to extract its input (the password in the case of PAKE, and the receiver's choice bit in the case of OT). To complement these negative results, we establish that both compilers yield certain notions of game-based security. Along the way, we establish a novel “advantage-tight” one-way to hiding lemma that may be of independent interest.

Self-tallying quantum anonymous voting (SQAV) has drawn considerable attention since it was proposed. However, constrained by design challenges, all existing protocols only accommodate single-selection voting and cannot support multi-selection voting. In this paper, we propose a SQAV protocol with multi-selection voting functionality. In our protocol, $nm$ $n$-particle entangled states are equally divided into $n$ groups, and the $n$ particles in each entangled state are delivered to $n$ voters, one particle per voter. Each voter obtains $n$ voting vectors by sequentially measuring all his (or her) particles that belong to $n$ different group, and then encodes his or her voting information into the vector corresponding to the secret index. Due to entanglement correlation, each voter can verify whether his or her ballot is correct through computation, while any participant can obtain the vote count for each candidate through computation. Our protocol satisfies self-tallying, nonreusability, verifiability, and fairness.

Implementing high-fidelity multiqubit gates is critical for reducing circuit depth in near-term quantum processors and fault-tolerant architectures. However, realizing multiqubit interactions and entanglement remains a critical challenge that limits the implementation of multiqubit gates. Here we propose an all-microwave scheme to realize single-step multiqubit gates incorporating n control and m target qubits, tailored for frequency-tunable superconducting transmon networks. By leveraging cross-resonance (CR) drives, this approach induces effective two-body ZX interactions that are significantly stronger than those achieved in conventional resonant regimes, circumventing the need for tunable couplers. The system's effective Hamiltonian is analytically derived using both quad frame rotation and rigorous block diagonalization. These combined theoretical methods facilitate the identification of optimal parameter regimes that simultaneously enhance desired target couplings and suppress parasitic higher-order terms, such as ZXX interactions. Through numerical simulations and gradient-based pulse-shape optimization, we demonstrate three-qubit gates achieving fidelities exceeding 99.9% within a 60 ns gate duration. Furthermore, we evaluate the fundamental scalability of this framework by extending the optimization to a five-qubit CXXXX architecture, confirming the physical viability of the multi-target driving scheme. Because these multiqubit operations naturally emulate stabilizer measurements, this architecture provides a hardware-efficient strategy for reducing the circuit depth of stabilizer-type operations by replacing sequential two-qubit gate decompositions with single-step multiqubit gates.

We propose a novel framework for discrete-variable (DV) distributed quantum sensing, wherein traditional polarization-based probes are replaced with time-bin entangled qubits. We show that the intrinsic temporal structure of time-bin Bell states can be utilized as a tunable, built-in two-time differential sampling reference for sensing radio-frequency (RF) fields. Unlike existing protocols based on polarization Bell states, which are limited to static measurements, our proposed architecture enables the coherent mapping of dynamic RF phase signals onto static quantum optical phases. By matching the time-bin separation to the RF or intermediate frequency (IF) half-period (antipodal sampling), we theoretically demonstrate that our protocol provides a 6 dB sensitivity enhancement over one-sample static polarization encodings while preserving the 3 dB per-pair entanglement advantage over the separable standard quantum limit benchmark. The performance enhancement is validated with Monte Carlo simulations. This approach provides a solution for RF sensing in DV photonic quantum networks, offering a clear path toward quantum-enhanced and frequency-agile distributed sensor arrays and broader utilization of time-domain quantum probe encodings.

We study quantum random self-reductions for linear problems over finite fields. Let $M\in\mathbb{F}^{n\times n}$ be an arbitrary matrix, and let $\mathcal{O}$ be an oracle that agrees with the linear map $x\mapsto Mx$ on an $\varepsilon$-fraction of inputs $x\sim\mathbb{F}^n$. Given coherent access to $\mathcal{O}$ and coherent entry access to $M$, we give a uniform quantum reduction that computes $Mx$ on any prescribed input $x$ with probability at least $2/3$ in time $\widetilde{O}(nT^{1/3})$, for $n\le T\le n^{3/2}$ and constant field size and $\varepsilon$, where $T$ is the cost of one coherent query to $\mathcal{O}$. In particular, when $T=\widetilde{O}(n)$, the reduction runs in time $\widetilde{O}(n^{4/3})$, improving the $\widetilde{O}(n^{3/2}+T)$ reduction of Asadi, Golovnev, Gur, Shinkar, and Subramanian (SODA 2024). Our reduction uses the Bogolyubov–Ruzsa subspace guaranteed by additive combinatorics, but it avoids learning this subspace explicitly, which was computationally expensive for the previous reduction; in particular, it does not recover a basis for its orthogonal complement. The main technical step is to decompose the inputs into sparse pieces and find a vector that lies outside the Bogolyubov–Ruzsa subspace via a quantum search based on amplitude amplification. This yields a tunable tradeoff between the cost of querying the average-case oracle and the cost of verifying matrix-vector products.

We give an efficient algorithm for learning $k$-dimensional brickwork random quantum circuits using only copies of the output state obtained by applying $U$ to the all-zero input. For a depth-$d$ circuit on $n$ sites with random $2\ell$-qubit gates, the algorithm learns the original circuit $U$ with high probability in $\text{poly}(n,2^{\ell d})$ time for every constant dimensional lattice. In particular, the algorithm is polynomial time as long as $\ell d = O(\log n)$. In one dimension, this reaches the natural boundary suggested by pseudorandomness: pseudorandom states require $\ell d=\omega(\log n)$, and structured cryptographic constructions suggest that this scale may be achievable from above. In higher dimensions, it remains plausible that the same $\ell d=\omega(\log n)$ scale remains the threshold for ancilla-free pseudorandomness, and our results help clarify the conditions under which pseudorandomness can arise in this setting. The main idea behind our algorithm is a local correlation criterion that identifies gates in the final layer without learning their entire backward light cones, avoiding a bottleneck in the previous approaches. A key technical ingredient is a Carbery-Wright type anticoncentration inequality for low-degree polynomials of Haar random unitaries whose small-ball exponent is independent of the matrix dimension. The dimension-independent exponent is crucial for handling gates of growing locality. This anticoncentration result may also be of independent interest.

At what rate does the von Neumann entropy of an ensemble of quantum states change under Hamiltonian evolution of its constituents? Bravyi proposed the small incremental mixing conjecture controlling the mixing rate of a binary ensemble $\{(1\!-\!p,\rho_1),(p,\rho_2)\}$ by $c\,\|{H}\|h_{2}(p)$ (with the binary entropy $h_{2}$). The proof of Bravyi's conjecture was subsequently reduced to the matrix inequality $\|[A,\log B]\|_{1}\!\leq\! c\,h_{2}(p)$ for positive trace-class operators $A\!\leq\! B$ with $\text{Tr} A\!=\!p$ and $\text{Tr} B\!=\!1$ on separable Hilbert spaces by Mariën, Audenaert, Van Acoleyen, and Verstraete, and they conjectured the optimal constant to be $c\!=\!1$. Here, I prove the latter conjecture using an exact integral representation of the commutator $[A,\log B]$ obtained from the operator layer cake theorem, due to Cheng and Liu. The result gives a sharp dimension-independent limit on how rapidly unitary evolution of one component can change the entropy of a binary quantum ensemble. It follows that mixing rates satisfy small incremental mixing with the optimal constant, and entangling rates of bipartite Hamiltonians are bounded by $(2\log d\!+\!1)\|H\|$. Moreover, the result corrects a conjecture by Lieb and Vershynina for mixing rates of general ensembles.

We introduce double localization, a framework for proving spectral gaps of quantum Gibbs samplers through two complementary operations: geometric localization, which selects updates supported in small spatial regions, and interface localization, which focuses on a model-defined subspace of observables while remaining geometrically global. Our abstract gap theorem combines a global bound on this subspace, called the interface, with local quantum gap estimates under quantitative coupling and geometric assembly conditions. The resulting explicit lower bound controls the gap of the full dynamics without requiring the interface to be invariant under the generator. This separation allows global estimates, including classical comparison, to be combined with local control of the remaining quantum directions. We apply the framework to Hamiltonians built from the vertex terms of Kitaev's finite-group quantum double construction, without plaquette terms, on finite simple three-regular graphs of girth at least six. For the specified local Davies dynamics, we prove an unconditional spectral-gap lower bound by a positive constant independent of graph size for every fixed nontrivial finite group and each fixed inverse temperature $\beta$ with $0\le\beta J<\log(5/3)$, where $J>0$ is the coupling strength. For the smallest non-Abelian group $S_3$, double localization yields a positive lower bound uniform in both graph size and the entire interval $0\le\beta J\le\log 3$, providing a guarantee that does not follow directly from existing results. This demonstrates how model-specific finite calculations can extend spectral-gap guarantees for the full quantum dynamics.

Hamiltonian simulations of lattice gauge theories promise new insights into the inner workings of QCD. The rapid development of quantum computing hardware suggests that large scale simulations may soon become feasible. However, no efficient formulation suitable for simulations near the continuum limit is currently known for the non-Abelian case, and existing candidates typically feature long range interactions in the electric part of the Hamiltonian. We prove that such non- localities are unavoidable when the gauge configuration is reparametrised while preserving both the number of degrees of freedom and the fundamental commutation relations. We then attempt to mitigate this by introducing additional gauge links alongside additional constraints. Although this approach is successful in U(1), we prove that the corresponding construction is inconsistent for non-Abelian lattice gauge theories.

Measurements and feedforward enhance the power of shallow quantum circuits, enabling the deterministic implementation of global unitary operations and the preparation of long-range entangled states. We establish a general correspondence between all such protocols and quantum error-correcting codes: the circuit preceding the measurements acts as an encoder, and unitary feedforward can eliminate post-selection if and only if the measurement projectors are detectable errors on the codespace. This correspondence provides a common framework for state preparation and implementation of global unitaries with measurements and feedforward, turning both into a code-design problem. For stabilizer codes with Pauli measurements, although the resulting operation can be non-Clifford, we show that its nonstabilizerness originates entirely from the encoder. We overcome this restriction using non-Pauli measurements or non-additive codes, constructing protocols that generate long-range nonstabilizerness while requiring only single-qubit unitary corrections.

We present a unified algebraic theory of Clifford spacetime quantum fault tolerance, which underpins universal fault-tolerant quantum computation. We construct a spacetime chain complex from a tensor network representation of a circuit that encodes fault propagation, detector syndromes, and logical actions through the associated gauge and stabilizer structure. We show that this theory (1) unifies various formulations of quantum fault tolerance including spacetime codes, Gottesman's gadget framework, fault complexes, and ZX calculus; (2) connects spacetime distances to the gadget-level correctness properties in Gottesman's formalism; (3) naturally accommodates a range of fault models, in particular phenomenological and circuit-level models, bringing these often separately formulated descriptions into a common algebraic framework through different tensor decompositions and fault assignments; and (4) recovers many known fault tolerance constructions and results as special cases, including repeated syndrome extraction, correlated detectors for transversal and fold-transversal gates, Steane- and Knill-type syndrome extraction gadgets, and single-shot error correction.

We study the noise threshold for positive quantum capacity for the qubit depolarizing channel. We explore analytically the action of the qubit depolarizing channel on the symmetric subspaces of the input qubits, in the limit of asymptotically many uses of the channel. We observe the emergence of a bosonic Gaussian channel. Furthermore, the codes previously developed for the depolarizing channel can be translated to codes for the emergent Gaussian channel, and it is easier to further optimize these codes for the simpler emergent Gaussian channel. Translating these codes back to the depolarizing channel leads to extremely good input states for the coherent information of the depolarizing channel producing new lower bounds on the noise threshold for positive capacity. In addition to improved lower bounds on the threshold, this newly found link between depolarizing noise and Gaussian channels offers a novel perspective contributing to our understanding of these symmetric codes.

Causal loops escape paradoxes if they generate valid probabilities under arbitrary independent local interventions. We show that a deterministic classical process is logically consistent if and only if it contains no signaling loops: cyclic signaling is forbidden but cyclic causation is not, allowing indefinite causal order. Logical consistency is then found to hold exactly when the list of events of a process is pairwise exclusive and complete, providing the first event-based, intervention-free, non-recursive characterization of consistent causal loops. Our results repair a previously introduced intervention-free criterion that misses global loops and reveal that what makes deterministic classical communications without causal order consistent is a multipartite form of Specker's principle: if any two of several questions can be answered jointly, so can all of them.

Claims of quantum advantage rest on the classical hardness of simulating quantum circuits. Magic, operator scrambling, anticoncentration, and non-Gaussianity for fermionic circuits are standard diagnostics of complex quantum dynamics. For pure states, some of these have been rigorously connected to classical simulability. Whether these diagnostics reliably track the limits of efficient classical simulation under noise remains unclear. Here, we show that in noisy Clifford+$T$ and nearest-neighbour matchgate+SWAP circuits, dynamical diagnostics and classical simulability can separate in both directions. In particular, the diagnostics can remain nontrivial after classical simulation becomes efficient, or become trivial before known efficient classical algorithms apply. We trace this mismatch to the different statistical properties they probe: magic and scrambling depend on fourth-order statistics of the Pauli spectrum, whereas the simulation algorithms depend primarily on second-order moments, which local noise suppresses at different rates. Thus, dynamical diagnostics measured on a noisy quantum device do not by themselves constitute evidence for classical hardness.

How much time is fundamentally required to extract the syndrome of a stabilizer code on hardware with a given connectivity graph? Previous bounds answer through a chosen list of checks (Delfosse, Beverland, and Tremblay, 2021) or through the global code parameters (Baspin, Fawzi, and Shayeghi, 2023). Here, we show that neither determines the interaction that a particular hardware cut requires. We therefore define the intrinsic cut cost, $\chi$, directly from the stabilizer group, independent of the generating set used to describe the code. It is computable from the check matrix alone, and equals the mutual information across the cut in the maximally mixed code state. We show that every exact extraction circuit, however adaptive, needs at least $\chi/2$ two-qubit operations across the cut, and alternatively with free local processing exactly $\chi$ shared Bell pairs. Guided by this intrinsic cut cost, we construct annular surface codes with constant-depth local extraction that give a counterexample to Corollary 1 of Delfosse, Beverland, and Tremblay. Furthermore, for a fixed quantum Tanner family, $\chi$ grows at least linearly with the size of every sufficiently small region, giving a depth guarantee at each corresponding bottleneck in every layout. This strengthens the global perspective of Baspin, Fawzi, and Shayeghi and, together with our matching square-grid construction, yields a tight space–depth tradeoff. Our results connect the interaction required by syndrome extraction to hardware communication capacity and thus provide a way to assess unavoidable circuit costs before committing to a particular layout.

Here we demonstrate quantum–classical break-even for chemical dynamics applications, reaching useful accuracy with a quantum-hardware wall-clock time comparable to that estimated for practical classical computing resources. Specifically, we construct a quantum workflow for electronic dynamics based on tensor-network circuit compression leveraging spatial locality, extending circuit compression beyond one-dimensional open-boundary systems. This enables application of the workflow to problems that are hardware-native but classically hard. The workflow targets one-dimensional periodic Hamiltonians: circuits classically optimized only for short-time evolution within a small spatial region can be replicated in both space and time to construct long-time dynamics of the full system without classically simulating the corresponding large-scale evolution. We apply the workflow to cyclic conjugated macrocycles with rotational periodicity, 12-qubit benzene and 120-qubit [60]annulene, by embedding their electronic structure onto loops of IBM quantum processors. For the annulene, the quantum-processing-unit (QPU) wall-clock times for hole-doped nonequilibrium dynamics became comparable to the estimated wall-clock time of two classical methods, Majorana propagation and matrix-product-state time evolution based on the time-dependent variational principle; this corresponds to tens to hundreds of compute nodes depending on the task (36 CPU cores per node), even assuming ideal scaling, bringing the quantum calculation into a wall-clock-time regime comparable to conventional parallel high-performance-computing resources. We also show a situation in which a hybrid quantum–classical calculation is a reasonable choice in terms of both accuracy and computational time. These results show that quantum hardware can become a realistic computational option for chemically relevant electronic dynamics.

As quantum networks move toward multi-user architectures, a central question is how the performance of entanglement distribution scales with the numbers of network nodes $N$ and active users $M$, yet existing studies use different objectives, resource assumptions, and normalizations. To account for delivery distance under multi-user demand, we define entanglement transport, which weights each delivered Bell pair meeting a fixed fidelity threshold by its endpoint separation. In a two-layer framework, (i) a resource layer measures capacity per activation slot under different aggregation regimes, and (ii) a physical layer measures service per second under implementation constraints. For matched implementations with a bounded number of activation slots per second, asymptotic-aggregation capacity sets a service ceiling, whereas achievable service must be established separately. On expanding honeycomb lattices with one random session, fixed-window entanglement-percolation constructions achieve $\Theta(N^{-1})$ entanglement transport per activation slot below their thresholds and $\Theta(\sqrt N)$ above them. For homogeneous chains, asymptotic aggregation exceeds fixed-window capacity by a factor $\Theta(N^2/M)$, and in spatial expansion a noisy physical implementation achieves $\Theta(M/N)$ service per second. These examples show that entanglement-transport scaling depends not only on connectivity but also on resource aggregation and physical implementation. The framework provides a common basis on which quantum-network scaling laws can be established.

We establish sufficient conditions for preparing quantum thermal states of noncommuting local Hamiltonians with polylogarithmic circuit depth in arbitrary fixed spatial dimension. Our conditions combine locality and stability bounds on the effective interactions of reduced density matrices of a Gibbs state with a quantitative high-temperature condition and access to coarse classical reference Hamiltonians. When these references can be generated locally, the classical preprocessing cost is $N^{1+o(1)}$ for $N$ sites at inverse-polynomial global accuracy. We construct the preparation circuit from spatially localized Petz recovery maps. Quantum corrections derived from the microscopic Hamiltonian enable accurate recovery while the classical references remain coarse. After preprocessing, the resulting circuit prepares the canonical purification using $N\operatorname{polylog}(N/\varepsilon)$ gates and qubits, where $\varepsilon$ is the preparation error. These results link two fundamental questions: how correlations are organized in thermal equilibrium, and how efficiently the corresponding states can be realized through operations allowed by quantum mechanics. By translating static equilibrium structure into explicit preparation circuits, they give equilibrium locality a constructive computational interpretation and a physically grounded role in quantum algorithm design.