Papers

Time and space (memory) are two of the most important measures of cost in computation, even more so for quantum computation. Yet, our tools for proving unconditional quantum tradeoffs between time and space are surprisingly limited. The first quantum time-space tradeoff lower bounds were proven for sorting by Klauck, Špalek and de Wolf. Unfortunately, their method is limited to proving output-oblivious lower bounds (i.e. the lower bounds only apply to algorithms with a non-adaptive output schedule) and other methods have yielded nothing beyond output-oblivious lower bounds for sorting. Here, we prove the first fully general quantum time-space tradeoff lower bound for sorting. We do so by introducing a novel method based on the noise operator to add to the analysis toolkit for proving quantum query and time-space tradeoff lower bounds. By combining our resulting quantum noise stability bound with quantum recording query methods, we prove an $\Omega(n^{4/3} (\log \log n)/(S^{1/3} \log n))$ lower bound on the number of queries that a fully general quantum algorithm with at most $S$ qubits of memory requires to sort $n$ numbers from $[n^2]$. Applying our noise operator argument involves purely classical reasoning, which makes it particularly simple to use. We also use it to prove that, for any strongly universal (pairwise independent) hash function family $H$ from $n$ bits to $m$ bits, almost all hash functions in $H$ require any algorithm with at most $S$ qubits of memory to make $\Omega(nm/S)$ quantum queries to input $x$ in order to compute $h(x)$, even with very small success probability. Previously, Mansour, Nisan, and Tiwari had shown a matching classical lower bound for computing $h(x)$ with both $h$ and $x$ as inputs using their hash mixing lemma. Our noise operator method allows us to use a related property of hash functions to prove our quantum lower bounds.

Quantum data hiding concerns pairs of states which are highly distinguishable with global measurements, yet nearly indistinguishable when restricted to local operations and classical communication. More than two decades after Eggeling and Werner introduced a multipartite hiding scheme based on Werner states, the optimal dependence of its uniform security guarantee on the number of parties and local dimension remained unknown. We resolve this problem by showing that the distinguishing bias of any pair of $n$-qudit Werner states is $O(n^2/d)$ under measurements whose effects remain positive under partial transposition (PPT) across every bipartition. An explicit pair attains this scaling using only nonadaptive local measurements, establishing worst-case optimality and showing that the PPT relaxation preserves the optimal dependence on both the number of parties and the local dimension. At fixed security, this extends the certified hiding regime from $n=O(d^{1/4})$ to $n=O(\sqrt d)$. Beyond data hiding, the same bound implies that testing any nontrivial unitarily invariant property with adaptive single-copy measurements requires $\Omega(\sqrt d)$ copies, yielding separations for any property with dimension-independent sample complexity under collective measurements. Our proof reduces the distinguishing bias to trace norms of partially transposed operators and analyzes them using mixed Schur-Weyl duality, demonstrating the utility of representation theoretic methods developed for port-based teleportation to data hiding and quantum property testing.

Linear threshold functions are $f_{w,\theta}(x)=\text{sign}(\langle x,w \rangle -\theta)$, where the weight vector $w\in\mathbb{R}^n$ is a unit vector, $\theta\in\mathbb R$ is a threshold, and typically $x\in\mathbb{R}^n$ or $x\in\{-1,1\}^n$. When $\theta=0$, the LTF is called homogeneous, and we write $f_w:=f_{w,0}$. Such functions are among the most important objects in machine learning, since they serve to linearly discriminate positive and negative examples. We give three positive results about learning LTFs: 1. Suppose we can make real-domain queries, meaning we can compute $f_{w,\theta}(x)$ at any $x\in\mathbb{R}^n$ of our choice. We give a quantum algorithm that learns $f_{w,\theta}$ up to Euclidean error $\epsilon$ using $O(\log(n/\epsilon))$ membership queries and $\widetilde{O}(n)$ other gates. Then we have also learned $f_{w,\theta}$ up to error $O(\epsilon)$ when $x$ is Gaussian. Classical algorithms need $\Omega(n\log(1/\epsilon))$ queries. 2. A homogeneous LTF $f_w$ on domain $\{-1,1\}^n$ where $w$ has only $k$ nonzero entries of the same value, is the Majority function on the support of $w$. Belovs gave a bounded-error quantum algorithm that identifies the hidden support exactly (and hence learns $f_w$) using $O(k^{1/4})$ queries. We give an exponential improvement, using $O(\log k)$ queries. 3. Suppose we have a unitary $U$ that can produce (discretized) quantum examples under Gaussian measure, corresponding to $\int_x \sqrt{\gamma_n(x)}|x\rangle |f_w(x)\rangle dx$. This is a weaker access model than membership queries. We give a quantum algorithm based on the efficient Hermite transform of Jain et al. to learn homogeneous LTFs $f_w$ with error $\epsilon$ under the Gaussian distribution, using $O(n^{1/4}/\sqrt{\epsilon})$ applications of $U$ and $U^\dagger$ and $\widetilde{O}(n^2/\epsilon^4)$ other gates.

We develop a spectral theory for dynamical large deviations in non-Markov jump processes and non-Markov chains, whose dynamics depends on the past through state- and jump-dependent empirical observables. We demonstrate that a multiscale Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) Ansatz separates fast configurational relaxation from slow memory evolution, reducing the Feynman–Kac equation for occupation and flux statistics to an eigenvalue problem for a new tilted operator coupled to Hamilton–Jacobi characteristics. This provides a computationally efficient framework for quantifying fluctuations in a broad class of non-Markovian systems. We illustrate our general results with a bistable self-induced East model.

Cooling an arbitrary mixed state to a pure ground state requires transferring its entropy to an environment. Can a single coherent bath contact accomplish this without repeated bath resets? We develop a new cooling mechanism that transfers the input information into bath degrees of freedom that subsequently decouple, while the system and the remaining bath follow a ground-state path. The bath is discarded only at the end, and the system Hamiltonian remains on and unmodified throughout. We rigorously realize this mechanism for a class of weakly interacting, gapped fermionic systems with local interactions. Starting from any mixed state, our protocol prepares the interacting ground state in total physical time polylogarithmic in the system size and inverse global trace-norm error. It uses two initially empty bath modes per system mode and a single pulse shared across all onsite system–bath couplings. The same pulse prepares each admissible system's own ground state without knowledge of its microscopic parameters. The guarantees follow directly from a non-Markovian system–bath dynamics without an effective Lindbladian description.

Modern smart grids generate increasingly rich operational data and deploy greater numbers of remotely controlled switching assets than ever before, creating new opportunities for data-driven distribution network reconfiguration (DNR). DNR optimizes grid topology to improve efficiency, reduce power losses, and maintain operational constraints, but finding optimal switch configurations remains a computationally demanding combinatorial problem. In this paper, we propose a deep reinforcement learning (DRL) framework for static DNR to systematically investigate how the Q-network architecture affects both solution quality and learning performance. We evaluate multiple architectures within a controlled DRL framework, varying only the Q-network to isolate the contribution of each architectural choice. Our results show that quantum-enhanced Q-networks can achieve higher rewards with fewer parameters than their classical counterpart, suggesting that such architectures are a promising direction for combinatorial power systems optimization.

Adopting the dimensional-reduction scheme, we diagrammatically compute, at four loops, the beta function of N=2 supersymmetric Yang-Mills theory, which is well known to vanish beyond one loop. This provides a formidable testbed for both the treatment of the problematic $\gamma_5$ Dirac matrix in D dimensions and the implementation of the dimensional-reduction scheme. In the use of the reading-point method of $\gamma_5$, being preferable for convenience, specific details of implementation start to matter at four loops. We thus rigorously validate these implementation issues, which have previously been advocated for the calculation of the gauge-coupling beta functions at four loops in the Standard Model.

We prove maximal separations: $n$-qubit systems can have $\Theta(n)$ ergotropy, while every efficient process extracts negligible work, even for Hamiltonians consisting of single-qubit terms. We establish an unconditional existential separation and give an explicit construction in the random oracle model. Assuming the existence of quantum-secure pseudorandom functions, this separation extends to the plain model. This work uncovers an important connection between ergotropy and the complexity of catalytic computation—computation where auxiliary qubits must be finally restored to their initial state. Relative to a random oracle, we establish relational and decision problems that: (i) can be solved efficiently with $\lambda$ catalysts; but (ii) cannot be solved by any algorithm with $c\lambda$ catalysts, for any $c<1$. We show this by proving query lower bounds for quantum-space bounded algorithms. As a consequence, for computational ergotropy, catalysts prove to be surprisingly powerful—there is a family of Hamiltonians and states for which catalysts enable efficient extraction of the full $\Theta(n)$ ergotropy, while every efficient non-catalytic process extracts negligible work. Furthermore, catalysts also allow us to introduce and instantiate the notion of pseudoergotropy—analogous to pseudorandomness. On the other hand, we show catalysts do not change (information-theoretic) ergotropy. Finally, our work also sheds light on the classical aspect of the problem. First, most of our constructions rely on classical states and Hamiltonians and therefore imply analogous results for classical ergotropy. Second, we show that certain proof of quantumness protocols can be used to generically separate classical and quantum catalytic ergotropy.

We study vector subset sum over $\mathbb{F}_3^n$: given $m$ random vectors from $\mathbb{F}_3^n$, find a nonempty subset that sums to zero; the smaller $m$, the more difficult it is to find such a subset. Chen, Liu, and Zhandry (EUROCRYPT'22) introduced an efficient quantum algorithm that solves this problem when $m\approx n^2/2$, where a naive classical algorithm would require exponential time. Subsequently, Kothari, O'Donnell, and Wu (STOC'2026) gave an efficient classical algorithm that only requires $m \approx n^2/3$ vectors, thus removing the hope for an exponential quantum advantage in this parameter regime. Using the framework of Chen, Liu, and Zhandry, we give quantum algorithms that require much fewer input vectors, renewing the possibility of an exponential quantum speedup: for any fixed $\epsilon>0$, our quantum algorithm solves $\mathbb{F}_3$-subset sum in polynomial time with $m=\epsilon\cdot n^2$ vectors. More generally, we establish a full sample–time tradeoff that interpolates between exponential and polynomial runtime. The main ingredient is a deterministic classical algorithm for the binary-error Learning-with-Errors problem, which is of independent cryptographic interest. For this, we rigorously establish a sample–time tradeoff that was predicted by earlier algebraic heuristics. For vector subset sums over larger fields, we also significantly improve classical algorithms in Kothari, O'Donnell, and Wu (STOC'2026).

Low-depth syndrome extraction for Calderbank-Shor-Steane (CSS) quantum low-density parity-check codes can be formulated as a proper ordered edge-coloring problem subject to quantum parity constraints. A proper edge-coloring of the CSS Tanner graph ensures that each data or ancilla qubit participates in at most one two-qubit gate per layer, but does not guarantee a valid interleaving of the X- and Z-check measurements as for every overlapping X/Z check pair, the number of shared data qubits on which the X interaction precedes the Z interaction must be even. The minimum number of colors in a proper ordered edge-coloring satisfying the quantum parity constraints equals the minimum two-qubit depth when each stabilizer check is measured with a single ancilla. We introduce local automorphism-aware syndrome compilation (LocalASC), which reduces the constraint system to edge-orbit variables under a subgroup of the Tanner graph automorphisms and lifts each feasible orbit assignment to the full graph. Although the $6$-layer degree lower bound is unattainable for the published weight-$6$ IBM bivariate bicycle codes, we show that this is not universal among two-block CSS codes. Among code instances for which the maximum check weight equals the maximum Tanner graph degree, LocalASC finds depth-optimal syndrome-extraction schedules for several two-block CSS codes with odd component weights, including instances with unequal odd weights. We also obtain lower-bound-saturating syndrome-extraction schedules for several quantum Tanner codes satisfying the same degree condition. To obtain the subgroups used by LocalASC without computing the full automorphism group of the Tanner graph, we construct translation subgroups for two-block group-algebra CSS codes over abelian groups. For quantum Tanner codes, we give conditions under which square-complex symmetries extend to Tanner graph automorphisms.

This note describes the laboratory setup at the University of Wuppertal and its use to measure charge sharing crosstalk, perform high rate and high occupancy tests of MAPMT-DIRICH readout elec- tronics using a realistic detector setup, and also includes the analysis of induced electronic noise characteristics of a new iteration of the DIRICH power module to be used in the CBM RICH readout chain.

The Kerr stability conjecture has been proved in the slowly rotating case, i.e., $|a|\ll m$, in the sequence of works \cite{KS-GCM1} \cite{KS-GCM2} \cite{KS:Kerr} by Sergiu Klainerman and the author, \cite{GKS22} by Elena Giorgi, Sergiu Klainerman and the author, and \cite{Shen} by Dawei Shen, and extended in \cite{Sze}, by the author, to the full subextremal range $|a|<m$, thereby completing the proof of the Kerr stability conjecture. The proof in \cite{Sze} crucially relies on the two companion papers \cite{MaSz24} \cite{MaSz26} by Siyuan Ma and the author, in which we prove energy-Morawetz estimates respectively for the scalar wave equation and for Teukolsky equations on perturbations of Kerr with $|a|<m$. In addition, two results in \cite{Sze}, concerning the derivation of the Teukolsky wave-transport system in perturbations of Kerr and energy-Morawetz estimates for Teukolsky in the setting of \cite{Sze}, are stated without proofs. The goal of the present paper companion paper to \cite{Sze} is to provide the proof of these two results.

We present a quantum algorithm that generates a uniform superposition over the spanning trees of a graph – also known as a q-sample – using only a sub-linear number of queries to the graph. This goes beyond previous work that focuses on generating classical samples, including a recent quantum algorithm by Apers, Gao, Ji, and Liu [ICALP 2025]. For an $n$-vertex, $m$-edge graph, our algorithm admits a pre-processing step of $\tilde{O}(\sqrt{mn} + m^{1-\delta})$, after which each q-sample can be generated in $\tilde{O}(n^{1+2\delta})$ for any $\delta$. Alternatively, $k$ independent q-samples can be generated at a total cost of $\tilde{O}(\sqrt{kmn})$. We also prove a matching lower bound up to logarithmic factors, showing that our algorithm is essentially optimal. Further tradeoffs are given in the paper. In comparison, the optimal classical algorithms (Anari, Liu and Vuong [FOCS 2022]) need an $\tilde{O}(m)$ pre-processing step, after which each sample costs $\tilde{O}(n)$ operations. These results yield faster quantum walk-based algorithms for counting spanning trees or finding a marked one. Our result is obtained via quantum walk sampling over a sequence of slowly-changing Markov chains. Each chain is an isotropized up-down walk that mixes rapidly to the spanning tree distribution of the input graph. A key ingredient is an amortized data structure supporting fast implementation of the associated quantum walk operators throughout the sequence. This data structure maintains access to a spectral sparsifier and a leverage score sampler that evolve with the underlying graph.

In classical coding theory, the quest for explicit codes achieving list decoding capacity has been an important driving force. While random codes are easily shown to achieve capacity, an explicit construction was only discovered decades later in the seminal work [Guruswami and Rudra, STOC 2006]. In quantum coding theory, it is highly desirable that a code family be LDPC. While good quantum codes were known for decades, obtaining the additional LDPC property was elusive. In fact, only very recently that good quantum LDPC codes were discovered in a breakthrough work [Panteleev and Kalachev, STOC 2022]. In this context, a natural question is to ask for an explicit family of quantum codes achieving list decoding capacity while also possessing the important LDPC property. In this work, we provide (to the best of our knowledge) the first explicit constructions of quantum LDPC codes achieving list decoding capacity, namely, with a list decoding radius approaching the quantum Singleton bound with constant list sizes. Furthermore, we provide near-linear time (in the block-length) list decoding algorithms approaching capacity. Our explicit code construction are based on expander graphs via the quantum analogue of Alon-Edmonds-Luby (AEL) amplification [Bergamaschi, Golowich and Gunn, STOC 2024], and this enables the important LDPC property. Our efficient list decoding algorithms are obtained by generalizing the classical expander-based weak-regularity list decoding algorithms [Srivastava and Tulsiani, FOCS 2025] [Jeronimo and Singh, 2025] to suitable instantiations of quantum AEL.

Mutually unbiased bases (MUBs) describe quantum measurements for which certainty in one basis gives uniform outcomes in the others. Their maximum number remains unknown in dimensions that are not powers of a prime. We introduce an ansatz that, in many dimensions, allows us to construct more MUBs than have previously been found. Each basis in the ansatz consists of a diagonal phase matrix applied to a fixed unitary, which is a tensor product of Fourier matrices and, optionally, any real Hadamard matrix. This construction yields five MUBs in dimension 12, six in dimensions 48, 96, and 192, seven in dimensions 36 and 108, and ten in dimension 648. These bases can then be extended to exceed the tensor product bound, asymptotically, in every eighteenth dimension. Moreover, we show that Paley's real Hadamard matrix can be used to construct $q+1$ bases in dimension $d = q(q+1)$ for every prime power $q\equiv3\pmod4$. This count grows as $\sqrt d$ and cannot be exceeded by tensor products of smaller sets.

We study how quantum encodings and symmetry-adapted measurements preserve information for planted-clique detection from one classical graph. For $k=\lfloor n^{1/2-\varepsilon}\rfloor$, with fixed $0<\varepsilon<1/2$, detection is statistically possible but conjectured hard for polynomial-time classical algorithms. For a compact binary phase encoding, we prove that constant-advantage detection requires $\Omega(n^{1+2\varepsilon}\ln^2 n)$ copies of the phase state of the same graph, even under arbitrary joint measurements. In the large-copy limit, the optimal decision rule thresholds the total number of $k$-cliques in the graph and its complement, but this characterization provides no efficient detector. We therefore explore measurements guided by the symmetries of the input distributions, starting with the efficient Schur transform on the full graph register. We show that weak Schur sampling, which measures only the representation label, depends only on edge count and has vanishing distinguishing power in this regime. When the label and multiplicity registers are discarded, the remaining quantum states are almost perfectly distinguishable. We show that the support of the planted state occupies only a vanishing fraction of the graph Hilbert space. Any subspace containing it still permits near-perfect detection if its relative dimension also vanishes. This gives us freedom to choose a subspace that is easier to measure. We propose exploring subgroup isotypic measurements to find such subspaces. Whether they can yield an efficient detector remains open. Finally, we show that a single supplied coherent quantum sample permits efficient detection, yielding a conditional computational separation from one classical sample under quantum planted-clique hardness.

The Quantum Approximate Optimization Algorithm (QAOA) is regarded as a promising candidate for near-term quantum advantage in combinatorial optimization, yet our ability to study it at scale is limited. Exact recursive formulas have been introduced for predicting QAOA performance on large spin glasses, but the computational cost of evaluating them grows exponentially with the number of QAOA layers, preventing the study of QAOA in the promising high-depth regime. In this work, we show that for the task of computing QAOA energy on any mixed dense spin glass problem, spins approximately decouple into independent spin-boson systems. In the infinite-size limit, the decoupling becomes exact, establishing the spin-boson mapping as a natural framework for the many-body physics of QAOA. This generalized spin-boson mapping gives a recursive procedure for computing QAOA energies that can be executed at modest cost using tensor networks. As a numerical application, we optimize QAOA on pure and mixed spin glasses at depths intractable for prior techniques, observing that higher-degree problems require more layers for a comparable approximation ratio while angle optimization becomes more challenging. While decoupling enables the evaluations of QAOA energies at large size and depth, it does not enable strong simulation of QAOA; a quantum computer is required to sample the bitstring corresponding to the predicted energy.

A strong negative enthalpy of mixing can lead to ordering in liquid solutions. To describe ordering in liquids, different thermodynamic descriptions of liquid phases have been developed in the CALPHAD approach, including the associate model and the modified quasichemical model. In this study, we show that the key to directly incorporate these liquid phase models and their corresponding CALPHAD-type free energy formulations in phase-field simulations, is to identify the internal processes and to properly define the internal thermodynamic variables. The free energy of the liquid phase can then be converted to a function of component compositions and internal variables, and the evolution of the internal variables will be determined via Allen-Cahn-type relaxation equations. We demonstrate this modeling strategy using the formation of stoichiometric phases from liquid phases in Na-Sb and Na-Sn systems. This study will pave the way for predicting microstructure evolution in liquids with ordering using phase-field simulations.

A central yet mysterious problem in quantum information is the asymptotic distinguishability of quantum states under restricted measurements. Here we look at asymptotic asymmetric hypothesis testing for general multi-mode bosonic Gaussian states restricted to arbitrary collective Gaussian measurements. We establish a single-letter formula for the Stein exponent for many pairs of states, featuring two distinct contributions, corresponding to first and second moments, respectively. Remarkably, the Gaussian-measured relative entropy exhibits genuine non-additivity, but the only effect of additivity violations is to asymptotically decouple first and second moments. We prove this by establishing sufficient conditions for additivity of the second-moment term via novel log-determinant matrix inequalities. Our results not only identify a single-letter expression for the Gaussian Stein exponent in a wide range of practical situations, but also rule out any possible advantage from collective Gaussian measurements when considering centred Gaussian states.

We give the first sublinear-time classical solvers for sparse semidefinite programs in the bounded-radius regime, without low-rank assumptions or Frobenius norm dependence on the constraint matrices. For constant precision and bounded primal and dual radii, prior quantum algorithms of Brandão et al. (2019) and van Apeldoorn and Gilyén (2019) achieved $\widetilde{O}(\sqrt{n}+\sqrt{m})$ dependence on matrix dimension $n$ and constraint number $m$. Compared with the $\widetilde{O}(mn)$ runtime of existing classical methods, this suggests a quartic quantum speedup when $m \approx n$. Beyond a usual Grover speedup, this separation relies on the Quantum OR lemma, whose sample-reuse mechanism decouples the cost of Gibbs-state preparation from constraint search. We show that this reuse mechanism is classically realizable for sparse SDPs. Our main technical contribution is a classical procedure for simultaneously estimating many expectation values with respect to a sparse Hamiltonian's Gibbs state. This combines randomized Lánczos filtering with an efficient sampling-based estimator. We also introduce a stochastic online-learning framework for SDP solving, substantially improving accuracy-dependence over standard oracle-based MMWU approaches. Let $s$ denote the the input matrix sparsity and $\gamma:=Rr/\varepsilon$ capture dependence on the primal $(R)$ and dual $(r)$ radii as well as target accuracy $(\varepsilon)$. When $\gamma^2\leq\min\{m,n/s\}$, our solver runs in time $\widetilde{O}\left(ns\gamma^{4.5}+ms\gamma^2\right)$. For $\gamma=O(1)$, this is $\widetilde{O}\left((n+m)s\right)$ and sublinear in the $O(mns)$ input size. Similar to the quantum algorithms, this matches known lower bounds with respect to $m$ and $n$, up to logarithmic factors. This implies that, with respect to dimensions $m$ and $n$, there is no super-quadratic quantum advantage for generic sparse SDP solving.

We construct quantum oracles relative to which quantum-secure one-way functions (OWFs) exist but pseudorandom states (PRSs) with superlogarithmic output length do not. At first glance, this appears to contradict the known black-box constructions of PRS generators from quantum-secure OWFs. The distinction lies in the access model to the oracles; our oracle separation uses classical-accessible random oracles that can be accessed only classically even by quantum algorithms. In fact, our impossibility of PRSs applies to any classically accessible classical oracle in place of the random oracle, while keeping the other oracle component unchanged, showing the need for coherent access in constructing PRSs. We further show that logarithmic output length pseudorandom function-like states (PRFSs) exist relative to our oracles, giving an oracle separation between classically accessible logarithmic length PRFSs and superlogarithmic length PRSs. This shows that fully black-box PRS length extension from logarithmic to superlogarithmic output length must use coherent access to the underlying short PRS.

Memristors have emerged as key building blocks of neuromorphic computing architectures due to their ability to integrate data storage and processing. While metal halide perovskites have recently shown significant promise owing to their mixed electronic-ionic conduction and low-cost solution processability, their reliance on toxic lead and limited stability presents critical challenges. Here, we report environmentally friendly, low-toxicity AgBiS2-based solution-processable memristors exhibiting an ultra-low SET voltage of ~0.08 V and a high ON/OFF ratio of >104. First-principles calculations identify Ag interstitials as the energetically most favourable native defect and reveal low migration barriers within the Ag sublattice, for both interstitials and vacancies, facilitating ionic transport in the AgBiS2 lattice. Through interface and thickness engineering, the resistive switching behaviour can be systematically tuned from abrupt digital to gradual analog modes. Notably, thicker switching layers promote the evolution of stable conductive pathways through intermediate metastable states, revealing a controllable filament evolution process. Electrochemical impedance spectroscopy reveals pronounced negative capacitance (inductive) behaviour at low bias voltages, arising from coupled electronic-ionic dynamics. Consistent with this behaviour, pulse measurements demonstrate gradual conductance modulation under pulse trains, emulating synaptic responses relevant for neuromorphic computing. Finally, post-operando structural analysis reveals substantial morphological evolution of the switching layer driven by repeated filament formation and rupture. Linking structural dynamics to switching variability provides important design principles for achieving reliable and durable sustainable memristors.

Classical circuits with unbounded fan-in can compute any Boolean function in constant depth when their size is unrestricted. We ask whether removing the restrictions on circuit size and ancillary qubits also allows quantum circuits built from arbitrary single-qubit gates and generalised Toffoli gates to implement every unitary in constant depth. We give exact constant-depth constructions for arbitrary permutations of computational basis states, diagonal unitaries and the preparation of arbitrary pure states. These connect quantum state preparation to reversible classical computation and the preparation of probability distributions. With fanout in the gate set, they use exponentially many gates and ancillary qubits and return all ancillary qubits to zero. Replacing fanout by an exact circuit over the original gate set preserves constant depth, although the size bounds can become doubly exponential. The implementation of arbitrary unitaries in constant depth remains open. We give equivalent formulations in terms of copying the vectors of a specified orthonormal basis, extracting their labels and implementing restricted families of unitaries. We also reduce arbitrary unitary implementation to that of traceless unitary involutions using one additional clean qubit. With adaptive measurements, gate teleportation gives depth proportional to the level of a gate in the Clifford hierarchy. Towards arbitrary unitary implementation in constant depth, we use port-based teleportation: for input dimension $d$ and $M\geq d^2-1$ ports, we construct a unitary circuit of depth $O(\sqrt d)$, independent of $M$ and including resource preparation and port selection, with entanglement fidelity at least $(1-(d^2-1)/(2M))^2$. Thus, at fixed $d$, the approximation can be made arbitrarily accurate without increasing depth. Whether the dependence on $d$ can also be removed remains open.

In classical fine-grained complexity, the 3SUM Conjecture is used to prove a variety of conditional lower bounds on data structure and graph problems via an initial reduction to the SetDisjointness problem. However, there is an $\tilde{O}(n)$-time quantum algorithm for 3SUM and a direct application of Grover's algorithm to SetDisjointness queries beats the state-of-the-art classical conditional bound by Kopelowitz, Pettie, and Porat (SODA 2016); this shows that these classical bounds do not apply in the quantum setting. Thus establishing analogous conditional lower bounds in the quantum setting requires applying the quantum 3SUM Conjecture to a quantum fine-grained reduction from 3SUM to SetDisjointness. We give the first sub-linear time quantum reductions from 3SUM to online SetDisjointness. Via our reduction, the quantum 3SUM conjecture implies a $p + 2q \geqslant 1$ tradeoff bound for quantum SetDisjointness algorithms with $O(N^p)$ preprocessing time and $O(N^q)$ query time. We also give an analogous reduction from 3XOR. These results are derived from a general framework for fine-grained reductions to SetDisjointness which applies to any Abelian 3-Orthogonal Array (3OA) problem with suitable almost-linear hash functions.

We uncover a connection between the classical limit of the Magnus expansion in quantum field theory and the Malvenuto-Reutenauer Hopf algebra of permutations. We study a cubic scalar theory describing a massive particle coupled to massless scalar quanta, which captures the propagator structure relevant to classical scattering in gravity and scalar QED. Using a Schwinger parametrisation of the massive propagators, we compute the classical limit of Magnus amplitudes at tree level in this theory. First, we prove that all hyperclassical contributions cancel at the level of the Schwinger proper-time integrand, before integration. Then, we show that the classical Magnus amplitude precisely matches expectations from worldline quantum field theory. Both results rely on cancellations of disconnected diagrams which we relate to the Hopf algebra, specifically to the action of the adjoint first Eulerian projector, which annihilates the shuffle products associated with disconnected contributions. Moreover, the worldline diagrams include generic directed-tree topologies, whereas the field-theory diagrams only include directed chains. The correspondence we establish between the two therefore leads to a new formula for generic Murua coefficients in terms of simpler directed chain coefficients. Finally, we observe a suggestive connection between Magnus amplitudes and the web-mixing matrices governing the exponentiation of multiple Wilson lines.

We construct protocols for classically verifiable quantum advantage and classical verification of $\mathsf{BQP}$ computations using quantum indistinguishability obfuscation (qiO). Specifically, given qiO and assuming a slightly stronger version of $\mathsf{BQP}\neq\mathsf{BPP}$, we construct a two-message quantum-advantage protocol that is efficiently and publicly verifiable. Our result can be viewed as a rigorous cryptographic foundation for the heuristic quantum advantage proposals based on peaked random circuit sampling of Aaronson and Zhang (arXiv:2404.14493). We also construct two simple protocols for classically verifying arbitrary $\mathsf{BQP}$ computations. The first protocol is privately verifiable and assumes only the existence of qiO. This gives a rare example of a nontrivial cryptographic application of (quantum) iO that does not make additional computational hardness assumptions. The second protocol additionally assumes post-quantum one-way functions and is publicly verifiable. To our knowledge, this is the first publicly verifiable protocol for classical verification of $\mathsf{BQP}$ computations under computational assumptions in the standard model. As qiO is the basis for our results, we propose an approach to constructing qiO by adapting the local-mixing framework of Canetti–Chamon–Mucciolo–Ruckenstein.

Multi-tenant quantum processors expose a pulse-level attack surface in which coherent crosstalk can mimic benign calibration drift at matched average gate infidelity. We present a structural verification and detection framework based on the residual Pauli transfer matrix (PTM). We prove that products of local unital, trace-preserving channels cannot mix weight-1 and weight-2 Pauli operators, even under coherent drift of arbitrary strength or axis. Building on established PTM-to-Hamiltonian relations, we prove that, for any specified qubit pair in an arbitrarily large system, the first-order map from its nine interaction coefficients to the antisymmetric cross-weight feature is an isometry up to scale. Thus, every interaction direction is locally observable near the identity. We also exhibit cancellation of this feature under large local rotations and prove that the full cross-weight norm is invariant under local unitary composition, providing a structural countermeasure. For calibrated small local rotations, shared randomized-Pauli measurements support periodic verification using the evaluated antisymmetric detector. In simulation, $16{,}384$ randomized settings yield a detection threshold of $\lambda_{\min}\approx0.13$ at a $5\%$ calibrated false-positive target, with approximately $M^{-1/2}$ scaling in the number of settings $M$. Further experiments characterize detection under relaxation, depolarization, native ZZ fluctuations, and time-dependent pulse dynamics. Finally, an FRQI encoding with Pauli-graph quantum Hadamard edge detection reproduces the classical structural edge score to numerical precision.

Characterising open quantum dynamics requires identifying the environmental degrees of freedom that shape the system's evolution. The memory dimension, defined as the size of the smallest effective memory needed to reproduce this influence, quantifies the dynamically relevant environmental resources and provides a common basis for comparing different many-body environments. Here we introduce a pseudo-control protocol that encodes information about the memory dimension in an experimentally accessible interference matrix, whose rank certifies a lower bound on this dimension without direct access to the environment or full process-tensor tomography. Applied to quantum many-body environments, the protocol allows flexible adjustment of the interaction and interval times, revealing how these parameters, environmental dynamics, and system-environment interactions shape detectable memory. Our approach provides a new operational technique for characterising open quantum dynamics and probing the structure of system-environment interactions through their memory signatures.

We give a polynomial-time classical algorithm which samples from the syndrome distribution of a surface code state corrupted by coherent nearest-neighbor $ZZ$ crosstalk. Our algorithm complements the known efficient simulation algorithms for coherent single-qubit errors in the surface code. When both single-qubit coherent noise and coherent crosstalk are present, we find a complexity-theoretic obstruction to efficient simulation: unless the polynomial hierarchy collapses, there is no efficient classical algorithm for sampling from the syndrome distribution, even up to a constant multiplicative error. This is obtained by connecting the syndrome distribution under coherent noise to the output distribution of certain IQP circuits associated with a non-planar graph.

The $f$-routing protocol is a leading candidate for quantum position verification (Kent, Munro, and Spiller, 2011), but security guarantees for explicit functions remain limited. We prove unconditional resource lower bounds for uniform attackers; our new techniques bypass communication-complexity bounds central to previous works, which are inherently at most linear in the input length. We show that, for input length $n$ and sufficiently small constant $\epsilon>0$, a uniformly generated strategy using $q$ qubits and having description length $\mathrm{poly}(q)$, with success probability at least $1-\epsilon$ on every input, implies the following computational bounds on $f$: 1. If the strategies are arbitrary quantum channels, then $f\in\mathrm{QSZK}(\mathrm{poly}(nq))$, where $\mathrm{QSZK}(T)$ is the class of languages having quantum statistical zero knowledge proofs in which the verifier runs in time $T$ (and the simulator in time $\mathrm{poly}(T)$). 2. If the strategies are explicit Pauli-sparse unitaries on $q$ qubits that have at most $s$ nonzero Pauli coefficients, then $f\in\mathrm{DTIME}(\mathrm{poly}(nqs))$. 3. If the strategies are Clifford+T circuits using at most $t$ magic gates, then $f\in\mathrm{DTIME}(\mathrm{poly}(nq2^t))$. Time and space hierarchies then yield explicit functions secure against polynomial and even quasipolynomial qubits $q$ under our computational restrictions. These bounds exceed the $q\le\log n$ bound of Bluhm, Christandl, and Speelman (2022) for inner product function $f=\mathrm{IP}$, at the cost of restricting adversarial computation and increasing honest evaluation complexity.