Papers

Cryptographic security proofs often involve an adversary interacting with a larger, keyed oracle that consists of (potentially exponentially) many independent instances of a smaller, base oracle. However, showing quantum indistinguishability between two such keyed oracles can be tricky, since a single query made by an adversary may involve a superposition that covers all instances of the base oracles simultaneously. In this paper, we establish a generic indistinguishability lifting theorem of the following form: if the two base oracles are indistinguishable under quantum queries, then their corresponding keyed oracles are too, up to an O(q^2) multiplicative loss in distinguishing advantage, where q is the number of queries made by the adversary. Our lifting theorem applies to both statistical and computational settings, and to oracles that are stateful as well. It is also optimal in that it matches the obvious Grover search attack for a certain (contrived) choice of oracles. As an immediate application, we extend Carolan's compressed permutation oracle to an efficiently implementable compressed ideal cipher, and use it to prove preimage resistance of the Davies-Meyer compression function in the quantum ideal cipher model. Thanks to our lifting theorem, the soundness of our compressed ideal cipher reduces to that of Carolan's oracle, and any further improvement on the latter would automatically carry over to the former. As our second application, we give a modular construction that doubles the message length of any quantum-secure strong pseudorandom permutation. Along the way, we show that an existing two-round tweakable Feistel construction is indistinguishable from a random permutation under quantum bidirectional queries. This is done via a dedicated polynomial-method argument, which may be of independent interest.

We study quantum-state oblivious transfer over the quantum erasure channel under information-theoretic security guarantees. Specifically, Alice holds two quantum systems, Bob wishes to recover one of them, and the parties have access to independent channel uses and authenticated public classical communication, with no initial shared entanglement. We consider both honest-but-curious and malicious behavior. We establish finite-blocklength converse and achievability bounds, which match in the honest-but-curious setting. The malicious setting construction combines interactive hashing with tests of whether Bob received selected channel outputs, and distributes each input across several qubits so that erasures conceal an entire input from a dishonest receiver, even when the inputs are entangled with an external reference. We also derive fixed-error asymptotic expansions and show that both malicious and honest-but-curious settings have the same capacity.

Quantum computers are claimed to produce samples ordinary classical computers cannot reproduce. The sharpest such claim known pits constant-depth quantum circuits, given one entangled state per run, against shallow classical circuits of few-input gates and limited randomness. No efficient test was known that certifies such a claim from classical samples alone. Here we show that what such a test must read is decided by the classical class's pattern of single-bit and pair correlations, not by a distance. The test rests on one inequality: any machine producing the samples sits no further from the target than the fraction it mislabels plus the deviation of its string half, the bits beyond the label, from uniform. A collapse theorem, machine-checked in the Lean~4 proof assistant, confines that second term, one setting of the sampler's random input bits at a time. Four natural checks provably fail; a fifth, reading those same correlations, catches a far-from-target construction they cannot reach, and is exact on the class of few-input gates. The label test is proven and sample-optimal in its own tolerance up to a logarithmic factor; the fifth check is sound, not only effective, on the bounded pinned-residue class, pairwise-uniform samplers whose residue, the string's weight modulo the prime, is pinned by few seeds and whose seed sharing is bounded. What binds an experiment is the $43$-qubit entangled resource state at fidelity near $0.99$, not the readout. What remains are two named open problems; a positive answer to the first would extend the guarantee to the full class.

Bell nonlocal correlations cannot be reproduced by local hidden-variable models without communication, making classical communication cost a natural quantitative measure of nonlocality. Although finite communication always suffices to simulate any correlation in a fixed finite Bell scenario, determining the minimum amount needed to (exactly) simulate any given nonlocal correlation remains challenging, especially in the average-cost setting. Here, we derive lower bounds on input-average communication cost from nonlocal games, allowing variable-length, fully interactive two-way protocols. When applied to parallel games, these bounds yield explicit finite quantum correlations for which the exact simulation cost exceeds any prescribed finite input-average communication budget. For $n$ parallel Magic-Square-winning correlations, we prove a lower bound of $n\log_2(3/2)$ bits and give a one-way communication protocol that attains this rate asymptotically. For the quantum correlation maximally winning the $n$-copy of the Clauser–Horne–Shimony–Holt nonlocal game, we obtain an input-average lower bound of approximately $0.04627n$ bits for exact simulation. Finally, we formulate a hierarchy of lower bounds and complementary upper bounds using deterministic correlations up to chosen communication costs. Both recover the exact input-average cost at their final levels, and if the bounds agree at lower levels, their common value yields the exact input-average cost without needing to consider all communication strategies.

Entangling measurements can reduce the statistical cost of learning many-body correlations. We study Pauli strings with full support on a specified $k$-qubit region using classical shadows with two independent, uniformly random product single-qubit Clifford layers around a controllable unitary acting on that region, followed by computational-basis readout. In this architecture, we prove that a circuit $U_*$ of two collective Pauli rotations attains the exact minimum squared shadow norm over all Clifford choices of the controllable unitary for every $k\geq1$, namely $C_k^{\rm opt}=4\cdot 9^k/(3\cdot 5^k+3^k-6)$ for odd $k$ and $C_k^{\rm opt}=4\cdot 9^k/(3\cdot 5^k-3^k+2)$ for even $k$. The asymptotic optimum $(4/3)\cdot(9/5)^k$ establishes Wu et al.'s exponential base as optimal and improves their prefactor from $2$ to $4/3$. For $1\leq k\leq6$, exact rational certificates prove that the same optimum holds over the entire unitary group $\mathrm U(2^k)$, including all non-Clifford unitaries, within the same measurement architecture. These finite-size results motivate the conjecture that $U_*$ is optimal over all unitaries for arbitrary $k$ within this architecture.

In this paper, we present a method for constructing linear codes derived from book graphs. Applying such a method, we construct binary codes that have the greatest possible minimum distance for their length and dimension by means of the $2$-sum of two equal book graphs. We then utilize matroid and graph theory together to investigate some properties of the resulting linear codes. Furthermore, we show that, from the incidence matrix of any graph, we can obtain a linear code over any finite field maintaining the same parameters. Furthermore, we show how the condition for two linear codes to generate a Calderbank-Shor-Steane (CSS) code translates into matroid theory and, utilizing cycle graphs, we exhibit a way to generate codes that meet this condition.

The surface code is the leading candidate for fault-tolerant quantum computation owing to its planar nearest-neighbor connectivity, high threshold, and efficient decoding, but its low encoding rate demands on the order of a thousand physical qubits per logical qubit in the teraquop regime. Yoked surface codes improve the density by a factor of two or three by concatenating a high-density parity check code on top of the surface code while retaining planar nearest-neighbor connectivity. In this work, we generalize this idea to multiple levels of concatenation and introduce multi-yoked surface codes. Our construction rests on two new ingredients. First, we propose a family of outer codes called chain codes, built by chaining copies of a seed code that detects the block errors of the code one level below; the resulting codes use all logical qubits of the lower level and achieve a high encoding rate within a few concatenation levels. Second, we design a patch allocation in which movable workspaces perform the yoking checks by lattice surgery with a hierarchy of yoking intervals, so that lower-level checks are performed frequently while higher-level checks are performed less often, which avoids the long yoking intervals that a single large-distance outer code would require. As a benchmark, we construct a three-yoked surface code with a $[[256,166,8]]$ outer code and evaluate it numerically under the SI1000 noise model using soft information from the surface code decoder. The logical error rate is suppressed exponentially in the inner code distance, and in the teraquop regime the three-yoked surface code is about 4 to 4.5$\times$ denser than the unyoked surface code.

We study the following quantum state identity problem: given access to copies of $n$ unknown pure quantum states, the goal is to determine whether every pair has fidelity at least $1-\varepsilon$ or some pair has fidelity at most $\varepsilon$. This problem relaxes the identical-or-orthogonal promise considered in previous work. For any fixed overlap parameter $\varepsilon\in(0,1/4)$, we present two quantum algorithms with complementary guarantees on circuit depth and sample complexity. The first runs in constant depth using parallel swap tests and takes $O(\log(n/\delta)\log(2/\delta))$ copies of each input state to succeed with probability at least $1-\delta$. The second uses the Schur transform to reduce the sample complexity to $O(\log(n/\delta))$, through an analysis relating Jucys–Murphy elements to Schur sampling. We also prove a matching sample complexity lower bound of $\Omega(\log(n/\delta))$ for any quantum algorithm with failure probability at most $\delta\le 1/2-c$, for any constant $c>0$, establishing that the second algorithm achieves the optimal dependence on both $n$ and $\delta$ for fixed $\varepsilon$.

Molecular property prediction is central to computational drug discovery, where graph neural networks learn to weight neighboring atomic environments during message passing. Yet it remains unclear how variational quantum circuits alter learned attention behavior in molecular graphs. We introduce an edge-aware variational quantum attention mechanism for molecular graph learning, in which the receiving atom, neighboring atom, and connecting bond jointly determine the quantum attention state. Across five molecular property and bioactivity prediction tasks, QGAT achieves competitive performance relative to GATv2, with a consistent improvement on BBBP across all six evaluated circuit ansatzes. We further compare how the quantum and classical attention scores weight molecular structure beyond accuracy. In the Verubecestat BACE1 inhibitor series, QGAT achieves a higher Spearman correlation than GATv2 and assigns positive attributions to several structural changes consistent with reported structure-activity relationships (SARs). This case study shows that the two attention mechanisms can exhibit different prediction and attribution behavior across structurally related BACE1 analogues, while broader validation is required to determine how consistently these differences generalize across chemical series and targets. Circuit ablations further show that performance depends on the circuit design. Together, these results show that variational quantum attention can serve as a viable alternative molecular attention parameterization while inducing circuit- and chemistry-dependent behavior distinct from a matched classical scorer.

Photonic qubits play an important role in quantum information processing. However, to date, efficient high-speed single photon sources and photon number resolving (PNR) detectors are still difficult to make. Here, we use phase-randomized coherent states and threshold detectors, combined with decoy-state post-processing, to simulate single photon sources and PNR detectors and perform various quantum information processing tasks. We propose a simple linear regression method to predict Fock state statistics based on observable statistics from coherent-state probes, combined with random/structured sampling of probe settings. Compared with traditional decoy-state post-processing based on linear programming and Cartesian product grid sampling, our method enables drastically improved accuracy and much reduced probe resources. It works particularly well for unknown unitary circuits of interest with fixed-size Hilbert space dimensions. For instance, it can accurately simulate 4-photon interference in linear optics with just 32 input/output probe settings and 6-photon interference with 256 probe settings. Moreover, it also works for non-unitary (such as lossy, nonlinear, or arbitrary) quantum channels. This enables a wide variety of applications that can be implemented with easily attainable coherent light sources and threshold detectors, such as characterization of small-scale linear optical quantum computing circuits or quantum sensing/metrology devices.

Harnessed nonclassical resources to enhance the performance of quantum batteries is an important goal of quantum technology. In this work, we investigate multi-emitter batteries coupled to a one-dimensional waveguide driven by a broadband squeezed-vacuum reservoir, and determine how the waveguide geometry controls the battery performance and and their thermodynamic features. We show that for a single emitter, the squeezed reservoir deposits finite energy while the state remains passive, yielding zero ergotropy. For two emitters, however, phase-sensitive reservoir correlations generate coherence and can drive the steady state into a fully nonpassive regime. For three emitters, collective thermal dynamics already supports finite ergotropy, while squeezing further increases the extractable component of the stored energy. Crucially, because the collective and phase-sensitive couplings depend on the emitter positions, geometry provides direct control over the nonclassical correlations and, consequently, over the nonpassivity of the steady state. The ergotropy can therefore be strongly modulated while the stored energy changes only weakly, and in the two-emitter configuration geometry alone can switch the battery between a passive steady state and one in which all stored energy is unitarily extractable.

We study the quantum query complexity of maximizing a non-negative submodular function, considering both the unconstrained setting and, for monotone functions, a cardinality constraint $k$ on an $n$-element ground set. In the exact reversible digital value-oracle model, our unconstrained algorithm achieves an expected $(1/2-\varepsilon)$-approximation using only $O_\varepsilon(\log n)$ queries. In contrast, any classical randomized algorithm that attains a fixed expected ratio above $1/4$ requires $\Omega(n/\log n)$ queries (Li, Feldman, Kazemi, and Karbasi, 2022), establishing an exponential separation in query complexity. For cardinality-constrained maximization, we give a bounded-error quantum algorithm that achieves a $(1-1/e-\varepsilon)$-approximation using $\widetilde O_\varepsilon(\min\{\sqrt n,n/k\})$ queries. When $k=o(n)$, our algorithm achieves at least a quadratic speedup up to logarithmic factors over classical randomized algorithms (Mirzasoleiman, Badanidiyuru, Karbasi, Vondrák, and Krause, 2015; Peng and Rubinstein, 2025). Moreover, when $k=cn$ for any fixed rational $c<1-1/e-\varepsilon$, the query complexity reduces to $O_{\varepsilon,c}(\log n)$, yielding an exponential separation from the classical $\Omega(n/\log n)$ lower bound (Li, Feldman, Kazemi, and Karbasi, 2022). We further prove quantum lower bounds of $\exp(\Omega(\varepsilon^2n))$ queries for achieving a ratio beyond $1/2+\varepsilon$ without constraints, and $\exp(\Omega(\varepsilon^2k))$ queries for exceeding $1-1/e+\varepsilon$ when $k/n\le\varepsilon$. These barriers demonstrate that quantum computation offers no exponential speedup at these approximation thresholds.

We determine the time required for local weak measurements to collapse to one occupied site in an initial superposition of $N$ alternatives in the model of PRA 111, 032217 (2025). For equal initial occupation probabilities and a fixed confidence threshold $1-\delta$, we prove $T_N/\ln N\to1/2$ in $L^1$, with time measured in units of the characteristic measurement time $\tau_m$ of each detector. We also connect the asymptotic stabilization theorem of that work to a finite measurement: the first site to reach $1-\delta$ is the eventual outcome with conditional probability exactly $1-\delta$. The result corrects the previously proposed double-logarithmic asymptotic scaling. The finite-range numerical fit does not determine a constant asymptotic correction or a precise finite-$N$ law.

Cavity Quantum Electrodynamics (Cavity-QED) offers a powerful framework for controlling light-matter interactions, yet first-principles approaches commonly assume ideal, lossless cavity fields. Here, we introduce a minimal extension to the Pauli-Fierz Hamiltonian that accounts for cavity dissipation through the experimentally accessible cavity quality factor Q. The electromagnetic field is described as a damped harmonic oscillator within the very weak damping approximation. In this framework, cavity losses only enter the light-matter interaction and dipole self-energy terms, without introducing additional photonic degrees of freedom. A time-dependent unitary transformation yields a real-valued Hermitian Hamiltonian that can be incorporated into existing ab-initio QED methods without additional computational cost or changes in scaling. We combined the approach to the QED-CCSD method and investigated the effects of cavity dissipation on the optical spectrum of a p-nitroaniline molecule under strong light-matter coupling. We found that, for realistic quality factors, cavity dissipation can reduce the Rabi splitting by more than 20% compared to the ideal-cavity limit, even though the system remains in the strong-coupling regime. Convergence towards the ideal-cavity limit then requires substantially higher quality factors than those needed to establish strong coupling. These results demonstrate that cavity dissipation can significantly affect polaritonic energetics and highlight the importance of incorporating experimentally realistic cavity losses into quantitative ab-initio Cavity-QED simulations to accurately guide experimental protocols.

We study the charge resolved structure of the pairwise mode entanglement produced by the Schwinger effect. Using the $U(1)$ electric charge of quantum electrodynamics, we decompose the entanglement of the reduced density matrices of momentum modes into individual charge sectors, applying the symmetry resolved entanglement entropy to the pure bipartition reductions and the charge imbalance resolved negativity to the mixed particle-antiparticle pair. For a constant electric field we obtain closed form results for every mode pairing, with all field dependence controlled by the single pair production probability $|\beta|^2=e^{-\pi\mu}$. For the particle, particle and antiparticle antiparticle pairs the entanglement entropy within each charge sector is field independent, so that the field acts only by redistributing statistical weight among the sectors; for the mixed particle antiparticle pair the populated sector additionally carries a field dependent entropy. The vacuum created pair is the richest case: its resolved negativity is distributed over three imbalance sectors and is transported from one sector to the next as the field increases, the sectors contributing equally only at the critical field. The entanglement across a fixed momentum bipartition, by contrast, is frozen at its initial value because pair creation conserves the sector charge. Symmetry resolution thus refines the total entanglement measures into a sector resolved picture, exposing where in charge space the entanglement of the Schwinger mechanism resides and how the electric field moves it, information beyond that contained in the total measures or in particle number distributions.

The quest for a quantum theory of gravity remains a central challenge in modern physics, driven by the goal of unifying general relativity and quantum mechanics. Direct experimental access to quantum gravitational effects is notoriously difficult due to the inaccessibility of the Planck scale. Recent proposals, however, suggest that gravitationally induced quantum entanglement between two massive particles, realized through advanced quantum interferometric techniques, could provide empirical evidence for the quantum nature of gravity. We demonstrate that the geometrical configuration of an interferometer plays a decisive role in entanglement generation. Our analysis reveals that geometric optimization can substantially enhance the gravitationally induced phase shift, thereby improving the prospects for experimental detection of gravity-mediated entanglement. Moreover, we show that standard approximations employed in prior proposals may severely limit predictive accuracy and compromise experimental feasibility.

We investigate the sequential version of Shor's order-finding algorithm from the perspective of the imaginarity of quantum channels. By fixing an eigenbranch of the modular multiplication unitary and a target output path, the process is effectively decomposed into a real diagonal factor and a residual phase channel. We find that for the ideal residual phase channel, the three trace-norm induced imaginarity measures are all equal. On good output paths, a smaller residual imaginarity corresponds to a higher single-block success probability. By combining the branch-wise probabilities, we obtain the exact ideal success probability of the sequential order-finding protocol and derive lower and upper bounds in terms of residual phase-channel imaginarity. We further extend the analysis to noisy residual phase channels, and obtain the lower and upper bounds on the noisy success probability. These results clarify the role of imaginarity of channels in Shor's algorithm and provide a refined perspective on quantum-resource behavior in ideal and noisy sequential quantum algorithms.

Despite the importance of the non-uniform Polynomial-Time Hierarchy (PH/poly) in classical complexity understanding the collapse conditions of the Polynomial-Time Hierarchy (PH), a quantum equivalent of PH/poly has yet to be studied in the literature. We introduce the non-uniform computational Quantum Polynomial-Time Hierarchy (QCPH/mpoly), the quantum equivalent of PH/poly, and show that it collapses if and only if QCPH, the quantum equivalent of PH introduced by Gharibian et al. (comput. complex. 2022), also collapses. We also show that QCPH collapses if coQCMA is contained in QCMA/mpoly. These results are analogous to those of Yap (TCS 1983) commonly used to invoke the collapse of PH in classical complexity. QCPH/mpoly is analogous to QCPH with non-uniform quantum verifier circuits.

Circuit cutting runs a quantum computation on processors smaller than the circuit, at the price of classical knitting whose cost grows exponentially with the number of cut gates. Keeping this cost affordable is necessary but not sufficient for an advantage, since knitting classically easy subcircuits is itself classically easy. We formulate three requirements for distributed quantum advantage under a stated budget: affordable knitting, classical difficulty that survives the cut, and, for variational circuits, resolvable gradients. We prove that under stated assumptions knitting stays affordable when subcircuits grow behind a bounded interface and becomes exponentially expensive when fixed-width subcircuits multiply. We turn the requirements into screening criteria and apply them to eighteen circuit families. We identify finite local-depth circuits with bounded interfaces as a setting in which the requirements can coexist, with hardness established only in the worst case. As a classically verifiable proof of principle, we knit one gate joining two field-perturbed toric-code patches on an IBM Nighthawk processor for up to 142 spins, and confirm that the reconstruction can at least resolve the contact correlation beyond independent execution for up to 98 qubits.

Quantum networks will rely on intermediate nodes to distribute entanglement, but the same nodes may learn which users are being connected. We introduce a minimal two-call routing primitive in which a user, Alice, establishes an entangled link with one of several clients while testing whether the provider, Bob, has disturbed a coherently encoded request. The construction adapts the hidden-order mechanism of quantum private queries: one call contains a direct request, the other a coherent superposition of the desired and null addresses, and Alice keeps their order secret. A private matching qubit held by the selected client restores the coherent test state after a favorable Bell-measurement outcome, so that Alice can test the returned query without any further operation by Bob. The claim is deliberately limited. The protocol shows that a routing request can carry a physical cheating test, and it detects an explicit destination-reading attack with nonzero probability. It does not yet provide a quantitative information-disturbance tradeoff, composable security, or certification of an unmeasured output against arbitrary attacks. We also characterize the exact perfect-pass limit, in which Bob's residual state, averaged over the private matching states, is independent of the destination.

We study the effect of repulsive interactions on skin modes and entanglement in the unidirectional Bose–Hubbard model. Although the ground state of this integrable model undergoes a superfluid–Mott transition with suppressed skin accumulation, the corresponding change in entanglement depends on the selected many-body state. We compare the ground state with the steady state, defined as the largest-imaginary-energy eigenstate in the zero-momentum sector. For sixteen sites at unit filling, we find that the ground-state density approaches uniform filling and its entanglement decreases toward the Mott limit, whereas the steady states exhibit a nonmonotonic entanglement crossover. At intermediate interaction ($U/t=10$), the second Rényi entropy of the steady state develops four spatial maxima. We show that these maxima are accounted for by competing subsystem-number sectors within a dominant configuration manifold of four doublons and four holons, but not by the subsystem particle-number variance alone. The dominant global onsite-pair manifold retains the same entropy peak structure. At strong interaction, projection onto the one-doublon–one-holon manifold closely reproduces the full entropy profile and its two edge peaks. Furthermore, we demonstrate that the many-body winding about the origin remains nonzero at strong interaction; an exact two-site example shows how it becomes ill-defined in the singular projected $U/t\to\infty$ limit. Our results distinguish ground-state skin suppression from state-selective entanglement and point-gap topology.

This work investigates a class of exactly solvable quantum systems described by a generalized Dunkl–Schrödinger equation with energy-dependent interactions. A two-parameter extension of the Dunkl differential operator is introduced, incorporating both the conventional reflection contribution and an additional derivative-reflection coupling. The resulting formalism leads to a modified Heisenberg algebra, from which the continuity equation, conserved probability current, and generalized normalization condition are derived for energy-dependent potentials. As an application, an energy-dependent harmonic oscillator is studied in detail. Exact analytical expressions for the eigenfunctions and energy spectrum are obtained in terms of associated Laguerre polynomials. The combined effects of the Wigner parameter, the deformation parameter, and the energy-dependence parameter are shown to produce parity splitting, nonlinear energy spectra, and nonuniform level spacing while preserving exact solvability. The thermodynamic properties of the model are then examined through the canonical partition function using the Euler–Maclaurin summation formula. Analytical expressions for the partition function, internal energy, entropy, and specific heat are derived and analyzed numerically. The results demonstrate that the generalized Dunkl deformation and energy-dependent interaction provide effective control over both the spectral and thermal characteristics of the system, extending the class of exactly solvable quantum models with reflection symmetry.

Modelling molecular absorption spectra from scalable ground-state representations is challenging because conventional approaches often require explicit excited states or time propagation. Here, we introduce a method to obtain Absorption Using Recursive Operator Response with vibronic Augmentation (Aurora), which combines neural quantum states (NQSs) with continued-fraction memory-kernel coupling theory (CF-MKCT). Aurora maps the zero-temperature Liouvillian response hierarchy onto repeated wavefunction-space applications of a shifted Hamiltonian to a dipole-prepared state, enabling direct spectral reconstruction from variational ground states. The implementation combines variational Monte Carlo, implicit-restarted-Lanczos-assisted NQS optimization, matrix-free Hamiltonian application, and adaptive recursion control. The resulting electronic spectra closely agree with full-configuration-interaction and conventional MKCT references for tractable molecules, with the restarted-Lanczos strategy improving difficult NQS cases. For electron-phonon Hamiltonians, Aurora combines Huang-Rhys mode selection with local singular-value-decomposition (SVD) phonon encoders. The H2 benchmark indicates that compression retains the dominant vibronic envelope and improves upon bare local-basis truncation, while paired calculations for N2, H2O, H2S, and NH3 yield similar principal features with and without encoding. We further obtain vibronic spectra for C6H6 and a 10-electron, 10-orbital C10H8 active space. Overall, Aurora provides a unified route from variational molecular ground states to electronic and vibronic spectra without constructing excited-state manifolds.

The minimum fault weight of a logical readout depends jointly on data-error persistence, check redundancy and time-boundary constraints. For any binary check matrix $H$ and nonzero parity support $w$, we prove that a repeated-readout model with a zero-syndrome endpoint has exact distance $\min_{w\cdot y=1}[\operatorname{wt}(y)+q\operatorname{wt}(Hy)]$ for at least $q$ wrong readouts. This reduces the search over fault histories to one weighted spatial minimum and gives the minimum repetition count for each adjacent-column check in square Bacon–Shor and generalized Shor readouts. Combining those checks with redundant Gauss-check pair products yields an exact joint distance and an outcome-count optimum within the specified gauged-readout family. At target distance $m$, one round uses $m^2$ outcomes, compared with $m(2m-1)$ for the repeated baseline in the same phenomenological model. For a one-epoch bare-ancilla CNOT implementation, we prove a schedule-dependent distance upper bound by constructing an accepted wrong readout from one gate fault and outcome flips. The bound identifies necessary timing conditions for retaining the target distance and gives matching upper bounds of three for the best tested schedules at both $m=3$ and $m=5$.

One-way local operations and classical communication (LOCC) can fail to distinguish four orthogonal maximally entangled states in every local dimension $d\ge4$. We show that every set of $k$ pairwise orthogonal maximally entangled states in $\mathbb C^d\otimes\mathbb C^d$ is perfectly distinguishable by an $A\to B\to A$ protocol whenever $d\ge Ck^4[\log(2k)]^\nu$, for universal constants $C,\nu>0$. A single feedback message therefore raises the number of candidates that can always be distinguished from a constant to $\Omega\!\left(d^{1/4}/(\log d)^{\nu/4}\right)$, establishing a polynomial separation between one-way and two-way LOCC. In our protocol, Alice preserves exact orthogonality while reducing overlaps between Bob's conditional subspaces. Bob reduces the candidates to a singleton or an orthogonal pair and refines his outcome so that Alice can complete the discrimination. As a corollary, nine copies suffice for perfect two-way LOCC discrimination of any orthogonal maximally entangled set in all sufficiently large local dimensions.

How far from finite can an amenable group be? Every finite piece of an amenable group can be imitated by permutations of a finite set, and Cornulier's sofic profile counts how many points such an imitation needs at accuracy $1/r$. We build a finitely presented elementary amenable group with a finite piece whose profile is $\exp(r^{1+o(1)})$, close to the most our counting method can ever detect. The construction is a lamplighter with its lamps on configurations rather than on points. Houghton's group moves the points of three rays, finitely supported affine maps act on their binary configurations, and a copy of $S_3$ sits on every configuration. Then $N$ points carry $2^N$ lamps, yet any two lamps can be brought together by moves that each involve at most three points. The group embeds in Brin's group $3V$, so $3V$ too has a finite piece of nearly exponential profile. The group also gives an explicit quantum channel on $\mathbb C^{873}$ that is cheap to use once and expensive to use many times. A device that applies it $n$ times, releasing each output before the next input arrives, needs about $n/B$ qubits of memory when it may spend $B$ bits of purity, and exact devices achieve this up to polylogarithmic factors. With exchange at the optimal rate, the least memory is about $\sqrt n$, attained with purity of the same order. The channel is factorizable and lies in the closure of channels with finite maximally mixed baths, yet any such bath that imitates it to accuracy $u$ needs dimension $\exp(u^{-1+o(1)})$, although its minimal Stinespring dilation implements it exactly with a pure environment of dimension $130$. The engine is a one-round theorem: after a single use, the memory of any such device carries an approximate representation of the group.

Quantum processing of classical data fundamentally relies on efficiently mapping classical datasets onto the amplitudes of quantum states. Preparing large amplitude-encoded states, however, remains a major bottleneck in quantum computing. In this paper, we introduce a novel state-preparation framework we call Q-MERGE, that addresses this bottleneck by partitioning a large target state into $M$ $n$-qubit segments, preparing these segments independently and in parallel, and then coherently combining them into a single amplitude-encoded state using SELECT-SWAP operations and measurement. Q-MERGE is agnostic to the segment-level preparation method, allowing existing techniques to be applied to smaller subproblems while providing a tunable trade-off between circuit depth and qubit count. With mid-circuit measurement and preparation-register reuse, the required ancilla qubits can be reduced from $\mathcal{O}(Mn)$ to $\mathcal{O}(n)$. Applied to a real-world \(128\times256\) ultrasound dataset, Q-MERGE achieves an infidelity of $1.066\times10^{-8}$, compared with $3.413\times10^{-1}$ for direct preparation using the same underlying method, a seven-order of magnitude improvement. We demonstrate its feasibility experimentally on the Quantinuum System Model H2 trapped-ion quantum computer and validate the prepared state using shadow-overlap tomography. Numerical analysis of Haar-random states indicates consistent success probability for up to $M=10^7$ segments, supporting the scalability of Q-MERGE for encoding massive classical datasets.

A tilted nonselective measurement can close the upper transition of a three-level quantum refrigerator, but it also generates coherence that feeds back on the populations and suppresses the cooling current. We formulate randomized open-loop control of the measurement azimuthal phase \(\alpha\), sampled independently at each event from a probability distribution \(P(\alpha)\), while keeping the event rate, polar angle, and single-event population-transfer probability fixed. Direct population transfer is phase independent, whereas the coherence source carries the factor \(e^{-i\alpha}\). Exact elimination of the stationary coherence gives \(0\leq k_{\rm eff}[P]\leq A_m\), where \(k_{\rm eff}[P]\) is the effective population-transfer rate between the upper levels and \(A_m\) is the bare direct mixing rate. When the fixed measurement couples populations and coherence, the upper bound is attained if and only if \(\langle e^{i\alpha}\rangle_P=0\), where \(\langle\cdot\rangle_P\) denotes an average over the phase distribution. The minimal realization uses two equally weighted phases separated by \(\pi\): the population-to-coherence source and its return to the populations then vanish at the generator level, while the full direct mixing remains. Because the cold current increases strictly with \(k_{\rm eff}\) in the refrigeration window, the same condition maximizes the stationary cooling power over the independent random-phase distributions considered here. For one representative parameter set, phase cycling increases the fixed-gap cooling power by about \(32\%\) relative to a fixed-phase measurement, while leaving the ratio of extracted cold heat to supplied measurement energy unchanged.

Quantum sensing is emerging as a practical means of improving sensing capabilities in consumer electronics, particularly where size, power, and noise constrain classical approaches. In this paper, we reviewed the near-term applicability of quantum sensing using a platform-and-application framework. Within this framework, we outlined the general sensing protocol and discussed the working of the four key quantum sensing platforms relevant to consumer electronics: nitrogen-vacancy (NV) centers, atomic vapor cells, Rydberg atomic sensors, and photonic quantum sensors. Through case studies involving navigation and positioning, healthcare and wearables, radio-frequency (RF) and wireless systems, the Internet of Things (IoT), and imaging, we examined the tangible engineering advantages offered by quantum sensing. Rather than replacing devices outright, quantum sensing is more likely to earn its place in the near-term by upgrading specific measurement components within hybrid classical-quantum systems. Right now, the clearest opportunities are in weak-field detection, compact RF reception, and sensing that remains robust in noise.

Narrow linewidth (high-Q) quantum discriminators are essential for realizing solid-state $^{229}$Th nuclear clocks, yet the observed transition linewidths remain at the tens-to-hundreds-of-kilohertz level, far exceeding the sub-Hertz linewidth set by the radiative lifetime of the nuclear isomer. Here, we investigate the origin of this broadening in $^{229}$Th:CaF$_2$ through systematic measurements of the linewidth as functions of temperature, thorium concentration, and quadrupole state, accompanied by theoretical analysis and first-principle simulations. We find that the linewidth is independent of temperature, increases linearly with thorium concentration, and depends strongly on the quadrupole state. Data analysis identifies variations of the local electric-field gradient (EFG) as the dominant source of inhomogeneous broadening and reveals that the EFG disorder increases linearly with thorium concentration. The observed Lorentzian line shapes and linewidth linear concentration dependence are explained naturally from the $1/r^3$ scaling of a random distribution of long-range dopant-induced perturbations. Complementary atomistic and ab initio density-functional-theory calculations reproduce these characteristic features and provide insights into the microscopic defect configurations responsible for the broadening. These results establish the dominant broadening mechanism in solid-state $^{229}$Th and provide guidance for engineering nuclear-clock materials with reduced inhomogeneous broadening.