Papers

How many past requests are needed to decide which qubits should share entanglement? We show that the answer depends on the allocation choices created by the queries: a larger memory can require no more data. The memory stores a classical bit and answers requests through a fixed detector that preserves coherence within each measured sector. For independent commuting $X$- and $Z$-type Pauli queries, we characterize the full attainable prediction-contrast region and construct encodings that preserve the bit at every nonzero vertex. With sharp reports, a $d$-qubit path and groups of at most $k$ qubits have minimax excess error after $m$ requests proportional to $k^{-1}\min\{1,\sqrt{d\log(k+1)/m}\}$, uniformly for $2\leq k<d$. Connected biclique regions can grow without increasing sample demand when depth, region count and connections per region stay bounded. Preparation noise introduces a separate calibration requirement. We derive an exact tradeoff with extra fresh detector calls and transfer the learning law to structured transaction co-location. Population-risk experiments test the statistical predictions. We also compare encodings on a native 15-qubit device and learned partitions on public purchase baskets. The full chain wins on the device; frequency grouping outperforms basket search in the largest-capacity retail setting.

Entanglement-assisted optical interferometry promises diffraction-limited imaging over baselines where light cannot be physically combined, but existing theory treats only a single visibility on one two-station baseline. This work formulates the multiparameter estimation problem for an M-station array imaging an extended scene. A reduction lemma shows that the multimode quantum Fisher information (QFI) equals the mean photon number times the QFI of a single delocalized photon, collapsing the problem to a finite-dimensional one. The local photon-number superselection rule (SSR) erases all phase information from the bare state, while shared entanglement restores a fraction f(r)=r/(1+r) of the QFI on a baseline supplied with r pairs – a factor shown to be achievable, since the reduced two-mode state of any pair is exactly the two-station weak-thermal state. The QFI matrix and its mean Uhlmann curvature reveal numerically that a point source is measurement-compatible, whereas for every extended-source model examined it is incompatible, the Holevo bound exceeding the symmetric-logarithmic-derivative (SLD) bound by up to ~74%. An explicit collective receiver – a global mode-sorting (quantum Fourier transform) measurement – then attains a weighted variance within ~7% of the SLD bound and roughly an order of magnitude below an explicit pairwise receiver, and a noisy-resource advantage threshold gives the break-even baseline (~20 km for near-term parameters) beyond which repeater-distributed entanglement beats direct transmission. Finally, the optimal allocation of a finite entanglement budget is a convex program with a closed-form proportional (square-root-law) solution favoring low-visibility baselines. These results recast quantum aperture synthesis as collective multiparameter estimation and give concrete design targets, illustrated on the CHARA array.

Photon subtraction is one of the most important techniques for generating non-Gaussian optical states and constitutes a key resource for quantum information processing and quantum metrology. The practical performance of a photon-subtraction device is primarily determined by the transmissivity of the beam splitter and the quantum efficiency of the heralding detector. Accurate knowledge of these parameters is therefore essential for assessing the quality of the generated non-classical states. In this work, we propose an experimentally feasible in situ scheme for the simultaneous estimation of these two parameters using only the measurement data produced during the operation of the device. Our protocol combines the click statistics of an on/off heralding detector with homodyne measurements performed on the transmitted mode of the beam splitter when fed by a displaced squeezed state. Within the framework of classical multi-parameter estimation theory, we derive the corresponding Fisher information matrix and investigate both joint and sequential estimation strategies. For simultaneous measurement of parameters, we evaluate the sloppiness of the underlying statistical model and analyze its dependence on the measured quadrature, probe photon number, squeezing fraction, beam splitter transmissivity, and detector efficiency. Our analysis proves that an appropriate choice of the homodyne quadrature substantially reduces parameter degeneracy and enables efficient simultaneous estimation. Furthermore, we show that the joint estimation strategy consistently provides a lower estimation bound than the sequential estimation approach over a broad range of experimentally relevant parameters.

Neutral-atom arrays are a leading qubit technology for large-scale, fault-tolerant quantum computing (FTQC). A dominant error source on this platform is qubit loss, which accrues with every operation and movement. The presence of loss undermines the promises of existing architectural work. Standard error correction targets stochastic Pauli errors and cannot correct loss, so most FTQC performance analyses are not directly compatible with it. Moreover, compilation and routing decisions, which strongly affect overall loss, are typically optimized against Pauli-error cost models and often remain loss-agnostic, potentially increasing exposure to the loss channel. In this work, we comprehensively model the effect of qubit loss on neutral-atom FTQC and develop a loss-tolerant transversal-gate architecture. We treat loss not as a predetermined error parameter but as a dynamic budget spent across a whole program, allowing us to control it by co-designing layout, compilation, and decoding. We target a physical implementation with no separate storage and entangling zones, eliminating the repeated SLM-AOD handoffs and long-distance shuttling that dominate loss in other layouts. We develop compiler optimizations that maximize gate parallelism while respecting the RF tone budget and AOD bandwidth constraints. Our work couples these with a loss-aware, delayed-erasure decoder and an end-to-end loss-aware magic state cultivation protocol. Overall, we improve accumulated loss per syndrome-extraction round by up to 2.15X against a zoned baseline and reduce logical error rates by over two orders of magnitude versus current architectures. Our framework also informs concrete device targets such as continuous reloading rates, AOD counts, and shuttling trajectory choices. We expect these insights to matter for system architects as neutral-atom hardware scales.

Two sharp yes/no questions are mutually unbiased if and only if their involutions anticommute. A set of unbiased questions is therefore a Clifford algebra, whose maximal size is odd, meaning four anticommuting questions typically imply a fifth: the two-level systems of real, complex and quaternionic quantum theory allow two, three and five questions, while four is skipped. Without this operator product restriction, a two-level system with four unbiased questions exists as the four-dimensional Bloch ball, the hyperbit. The single-system postulates that pick out the Jordan state spaces allow such a model, and only energy observability rules it out. We show what it lacks, and realise it inside two qubits: its Kirkwood-Dirac imaginary parts are hidden $\mathfrak{so}(4)$ generators, its composites allow entanglement but no interaction, and its 24-cell of states stays Spekkens preparation contextual down to depolarising strength $2/3$. In fermionic terms, the four questions are the Majorana operators of two modes while the fifth is parity: the four-question system is therefore the sector removed by parity superselection.

We study Haar-Bayesian prediction of one unmeasured copy of an unknown finite-dimensional pure quantum state after an arbitrary collective measurement on $n$ observed copies. Performance is evaluated by quantum relative entropy. For a fixed measurement, the Bayes predictive state is the posterior mean and the optimized conditional loss is its entropy. We then optimize the measurement over all POVMs on the symmetric subspace. For every nonzero positive effect $E$, the corresponding posterior predictive state is $\mu_E=(I+n\rho_E)/(n+d)$, where $\rho_E$ is the normalized one-particle marginal of $E$. Since a pure spectrum majorizes every density-operator spectrum, this identity gives an outcome-wise entropy lower bound. Coherent rank-one effects attain the bound, and their Haar orbit yields the highest-weight covariant POVM. Hence this POVM is globally Bayes optimal over all collective measurements and, by covariance, globally minimax. Its exact risk is $h_d((n+1)/(n+d))$, where $h_d(r)=-r\log r-(1-r)\log((1-r)/(d-1))$. The same arbitrary-effect reduction shows that the highest-weight POVM also maximizes the joint overlap between the latent pure state and its posterior predictive state, equivalently the mean posterior purity, with optimum $((n+1)^2+d-1)/(n+d)^2$.

Stabilizing superconductivity beyond its equilibrium regime has been one of the quests of nonequilibrium state engineering. We report the presence of nonthermal pairing gap in BCS superconductors coupled to two thermal baths, where one of the baths can be at a temperature well above the equilibrium $T_c$. Superconducting state is enabled by a highly non-equilibrium steady state stabilized by weak coupling to baths that break detailed balance condition. The steady-state is well described by a generalized Gibbs ensemble parametrized with chemical potentials for associated Bogoliubov quasiparticle. A strong, non-perturbative effect is reported for both $s$-wave and $d$-wave superconductors, and its possible realization in cavity-based experiments is discussed.

Quantum low-density parity-check (QLDPC) codes represent a promising approach for error correction in quantum computing. The recently proposed Tesseract decoder uses the A* search algorithm that guarantees finding the most likely error pattern. However, practical implementations of Tesseract often involve an extremely large graph, and the inherently sequential nature of the search results in high computational overhead and long runtime. To improve decoding efficiency, we propose a two-stage decoding framework. First, a belief propagation (BP) decoder efficiently processes the syndrome. This step generates hard decisions (a binary error vector) and soft information (per-qubit confidence levels). In non-convergent BP cases, a gating mechanism examines the BP decoder's output to identify and filter out qubits with oscillating confidence values. In these cases, the refined output serves as input to Tesseract, which then attempts to identify and correct any residual errors. This hybrid approach leverages the high speed of BP decoding and delegates the more challenging decoding instances to Tesseract. Numerical results demonstrate a substantial reduction in overall decoding complexity while maintaining the logical error rate (LER) of the stand-alone Tesseract. Across all tested physical error rates, the proposed method achieves at least 5x reduction in the number of expanded nodes in the Tesseract, with a peak reduction of nearly 15x at a physical error rate of p = 0.05 for the [[126, 12, d < 11]] T1 code, and approximately 8.8x at p = 0.05 for the [[72, 12, 6]] bicycle bivariate (BB) code.

Non-Gaussian interactions are a key ingredient for achieving universality in continuous-variable quantum computation, yet their experimental characterization and the validation of their correct implementation remain challenging tasks. In this work, we focus on a three-mode non-Gaussian trilinear Hamiltonian that has recently been realized in superconducting microwave platforms, and present a comprehensive theoretical analysis of the computational resources it generates, together with experimentally accessible protocols to validate their presence. We systematically investigate its ability to generate two key resources for quantum computation: multipartite entanglement and Wigner negativity. In particular, using displaced-parity Bell tests, we demonstrate the generation of nonlocal states and thereby provide an operational certification of multipartite entanglement in the non-Gaussian states produced by the dynamics. We further quantify the Wigner logarithmic negativity and benchmark it against that of established non-Gaussian resource states. Building on this resource-based characterization, we introduce a measurement-efficient protocol for the experimental validation of the Hamiltonian implementation without requiring full reconstruction of the Wigner function. The protocol combines the measurement of zero-variance observables (nullifiers and stabilizers) with a limited number of targeted phase-space measurements, leading to a drastic reduction of the experimental overhead.

Complex solid-state systems are promising platforms for scalable, high-bandwidth quantum random-number generation, yet certifying the quantum origin of their fluctuations remains difficult because the underlying microscopic dynamics are hard to model and validate. Here we demonstrate semi-device-independent quantum randomness certification from semiconductor spin noise, to our knowledge the first such certificate on any spin-noise source, without relying on a microscopic model of the spin system. The untrusted optical source is constrained by an experimentally tested mean-photon-number bound together with a declared analogue-range and per-sample clipping ceiling, while the trusted receiver is described as a calibrated, noisy, coarse-grained homodyne measurement. Using a semidefinite programme with rigorously controlled Fock-space truncation, we certify randomness that remains private against an adversary holding arbitrary quantum side information. Offline analysis yields certified entropy rates of $3.2$–$3.4$\,Gbit/s from a singly charged (In,Ga)As quantum-dot ensemble and $33$\,Mbit/s from $n$-GaAs in a spin-noise-matched detection mode. This exceeds the certified entropy rate of earlier spin-noise generators by more than two orders of magnitude, and the certificate tolerates a resolved per-symbol energy contribution from the solid-state emitter itself rather than requiring a near-vacuum input.

Unlike the two-qubit entangled and CHSH-nonlocal sets, the steerable and Bell-nonlocal ones have no known general closed-form criterion. For any such operational ability whose failing states form a convex set closed under local unitaries, and for a Bell mixture with arbitrary noise, the $X$ part of the noise gives an upper bound on the definitive threshold, the Bell weight above which the mixture attains the ability. That bound is the tightest that the seven of the fifteen Pauli expectation values fixing the $X$ part can support. The same theorem shows that a state has the ability whenever its $X$ part does, so partial tomography of a state can certify its ability. When noise is of $X$ form, the mixture carries a relative phase between the noise and Bell coherences that cannot be gauged away by local unitaries, and it controls the threshold through interference. We prove a monotonicity law: the threshold is nondecreasing in this phase, whether or not a closed-form criterion for the ability exists.

We investigate the impact of self-interactions on the Rényi and entanglement entropies of a scalar field on $(2+1)$-dimensional spacetimes, whose spatial sections are modeled by fuzzy spaces, specifically the fuzzy sphere and the fuzzy disc. We compute the first-order perturbative correction induced by a $\lambda\phi^4$ interaction using the Green's function approach. In contrast to the free theory, where the entanglement entropy is dominated by degrees of freedom near the entangling boundary and obeys an area law, we find that the interaction correction has an extensive bulk contribution, receiving significant contributions from degrees of freedom throughout the fuzzy space. For the fuzzy sphere, the correction exhibits strong infrared sensitivity associated with the zero mode. We isolate and resolve this zero-mode IR divergence by projecting out the zero mode, thereby obtaining a physically meaningful quantity. In the commutative continuum limit, the interaction correction has the same degree of UV divergence as the free entropy but does not obey a pure area law. Furthermore, we analyze the Moyal plane limit, where the interaction correction exhibits a distinct IR divergence. We discuss the physical origin of these extensive bulk features and examine their possible connection to the celebrated UV/IR mixing phenomenon in noncommutative quantum field theories.

We construct a nonlocal game that self-tests a maximally entangled qubit strategy among pure full-Schmidt-rank projective strategies, but admits an inequivalent optimum using one nonprojective measurement. This resolves a conjecture of Baptista et al. on imposing full rank and projectivity simultaneously. The construction combines CHSH with an auxiliary game $G$ that forces deterministic answers under these assumptions and admits a trine POVM optimum without them. We classify the optimal correlations of $G$ as a line segment parametrized by the tracial states of $\mathbb{C}\oplus M_2(\mathbb{C})$. Projectivity on the state support removes the matrix summand, whereas projective dilations with nonzero nonabort probability have a nontracial local state whose zero left ideal is not two-sided. Finally, a family in local dimension six shows that the full-rank PVM self-test is not robust.

Symmetry plays a central role throughout physics, from Fourier analysis on discrete lattices to the classification of elementary particles in the standard model. In finite quantum systems, symmetries are often discrete, such as reflection and rotational symmetries. Here, we present the SIM-GRAPH method (Symmetric Ising Models - Graph Reduction And Projected Hamiltonians), which uses such symmetries to efficiently calculate ground-state observables of interacting quantum systems. By projecting all interactions onto a symmetric subset of the system, the method effectively reduces the number of sites, thus providing an exponential speedup over standard exact diagonalization. Furthermore, we introduce two extensions that broaden the applicability of the method and allow for a controlled trade-off between computational cost and accuracy.

Magic-state cultivation suppresses errors by measuring logical Clifford checks and discarding inconsistent outcomes. For an entangled resource, several measurement branches are usable, so their outcomes form a multibit classical record whose corruption can produce a logical-frame error. We show that this measurement record can be protected as a binary linear code. For any third-level Clifford-hierarchy unitary $U\in\mathcal C_3$, every parity of the branch bits can be measured by a commuting Hermitian Clifford check $C(v)=UX(v)U^\dagger$. Choosing which parities to measure therefore defines a binary code $y(a)=aG$. If the valid records have minimum distance $d$, at least $d$ readout-bit flips are required to confuse one valid branch with another, giving $P_{\rm wv}=O(q^d)$. A Plotkin bound limits the length of any binary branch record, and the Clifford schedules attain this limit: at distance four, six logical measurements suffice for $|CS\rangle$ and seven for $|CCZ\rangle$, compared with eight and twelve under independent repetition. Thus restricting the logical schedule to Clifford parities requires no additional measurements. In a native-CZZ-assisted Steane implementation, the $[6,2,4]$ CS schedule is also the unique minimum-cost distance-four solution within the compiled Clifford-check family, reducing the cultivation core by $26.6\%$ in active locations. State-vector simulations without a final ideal code-space projection further show higher acceptance and approximately half the residual error weight on the two Steane blocks. Coding the logical measurement record therefore reduces both measurement redundancy and compiled fault-tolerant overhead.

Magic-state cultivation has so far focused mainly on single-qubit non-Clifford resources. We develop a direct cultivation architecture for the entangled state $|CS\rangle=CS|++\rangle$. Two commuting Clifford involutions project onto four usable branches related by Pauli-frame updates. A minimal six-bit $[6,2,4]$ record protects the branch label against readout errors that map one valid record to another. Verified CAT$_7$ gadgets, Steane error detection, CZZ-based controlled checks, and immediate Steane-to-surface expansion form the complete factory. The decoder uses 263 operational detector bits, while 168 additional bits are withheld for later validation. Decoding proceeds through exact low-order resolution, a precomputed higher-order catalogue, and four-coset BP+OSD. Under the stated active-location stochastic-Pauli model, exact enumeration finds no accepted closed-boundary logical-failure mechanism through fault order two, while explicit order-three failure mechanisms exist. Finite-$p$ simulations quantify acceptance, residual syndromes, and decoder workload, and targeted sampling of order-three faults estimates the leading logical-error channels. Optimizing the direct $d=5\rightarrow13$ expansion reduces accepted-output operation count by approximately 35–37%. We compare the two routes at the same binary logical-error rate. Direct CS remains cheaper in operation count at the two lower-noise benchmark points even when the three-$T$ route is given pre-existing output patches. The ordering reverses between $8\times10^{-4}$ and $9\times10^{-4}$. These results show that an entangled non-Clifford state can be cultivated directly with a protected branch record and an explicitly certified fault-order-three output channel.

High Performance Computing-Quantum Computing (HPCQC) platforms expose multiple Quantum Processing Units (QPUs) that may differ in size, topology, native gates, and noise characteristics. For current noisy devices, errors compound along the compiled circuits quickly, and minimizing them, that is, maximizing the circuits' execution fidelity, is essential for reliable results. Fidelity depends on the compilation to a specific target device: the same high-level circuit may produce different executables and, therefore, different expected fidelities across QPUs. We present a low-overhead fidelity-aware scheduling framework for multi-QPU systems based on a Graph Neural Network (GNN) that estimates, before compilation, the expected fidelity of each circuit on each available QPU. Then, a tunable scheduler uses these estimates to control the trade-off between execution fidelity and parallelism. Results show that this framework allows for approximating an exhaustive fidelity-based assignment, saving computational resources compared to a brute-force approach that compiles each circuit on every device.

Modern quantum algorithms are increasingly formulated as coherent procedures for implementing polynomial transformations of operators and singular values. This perspective provides a powerful and unifying language for quantum algorithm design, connecting a wide range of distinct problems through five closely related key tools: block-encoding, qubitization, QSP, QSVT and GQSP. Block-encoding embeds non-unitary matrices into larger unitaries; qubitization converts block-encodings into structured operators; QSP, QSVT and GQSP enable polynomial transformations with near-optimal query complexity. Together, these techniques form a general toolkit for transforming matrix functions into implementable quantum circuits. This paper develops these techniques from first principles as a unified framework for constructing quantum algorithms. We apply this framework to representative applications to highlight design principles and demonstrate how distinct algorithms can be constructed from a unified sequence of operator transformations. A central contribution is a systematic decision workflow for selecting the appropriate approach according to the operator structure and the desired transformation polynomial. This perspective clarifies when direct GQSP or through qubitization, or Laurent expansion, or QSVT is most appropriate. We organize algorithmic design into an end-to-end pipeline: identifying the target matrix function, constructing an appropriate block-encoding, determining the relevant spectral domain, designing a polynomial or Laurent-polynomial approximation, synthesizing the phase factors, and translating the transformation into an executable quantum circuit. By applying this unified framework to example applications, we showcase a practical methodology for reasoning, designing, and implementing quantum algorithms based on polynomial transformations.

Can propagating gravitational waves serve as operational probes of the quantum nature of gravity? We address this question by developing a unified theoretical framework that combines spacetime geometry, quantum information, and gravitational-wave physics. Starting from the geodesic deviation equation in linearized General Relativity, we derive the effective detector Hamiltonian directly from spacetime geometry and construct the complete quantum dynamics for detector subsystems interacting with both classical and quantized propagating gravitational-wave fields. This unified formulation enables a direct comparison between classical and quantum descriptions of gravitational radiation within the same physical framework. We demonstrate that classical gravitational-wave backgrounds can induce mixedness in the detector state but cannot generate genuine quantum correlations between the detector subsystems. In contrast, quantized gravitational waves coherently mediate gravity-induced entanglement, quantum coherence, quantum memory, and nonclassical correlations, providing clear operational signatures of the quantum nature of propagating gravitational radiation. We further discuss how mesoscopic quantum mechanical oscillators offer a promising route towards experimentally probing these effects. Our results establish a geometric and quantum-information-based framework for exploring quantum gravity through propagating gravitational waves.

Primitive quantum speedups are interface-relative: they depend on the input access used to run the primitive and on the output contract used to consume its state or samples. This paper introduces a transcript-level admissibility relation \(A_M\preceq_{\mathrm{int}}A_Q\), defined relative to the declared implementation package of the quantum interface. It identifies which adaptive classical access transcripts that same package licenses, with all setup, transcript-generation, and precision overheads charged. The main application is an operational audit for normalized-Betti estimation in clique-complex TDA, separating three declared-interface regimes. Reversible indexed simplex interfaces certify matched classical simplex sampling and local Laplacian row access by evaluating their reversible routines on single computational branches. Membership-based preparations induce a rejection route of overhead \(\binom{n}{k+1}/|S_k|\). Abstract spectral or block-encoding interfaces require an accompanying implementation package, transcript reduction, or shared representation. Under the indexed certificate and interface closure, the end-to-end cost is fixed by the imported estimator's spectral dependence on the gap \(\gamma\); the concretely realized bounded-treewidth family already admits exact \(\mathrm{poly}(n)\) classical Betti computation by rank over \(\mathbb{Q}\). A low-rank separation supports the role of access and output contracts.

Recent work in quantum key distribution (QKD) has yielded finite-size keyrates based on convex optimisation problems, using the framework of entropy accumulation. Multiple solvers have been developed to address these optimisations in recent years, but have been based on a somewhat elaborate framework using sophisticated algorithms, in order to accommodate a broad range of QKD protocols. In this work, we note that for basic QKD protocols such as qubit BB84, the keyrates can be easily computed using off-the-shelf solvers instead, by obtaining suitable tangent lines to lower bound terms in the objective function. We compute the resulting finite-size keyrates and compare them to previous work. Moreover, we extend this approach to the six-state protocol, by deriving closed-form expressions for the single-round Rényi entropies in the protocol. This should facilitate subsequent study of the six-state protocol via entropy accumulation.

Quantum channel discrimination is a primitive task for identifying, verifying, and benchmarking quantum dynamics. Previous studies have primarily considered either the best-case tester-input setting or the worst-case jammer-input setting. Here, we introduce a game-theoretic framework in which both the tester and jammer control separate inputs. Combining three input structures, characterized by whether the tester and jammer use entangled inputs or IID inputs across channel uses, with four information patterns, determined by the visibility of the jammer's strategy and its knowledge of the true hypothesis, yields twelve game models. We provide exact finite blocklength hypothesis testing characterizations of all twelve models in terms of nine minimax hypothesis testing divergences and derive their asymptotic Stein exponents. Notably, for entangled jammers, neither the visibility of the jammer's strategy nor its knowledge of the true hypothesis affects the asymptotic Stein exponent, whereas the information pattern remains consequential for IID jammers. As an example, we study the discrimination of a general channel from a replacer channel and show that all asymptotic Stein exponents coincide with the same additive, single letter quantity. We further develop a general argument that upgrades achievability results to strong converse results, thereby establishing strong converse properties for several game models, resolving an open problem in composite hypothesis testing posed by Berta et al. [Commun. Math. Phys. 385, 55 (2021)], and strengthening several recent results of Lami [arXiv:2510.06340]. The framework and techniques developed here may support future studies of quantum information tasks involving competing roles.

Device-independent certification of a quantum gate requires the input and output tests to identify the same reference qubits. Self-testing the output Choi state alone does not guarantee this consistency. We develop a robust certification scheme for Boolean-phase gates, a broad family of computational-basis diagonal gates specified by Boolean functions. Boolean derivatives convert the target-dependent phase information into classical signs that can be evaluated from local measurement outcomes. This leads to Bell tests built from CHSH blocks using two binary measurements per party and no entangling measurements. At maximal violation, the tests self-test the normalized Choi state and the measured observables. Away from the maximum, they give an explicit affine lower bound on the extracted-state squared fidelity that is uniform over all Boolean functions and valid in arbitrary local dimensions. We then combine an identity test and a gate-output test in an independent-source network in which the reference devices use the same physical observables, obtaining a closed-form Choi-fidelity bound for an effective \(n\)-qubit channel. For CCZ, a joint six-party analysis gives a stronger robustness bound without changing the Bell expression or measurement settings. The construction shows how the algebraic structure of a gate can shift target-dependent information from quantum measurement design to classical processing of local outcomes.

By decomposing quantum dynamics across the Lie orbits of a list of observables, we find polynomial bounded classical simulations for the dynamics of the quantum system given a polynomial sized dynamic Lie algebra (DLA) for the generators of the quantum system. To do so, we describe how to construct the Dynamic Observable Subspace (DOS) that captures all the relevant dynamics for calculating expectation values for a specific observable for Pauli strings, diffusor mixers, and general local generators. Efficient sparse matrix representation, decoupling nonlinearity from such representation and basis construction with permissible pruning allows us to simulate the closed dynamics of such systems with hundreds of qubits. Moreover, we find that while restricted DOS circuits may not express the space of an associated Hamiltonian, they can dramatically outperform a fully expressive circuit due to the absence of the Barren Plateau. While classically simulatable, such circuits can still exhibit a form of quantum advantage through inference, act as warm starting for more expressive circuits, and find high quality trial states for Quantum Amplitude Amplification or Quantum Phase Estimation. In the simulation of quantum dynamics, we find that our restricted circuit can be simulated in polynomial time while producing high quality guiding state for downstream tasks like Quantum Phase Estimation with significantly lower energy than circuits with full expressivity.

Distributed quantum networks rely on spatially separated, independently operated quantum systems as network nodes, whose emitted photons must be interfered with high visibility to establish end-to-end entanglement. Crucially, for network-relevant applications, high visibilities must be achieved over prolonged timescales to reduce overheads for error correction, and to increase network rates. Here, we demonstrate experimentally that silicon vacancy $\mathrm{V_{Si}}$ color centers in silicon carbide (SiC) achieve these requirements, notably in a mass-deployable fashion. We integrate $\mathrm{V_{Si}}$ centers in different industrial-grade SiC p-i-n diodes, which are controlled via voltage biassing. This way, we demonstrate both, spectral overlapping of 19 randomly selected $\mathrm{V_{Si}}$ centers in different diodes, as well as spectral narrowing close to the lifetime limit, i.e., typically below 60 MHz. Notably, these performance parameters are long-term stable, e.g., readjusting the p-i-n diode bias is required only every 8.4 hours, which reduces significantly the overall experimental overhead. We then use these assets to demonstrate high-quality two-photon interference between $\mathrm{V_{Si}}$ centers located in two different cryostat setups, which are spatially separated by two meters. Notably, we perform a 26-days long measurement campaign, demonstrating two-photon interference with state-of-the-art raw interference visibilities of 82%, which aligns with the current state-of-the-art. These results establish $\mathrm{V_{Si}}$ centers in industry-grade SiC devices as a scalable, spectrally stable building block for distributed quantum networks.

We study the two-weight decision version of quantum approximate counting: given oracle access to $x\in\{0,1\}^N$, distinguish $|x|=M$ from $|x|=M+\Delta$ with success probability $1/2+\zeta$. Using the multiplicative adversary method, we prove $\Omega\left(\max\left\{\zeta\sqrt{(N-M)(M+\Delta)}/\Delta,\sqrt{\zeta N/\Delta}\right\}\right)$. The same parameter dependence follows from the polynomial-method characterization of the two-layer symmetric function by Podder, Yao, and Ye. Our contribution is a multiplicative-adversary derivation that tracks the progress produced by individual oracle queries. For the first term, after complementing the input if necessary, we assume $M+\Delta\le N-M$. We use the Hamming-layer subspaces from the eigenspace method of Ambainis, Spalek, and de Wolf and compose their adjacent-layer unitary maps to relate the two nonadjacent promise layers. After fixing the queried coordinate, the analysis block-diagonalizes into four-dimensional subspaces. An exact calculation of the one-query progress ratio gives the first lower bound. The same estimate also implies $\left\|(I-\widehat{\Pi}_{\mathrm{bad}})\lvert\Psi^T\rangle\right\|^2=O\left(T^2\Delta^2/((N-M)(M+\Delta))\right)$ for the coherent input superposition used in the adversary argument. For the second term, we prove directly using a three-eigenvalue multiplicative adversary that unique OR on $n$ bits with success probability $1/2+\zeta$ requires $\Omega(\sqrt{\zeta n})$ queries, and then reduce unique OR to the two-weight counting problem.

Dirac Cellular Automata (DCA) provide a framework for simulating Dirac dynamics, yet the rigid coupling between spatial and temporal resolutions can introduce artificial phase-matching symmetries on finite grids that suppress interference phenomena such as Zitterbewegung. In this work, we propose a Split-Step Dirac Cellular Automaton (SDCA) that enables continuous-time Dirac evolution at fixed spatial discretization. By employing a Trotterized fractional-step scheme in the momentum representation, SDCA breaks the phase-matching cancellation present in the standard DCA and recovers the interference dynamics of the continuous-time limit. We benchmark the SDCA through analytical and numerical studies and demonstrate its implementation on IBM Quantum processors. Despite the increased circuit depth required for finer temporal resolution, the NISQ implementation reproduces the characteristic velocity oscillations and entanglement-entropy dynamics of the continuous-time model. We further investigate hardware-topology trade-offs and dynamic circuit implementations of the Quantum Fourier Transform (QFT), highlighting the competing effects of gate errors, measurement, and feed-forward latency. These results demonstrate that SDCA provides a practical framework for improving temporal resolution while maintaining a fixed spatial quantum register, enabling the exploration of relativistic quantum dynamics on near-term quantum devices.

In this note, we show that the generalized Bures–Wasserstein distance induced by the generalized fidelity does not satisfy the data processing inequality in dimensions greater than two. In dimension two, although we do not settle the DPI in full generality, we derive two sufficient conditions guaranteeing it by using an explicit formula for the real part of the generalized fidelity. Furthermore, we find a necessary and sufficient condition under which the generalized fidelity reduces to the Uhlmann fidelity. Lastly, we will show that the generalized Bures–Wasserstein distance is not convex in dimensions greater than two.

Generalized Arimoto–Blahut (AB) algorithms are widely used in information theory and quantum optimization, but monotonic objective decrease and numerical stabilization do not guarantee global optimality. We establish necessary and sufficient conditions for the global optimality of full-rank AB fixed points for convex differentiable objectives under linear constraints. An AB fixed point is globally optimal if and only if the AB update direction and the objective gradient differ by an element of the constraint normal space at that point. The same compatibility condition characterizes agreement between individual AB and mirror-descent (MD) updates, whereas pathwise equivalence requires it along the entire common trajectory. Thus, an AB algorithm may follow a trajectory different from MD and still reach the global optimum. We also develop a posteriori optimality certificates based on feasible directional derivatives, including finite-difference upper bounds on the objective gap that require only objective evaluations. For channel relative entropy between dephasing and depolarizing channels, we analytically identify the global minimizer as the unique full-rank AB fixed point, although pathwise equivalence fails. Numerical experiments illustrate convergence of AB and MD along different trajectories and validate the certificates. By contrast, an amplitude-damping example shows that a monotone AB iteration can stabilize at a suboptimal fixed point, whose nonoptimality is detected by the finite-difference certificate. These results provide structural and computable criteria for assessing global optimality in quantum AB algorithms.

Quantum approaches for combinatorial optimization problems have attracted considerable attention in recent years. Among these approaches, Pauli Correlation Encoding (PCE) has emerged as a promising framework for quantum devices with limited qubit resources because it embeds optimization variables in expectation values of Pauli strings. However, the mechanisms underlying its performance and the reasons for its saturation remain unclear. In this work, we investigate these questions through a systematic analysis of expressivity and trainability. First, we compare PCE with classical surrogate models based on tensor networks whose structures progressively approach the topology of the PCE circuit. The results show that PCE attains comparable solution quality with substantially fewer trainable parameters, indicating strong parameter efficiency. Second, to determine whether the performance saturation of conventional PCE is caused by insufficient expressivity or by optimization difficulty, we perform a diagnostic expressivity test in which the circuit is trained toward reference configurations for Max-Cut. The results show that even shallow PCE circuits can represent strong solutions, indicating that the main bottleneck is not the representational power of the ansatz, but the trainability under the relaxed objective function. Motivated by this finding, we propose a multistage continuation framework that gradually transforms a smooth relaxed objective into a sharper objective that more closely approximates the target discrete problem. Numerical experiments on G-set instances with 800 vertices show that the proposed method consistently outperforms conventional PCE and is competitive with representative graph neural network (GNN) methods. These results clarify the main factors behind PCE performance and provide a practical strategy for improving PCE on quantum devices with limited qubit resources.