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arXiv2026

Non-Multiplicativity of the Holevo Barycenter of Quantum Channels

The Holevo barycenter of a quantum channel is the unique output state obtained as the average output of any ensemble achieving the Holevo capacity. Given two quantum channels, the multiplicativity problem asks whether this barycenter tensorizes under parallel composition, namely whether the barycenter of the product channel coincides with the tensor product of the individual barycenters. This question is closely related to the additivity problem for the Holevo capacity: additivity implies tensorization of the Holevo barycenter, while tensorization alone is not sufficient for additivity. Although a construction is known that demonstrates the existence of channels with non-additive Holevo capacity, their corresponding Holevo barycenters still tensorize, leaving open whether multiplicativity might ultimately hold universally. Here, we answer this question in the negative by exhibiting channels for which the Holevo barycenter is not multiplicative under the tensor product of the channel with itself. Moreover, we show that the entropy of the Holevo barycenter is neither universally subadditive nor universally superadditive under tensor product.

quant-ph↗

arXiv2026

A Block Tensor Train Burer-Monteiro Framework for Low-Rank Quantum State Tomography

Quantum state tomography is a fundamental technique for estimating the state of a quantum system from measured data and plays a crucial role in evaluating the performance of quantum devices. However, standard estimation methods become computationally prohibitive as the system size increases due to the exponential growth of the density matrix, describing a quantum state, with the number of qubits. We propose a low-rank tensor-network framework for mixed-state quantum state tomography based on a block tensor train (Block-TT) factorization. Specifically, the density matrix is represented as the contraction of a Block-TT with its Hermitian transpose, yielding a TT analogue of the Burer-Monteiro factorization. This parameterization guarantees Hermiticity and positive semidefiniteness by construction while compressing the number of optimization variables from exponential to linear in the number of qubits. Building on this representation, we develop single-site and two-site density matrix renormalization group (DMRG) algorithms for estimating quantum states from compressed measurements. The resulting methods operate directly on the compressed parameterization, support adaptive rank refinement, and exploit efficient tensor-network contractions for expectation-value evaluation. The framework is applicable to a broad class of low-rank quantum states, including pure states, nearly pure states, and ground states that admit accurate tensor-network approximations. Numerical experiments demonstrate accurate state reconstruction from limited measurements together with substantial reductions in memory requirements and computational cost compared with conventional low-rank tomography methods.

quant-ph↗

arXiv2026

DPRQ: A Dynamic Programming-based Qubit Routing Algorithm for Collective Communication in Distributed Quantum Computing

Distributed quantum computing (DQC) offers a promising approach to scale quantum computing by overcoming the resource limitations of a single quantum processor. However, inter-node communication remains a major bottleneck of DQC due to inefficient and error-prone entanglement distribution. Optimizing inter-node communication can not only reduce the amount of entanglement resource needed to execute a quantum circuit but also improve execution speed and accuracy of the results. This paper proposes DPRQ, a qubit routing algorithm for minimizing inter-node communication in distributed quantum circuits divided into collective communication blocks. Unlike current approaches that utilize greedy block-level qubit routing strategies, DPRQ employs a dynamic programming-based technique focused on global circuit-level optimization, while capturing inter-block dependencies. We evaluated DPRQ on four sets of quantum circuits and a variety of DQC configurations. The results demonstrate that DPRQ's innovative routing strategy achieves an average of 24.40% reduction with a maximum of 85.06% reduction in inter-node communication, when compared to the state-of-the-art collective communication-based DQC compiler QuComm.

quant-ph↗

arXiv2026

Comparison of D-Wave Quantum Annealing and Gibbs Monte Carlo for Sampling from a Probability Distribution of a Restricted Boltzmann Machine

A local-valley (LV) centered approach to assessing the quality of sampling from Restricted Boltzmann Machines (RBMs) was applied to the latest generation of the D-Wave quantum annealer. D-Wave and Gibbs samples from a classically trained RBM were obtained at conditions relevant to the contrastive-divergence-based RBM learning. The samples were compared for the number of the LVs to which they belonged and the energy of the corresponding local minima. No significant (desirable) increase in the number of the LVs has been achieved by decreasing the D-Wave annealing time. At any training epoch, the states sampled by the D-Wave belonged to a somewhat higher number of LVs than in the Gibbs sampling. However, many of those LVs found by the two techniques differed. For high-probability sampled states, the two techniques were (unfavorably) less complementary and more overlapping. Nevertheless, many potentially "important" local minima, i.e., those having intermediate, even if not high, probability values, were found by only one of the two sampling techniques while missed by the other. The two techniques overlapped less at later than earlier training epochs, which is precisely the stage of the training when modest improvements to the sampling quality could make meaningful differences for the RBM trainability. The results of this work may explain the failure of previous investigations to achieve substantial (or any) improvement when using D-Wave-based sampling. However, the results reveal some potential for improvement, e.g., using a combined classical-quantum approach.

cs.LG↗

arXiv2026

Ancilla-Efficient QSAMPLE Preparation for Reversible Markov Chains

Preparing quantum samples (QSAMPLES), coherent encodings of stationary distributions of reversible Markov chains, is a fundamental primitive in quantum sampling, particularly for quantum simulated annealing. A central limitation of existing phase-estimation-based frameworks is the ancilla qubit overhead. In this work, we present a new end-to-end framework requiring only one ancilla qubit in the working register. The key technical ingredient is a selective phase compiler circuit using one ancilla qubit, built from a generalized quantum signal processing (GQSP)-based projector onto the 1-eigenspace of the qubitized Szegedy walk. Embedding these selective phase compilers into the fixed-point amplitude amplification (FPAA) procedure and iterating yields a quantum algorithm that, given an initial state, oracle access, lower bounds on the overlaps between adjacent states, and lower bounds on the phase gaps, outputs a QSAMPLE within any desired trace distance and thus total variation distance. The query complexity scales inversely with the square roots of both the minimum overlap and the minimum spectral gap of the Markov chains across the cooling schedule, up to polylogarithmic factors. We also perform simulations to verify how our qubit and query complexity evolve with the trace distance, and how this work compares to the previous framework. These results establish two improvements over the previous framework by Wocjan and Abeyesinghe. First, the working-register ancilla cost is reduced to one. Second, by inserting our GQSP-based selective phase compiler into the FPAA procedure, we improve the QSAMPLE transport overlap dependence from inverse minimum overlap to inverse square-root minimum overlap, relative to their Grover pi-over-three fixed-point method. Finally, as a direct application, we apply the quantum algorithm to prepare a Gibbs QSAMPLE and obtain a rigorous complexity analysis.

quant-ph↗

arXiv2026

Random Garbage Separates XOR from Forward-Only Queries

We give exponential quantum query separations between the standard XOR interface and two forward-only interfaces that supply neither an adjoint nor an inverse oracle. Let $X=\F_2^n$, $N=|X|$, and $f_{h,r}(x)=(h(x),x,r_x)$, where $h:X\to X$ is promised to be either a permutation or a Simon two-to-one function, and $r$ is a fixed table of $n$-bit tags, unrestricted by the promise and reused on every query. The resulting problem is solvable with at most $n+2$ standard XOR queries, but has forward-erasing query complexity $Θ(\sqrt N)$. This answers affirmatively open question 11 in [Scott Aaronson. Open problems related to quantum query complexity. ACM Transactions on Quantum Computing, 2(4):14:1-14:9, 2021] . We also embed these instances into permutations. The detailed construction retains the copy of $x$ in each prescribed output, but for these promises that copy can be replaced by one bit that distinguishes the two inputs in every Simon pair. This gives a permutation domain of size $L=4N^2$ and a permutation problem with the same standard-query upper bound and forward-only in-place query complexity $Θ(\sqrt N)=Θ(L^{1/4})$. Both lower bounds remain valid with a clean coherent bypass. The common lower bound uses an analysis-only recording replacement. In the replacement computation, tracing out the fixed random tag table after $T$ calls gives a sum of positive-semidefinite operator contributions, each depending on $h$ at no more than $T$ addresses. On such a set, the restrictions induced by random permutations and random Simon functions differ only if the set contains a hidden Simon pair, an event of probability $O(T^2/N)$.

cs.CC↗

arXiv2026

Capability-Gated Conformance Testing of Quantum Error-Correction Decoder Libraries

A quantum error correction decoder is a library other people's results depend on, judged in one dominant way. Sample errors, decode, and count wrong logical observables. We ask what else can be checked there. Our conformance contract needs no oracle. One check asks that a returned correction explain the syndrome in the caller's index space. The other hands a decoder one instance under two presentations differing only in bookkeeping, where two feasible corrections of different weight prove the heavier is not minimum-weight. Verdicts are gated on what each library declares, so a firing contradicts a published guarantee. Nine configurations from five public libraries give three results. Documentation answers 4 of 54 capability questions. Bounded-distance correctness, the property callers most depend on, has a direct declaration yield of 0.0%, though its hypotheses hold in 62.1% of cases. Presentation sensitivity is real but shallow. One solver moved to a 26% heavier correction under a different numbering, which reaches the logical class at most once in twenty thousand shots. Established evaluation misses corruptions that preserve logical parity, while one summation over the caller's weights catches every one we injected. All 639 certificates ship as bundles a standalone verifier re-derives from first principles.

quant-ph↗

arXiv2026

2-Fold Forrelation is in QAC$^0$

We show that 2-fold Forrelation with inverse-polylogarithmic promise gap can be solved, with bounded error, by polynomial-size QAC$^0$ circuits. Unlike the standard oracle-based Forrelation algorithm, our circuits receive the input explicitly, in the same form as the AC$^0$ circuits against which Forrelation is known to be hard. At constant gap, this yields a natural promise-problem separation between QAC$^0$ and AC$^0$.

quant-ph↗

arXiv2026

QCxSimulation: Scatter-Aware X-Ray Projection Radiography via Discrete-Time Quantum Walks

X-ray projection radiography is a non-invasive imaging technique used in medical diagnostics and industrial inspection. The simulation of X-ray projections is commonly used to optimise acquisition protocols and improve image quality before performing costly scans. Classical photon transport simulations that include realistic X-ray scattering physics are computationally expensive because they require the sampling of a large number of distinct scattering paths. This limits the practical exploration of parameter spaces such as beam energy. Quantum computing offers the potential to solve high-dimensional problems faster by making use of quantum properties such as superposition. This work introduces a discrete-time quantum walk algorithm that simulates the transport of X-ray photons through heterogeneous volumes. It approximates the physics of X-ray projection radiography, including processes such as photoelectric absorption and higher-order scattering, including Compton and Rayleigh scattering. The quantum walk encodes all admissible photon paths into a single quantum state, enabling all scattering histories to be propagated simultaneously via the superposition principle. This quantum state representation enables flexible readout of various imaging modalities, including the primary, i.e., unscattered, image, or images exclusively containing Rayleigh and Compton scattering of specified orders. A quantitative comparison with classically computed reference simulations shows that the proposed quantum walk accurately reproduces radiographic projections, given the limitations of the underlying physical model. These results indicate that quantum circuits for X-ray transport can produce accurate radiographic images and imply that, as quantum hardware scales up, these algorithms could outperform classical Monte Carlo-based approaches in large-scale, scatter-aware virtual imaging studies.

quant-ph↗

arXiv2026

Asymmetric quantum error correction efficiently tackles application-specific noise effects

Noise is a major challenge for current quantum computers. It can be broadly categorized into bit-flip and phase-flip errors. These two types do not necessarily affect the executed algorithm, thus also the application, in the same way. We illustrate this general effect for the example of the quantum approximate optimization algorithm (QAOA) applied to a small instance of the flight-gate assignment (FGA) problem. We compare bit-flip and phase-flip Pauli noise under both layer-level and gate-level noise models, using two circuit decompositions of the same ideal QAOA unitary: a CNOT-based decomposition and a native-$R_{ZZ}$ decomposition. In the simulations, bit-flip noise produces the larger degradation in the performance of the quantum optimization. The asymmetry is most visible in the layer-level and native-$R_{ZZ}$ simulations. We explain this by how the errors affect mixing, final measurements, and how they propagate inside the circuit. We then exploit these insights to tackle noise particularly efficiently using asymmetric error-correcting codes. As an illustration, we use the quantum parity code (QPC), a generalization of the 9-qubit Shor code, and show that a smaller asymmetric code can achieve nearly the same improvement as a larger symmetric choice. This demonstrates that error-correction resources should be assigned not only according to physical error rates, but also according to how strongly each error channel affects the application. As a result, asymmetric quantum error correction proves useful even in cases where the noise model is symmetric. Finally, we discuss how information about the noise obtained through calibration can be exploited in our approach.

quant-ph↗

arXiv2026

Topology Obstructs Pure Foundation Neural Quantum States

Foundation models for ground states in spin-1/2 systems are a promising method for problems ranging from quantum chemistry to identifying new phase diagrams. Nearly all such models are currently pure-states that condition on the Hamiltonian's parameters, whose Monte Carlo samples give energy estimates according to the variational principle. In this contribution, we show that this representation is topologically obstructed. For any gapped Hamiltonian family whose ground-state bundle is non-trivial, every continuous normalized state-vector model has zero fidelity with the ground state at some parameter value in the Hamiltonian family. For that value, the energy is at least one spectral gap, $Δ$, with an $O(Δ)$ gap in an open-neighbourhood of that point. We show that this is a sufficient no-go also in the case of degenerate ground-state manifolds, time dynamics, and periodic systems with mixed space-time topology, demonstrating these obstructions on one- and two-qubit systems. We discuss how this causes a spike in the fidelity susceptibility, giving a numerical signature of a phase-transition where there is none. We then show that operator-valued models canonically avoid these obstructions and preserve topological information, implying a structural necessity in representation for foundation neural quantum states.

quant-ph↗

arXiv2026

QROB: Quantifying Realization Overhead in Quantum Compilation via Reverse Construction

Quantum compilation reconciles a program's idealized interaction topology with hardware locality constraints, yet evaluations at scale lack calibrated references for realization overhead. We present QROB, a scalable reverse-construction methodology that generates compilation instances backward from directly realizable configurations, retaining the inverse paths as feasible, compiler-independent references. QROB provides a common evaluation substrate for NISQ SWAP routing and fault-tolerant lattice-surgery scheduling, while extending its reference-preserving principle to capacity-constrained quantum memory-access scheduling. Across systems ranging from 9 to 156 qubits, evaluations highlight QROB's utility as both a diagnostic benchmark and a data source. First, for compiler characterization, QROB reveals substantial realization gaps in existing tools, with NISQ compilers incurring up to 24.1x the reference SWAP cost and fault-tolerant compilers requiring up to 7.0x the reference makespan. Second, as a supervision source for data-driven compilation, a router trained on QROB references outperforms Qiskit SABRE on 84.8% of real-world application circuits. Finally, on real hardware, QROB reference realizations achieve a median mirror-circuit survival rate 1.65x that of full Qiskit O3 compilations across three 156-qubit IBM Heron-r2 processors, demonstrating that closing algorithmic compilation gaps translates directly into physical fidelity gains.

quant-ph↗

arXiv2026

A Novel Steganography Scheme Using Quantum Hilbert Transform

The main goal of steganography is to transmit hidden messages in legitimate-looking communication messages. Phase-domain information hiding, however, has not been fully explored for quantum systems. This work introduces a finite-dimensional Quantum Hilbert Transform (QHT) as a unitary phase operator based on the Quantum Fourier Transform. Using this construction, we develop a QHT-based quantum steganography scheme that embeds classical bits as weak signed phase perturbations of quantum cover states. Bob recovers the hidden message through binary state discrimination, block aggregation, and classical error-correcting decoding.

quant-ph↗

arXiv2026

Promises should be taken seriously: On relativization with promise problems

Relativization is concerned with comparing computational models with black-box access to an oracle. For promise problems, black-box access is not canonical due to inputs outside of the promise being unconstrained. We study two semantics for such access. Under robust queries, a machine must correctly answer regardless of the completion of the problem,, while loose access requires that the internal choices of a machine do not change based on off-promise queries. Our first result separates the language and promise settings. Namely, we construct an oracle $O$ such that $\mathsf{P}^O = \mathsf{BQP}^O = \mathsf{AWPP}^O$, but $\mathsf{PromiseBQP}^O\not\subseteq\mathsf{PromiseP}^O_{\mathsf{/poly}}$. In particular, $\mathsf{BPP}^O = \mathsf{BQP}^O$, but $\mathsf{PromiseBQP}^O \neq \mathsf{PromiseBPP}^O$, showing that results for languages need not transfer to promises. Next, we use loose queries to strengthen the upper bound on the Quantum-Classical Polynomial Hierarchy from $\mathsf{P}^{\mathsf{PP}^{\mathsf{PP}}}$ to $\mathsf{QCPH} \subseteq \mathsf{BP\cdot PP} \subseteq \mathsf{PromiseBPP}^{\mathsf{PP}}$. The same proof also shows $\mathsf{PP}^\mathsf{PromiseBQP} = \mathsf{PP}$. Additionally, we show that $\mathsf{PromiseBQP}$, even when given quantum advice, is self-low under robust queries. Finally, we exhibit an obstruction to transferring language-level counting results to promise classes. Although $\mathsf{AWPP}$ and $\mathsf{APP}$ are low for $\mathsf{PP}$, a corresponding promise analogue would collapse the counting hierarchy as $\mathsf{GapP} \subseteq \mathsf{FP}^{\mathsf{PromiseAWPP}}$. This motivates the introduction of $\mathsf{PromisePostBQP^*}$, which restricts $\mathsf{PostBQP}$ to input-indepencent postselection. By showing that it is low for \PP, we obtain $\mathsf{PP}^{\mathsf{PromiseYQP^*}} = \mathsf{PP}$.

cs.CC↗

arXiv2026

Accelerating Fourier--Motzkin elimination: redundancy removal and the choice of variable elimination order

Fourier-Motzkin elimination computes an inequality description of the projection of a polyhedron onto a subset of its coordinates by eliminating one variable at a time. It is used in several areas of optimisation and computer science, and it is a standard way of obtaining the entropic constraints of a causal structure, where the marginalisation over the latent variables produces such a projection. Its limitation is the growth of the intermediate systems of inequalities, which can be doubly exponential in the number of eliminated variables even though the projection itself grows only as a single exponential. In practice the computational overload of the method therefore depends on two choices: how the redundant inequalities are removed after each step, and the order in which the variables are eliminated. We consider both. We first show, by an explicit example, that Imbert's redundancy test cannot be interleaved with redundancy removal by linear programming. We show that the two methods, however, can be combined soundly if the derivation records used by Imbert's test are re-initialised after every step at which linear programming is used. We then propose a rule for choosing the elimination order of the variables that gives a significant computational advantage, however, at the cost of increased resource usage. We demonstrate this advantage on some random polytopes, where the rule reduces the running time by factors of between 6 and 25 compared with the same elimination under a fixed order. For entropic descriptions of causal structures, with more than 250 inequalities and more than 100 variables to eliminate, our rule keeps the number of inequalities handled at each step one to two orders of magnitude lower than a fixed order.

cs.CC↗

arXiv2026

Adaptive Entangled Game Modules in Artificial General Intelligence

We introduce a probability-wave framework for modeling the collective behavior of interacting adaptive agents, deriving testable eigenmodes through a generalized behavioral intelligence (GBI) nonlocal probability-wave equation. This framework captures a broad range of human intelligence behaviors with analytical mechanisms and offers an indirect method to examine the Liu-Chen-Ao (LCA) hypothesis of nonlocal entangled nerve fibers in the brain through collective trader behaviors. Our empirical analysis of Chinese intraday stock market data demonstrates that adaptive entangled game modes explain 82-94% (89% overall) of observed decision patterns, a sharp contrast to the predictions of neoclassical finance based on independent rational agents. Moreover, 2-12% of behaviors show adaption to intraday news, events, and environments, characterized by dual equilibrium states and abrupt reference point shifts, while purely independent modes occur in less than 5% of cases. These findings empirically support the LCA hypothesis, as observable trading behaviors reflect underlying brain mechanisms and internal intelligence decision-making in behavioral psychology. Our results highlight the necessity of incorporating adaptive entangled game modules into artificial general intelligence (AGI) architectures, addressing the limitations of conventional artificial neural network (ANN)-based AI, which relies on trillions of opaque parameters. By integrating ANN-based AI with probability-wave-based entangled-brain simulations, machine learning can enrich AGI foundation models (FMs) and facilitate the development of human-like processing units (HPUs) that leverage brain-inspired mechanisms. Such HPUs may ultimately create more compact, efficient, and robust AGI systems, particularly for embodied intelligence and robotics.

cs.AI↗

arXiv2026

Nonlinear path-following via the asymptotic numerical method on a quantum processor

Quantum computing offers a promising avenue for advancing computational methods in science and engineering. In this work, we introduce the quantum asymptotic numerical method (qANM), a framework for solving nonlinear path-following problems using quantum computing. Based on the principle of high-order perturbation techniques, the proposed method uses Taylor series expansions to transform complex nonlinear systems into sequences of linear equations, which are then solved using quantum linear solvers. The central objective of this study is to demonstrate nonlinear path-following with the required linear systems solved on real quantum hardware. To realize this objective, we develop the quantum-enhanced Jacobi method (q-Jacobi), an iterative quantum linear solver used in the hardware experiment. Numerical simulations on a quantum simulator validate the convergence of the method. A highlight of this work is a proof-of-principle experiment on a superconducting quantum processor. Despite the noise inherent in near-term quantum hardware, the experiment achieves 98% accuracy in tracking the nonlinear solution path. We believe this work provides a useful reference for applying quantum computing to nonlinear computational mechanics.

quant-ph↗

arXiv2026

Riemannian Optimization for Multi-Player Quantum Games on Product Unitary Manifolds

Quantum game theory is an extension of classical game theory that uses quantum principles in game theory. The Eisert-Wilkens-Lewenstein (EWL) quantum game is an early example of the two-player classical Prisoner's Dilemma transformed into a quantum Prisoner's Dilemma. In the EWL game, the players choose pure quantum strategies represented by unitary matrices. This extension can resolve the classical dilemma by enabling cooperative equilibrium with higher payoff. In this paper, we first discuss the Extended EWL (EEWL) for multiplayer quantum games with mixed strategies. In EEWL, each player controls a set of unitary operators as quantum actions and uses a classical mixed strategy over these actions. The payoffs are defined as expectation values of Hermitian reward operators acting on a shared quantum state, which is generated and measured according to the EEWL protocol. We then propose the Unitary Strategy Matrix Exponential Algorithm (USMEA), a geometry-aware sequential algorithm for the EEWL mixed-strategy setting, in which each player jointly learns a trainable set of local unitary actions and the associated classical mixing probabilities. Thereby it acts as a learning-and-control layer for multi-agent quantum decision systems. We analyze the convergence properties of USMEA under standard smoothness and step-size conditions and validate the theory with numerical experiments. These results show how classical optimization methods can be systematically integrated into the design and analysis of engineered quantum strategic interactions.

quant-ph↗