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186 records · Page 3Linked to original sources
arXiv2026

Quantum Federated Learning Based on Bures--Uhlmann Geometry for Heterogeneous Noisy Clients

Quantum federated learning enables collaborative model training across quantum devices without sharing raw data, and it faces the data and hardware heterogeneity inherent to noisy quantum devices. Utilizing the quantum geometric tensor is a natural remedy, yet pure-state approaches and diagonal approximations discard the correlations that encode parameter incompatibility. To address this, we extend the parameter-space geometry to the mixed states that noisy clients actually prepare. The real part of the resulting mixed-state geometric tensor is the Bures metric, which measures how fast the physical state changes under parameter variation, and the imaginary part is the mean Uhlmann curvature, which quantifies the incompatibility of estimating multiple parameters simultaneously. Accordingly, we employ the Bures metric as a local preconditioner and use the mean Uhlmann curvature to develop an achievable-precision aggregation rule that dynamically down-weights unreliable clients. Furthermore, we establish theoretical guarantees by proving a convergence theorem and a variance-dominance proposition. Empirical evaluations on a trapped-ion quantum emulator demonstrate that the proposed method maintains high accuracy across diverse device-heterogeneity conditions and outperforms standard federated averaging, whose accuracy degrades under strong noise.

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arXiv2026

Optimizing Encoder Circuits of Entanglement-Assisted Quantum LDPC Codes via Beam Search

In encoder circuits built on the stabilizer formalism, the dominant contribution to circuit complexity comes from the use of controlled (CNOT) gates, making CNOT-count reduction a central circuit-design objective. Entanglement-assisted (EA) quantum QC-LDPC codes offer strong error-correction capabilities with structured parity-check matrices, but their practical use depends on efficient encoder circuits and the availability of pre-shared Bell pairs (ebits). In this paper, we adopt a prior entanglement-assisted QC-LDPC (EAQC) encoder construction. We formulate the encoder optimization as a search over GF(2) row operations that decompose the binary matrix derived from its CNOT sub-sequence. We solve this problem using a beam search algorithm guided by a Hamming-distance heuristic. For the tested EA quantum QC-LDPC code families, the proposed method achieves CNOT-count reductions of 7.3-34.0% relative to the baseline EAQC encoder. The optimized circuits also outperform the Patel-Markov-Hayes and greedy cost-minimization baselines, and are verified by stabilizer-tableau simulation. These results show that substantial encoder simplification is possible for structured EA QC-LDPC codes.

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arXiv2026

Benchmarking Zero-Setup Quantum Circuit Simulators

Practitioners increasingly rely on hosted simulation environments, but their performance characteristics remain poorly documented. We present a systematic benchmarking study of GPU-accelerated approximate quantum simulation across two widely used methods: matrix product states (MPS) and Pauli path simulation (PPS), comparing BlueQubit (a hosted tool that handles hardware provisioning, simulator configuration, and job orchestration) against AWS Braket, Quantum Rings, Qiskit pauli-prop, and PauliPropagation (written in Julia). For MPS, we find that GPU runtime yields sub-quadratic scaling with bond dimension, with a growing advantage over CPU at increasing scale. For Pauli path simulation on IBM's 127-qubit kicked Ising benchmark, GPUs deliver up to ${\sim}1{,}700\times$ speedup at fine truncation thresholds ($δ= 2.5 \times 10^{-5}$, 27.6M Pauli terms), and are the only backends that reach accuracy regimes below $δ= 10^{-5}$, which remained inaccessible to the commodity CPU-based implementations and self-contained SDKs evaluated here. We also provide a reproducible characterization of these simulators across regimes, including tradeoffs that isolated evaluations do not show. All benchmarking code and configurations are in a public GitHub repository.

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arXiv2026

Reliable Sample-Level Quantum Error Mitigation via Dominance-Aware Clustering

Many quantum algorithms for classically difficult optimization tasks must return high-quality bitstrings from finitely many circuit executions, whereas most quantum error-mitigation methods target expectation values. We study sample-level recovery when measured probability mass is distributed around multiple latent bitstrings, called centers. Each component of the measured probability mass is called a source and we assume that each center is associated with one source. We identify dominance-at every coordinate, more than half of a retained region's probability mass comes from one source and agrees with its center-as a sufficient condition under which majority voting recovers that center with exponentially decreasing error probability. We show that nearest-center assignment, as used in clustering algorithms such as the $k$-modes algorithm, can fail to produce dominated regions even when the true centers are known. This failure motivates responsibility thresholding and a local dominance screen, whose combination we call dominance-aware (DA) refinement. Synthetic and simulated MaxCut-QAOA experiments show that DA refinement favors precision, while $k$-modes with DA refinement improves overall center recovery. All procedures are classical post-processing and require no additional quantum-circuit executions.

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arXiv2026

Fractal dimension predicts quantum kernel collapse in angle-encoded data

Angle-encoded quantum kernels on tabular data collapse when the feature map is wider than the intrinsic dimension of the data. We propose the correlation fractal dimension D2 as an a priori qubit budget: encode D2 coordinates chosen by FD-ASE instead of the PCA-95% width or all E attributes. On nine data sets and a statevector simulator (n= 32), a one-layer ZZ fidelity kernel at q=D2 stays geometrically alive while the same kernel at the PCA-95% width has already collapsed. The budget is map-dependent: product-state and IQP maps overshoot it; a second ZZ layer undershoots it. Packed dense-angle and re-uploading encodings still live at the fractal q, but not when PCA-95% features are stacked onto those qubits. Shrinking the angle bandwidth moves the ZZ knee later; stretching it kills the kernel earlier. On IBM Quantum (ibm_fez, 256 shots, n=8) the one-layer ZZ kernel at the fractal width matches the exact kernel (MAE 0.021); past that width both hardware and simulator have collapsed. The ceiling is a property of the map-data pair at a stated bandwidth, not of the classical table alone.

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arXiv2026

Verifiable quantum advantage in extremely low depth

We give a sampling problem that is solvable by shallow quantum circuits, hard for polynomial-time classical algorithms under lattice-based assumptions, and efficiently verifiable by a classical computer. The quantum sampler admits two implementations: one uses log-logarithmic-depth quantum circuits with one- and two-qubit gates, i.e., $\mathsf{QNC}^0[\log\log]$ circuits, while the other uses constant-depth quantum circuits with unbounded fan-in gates, i.e., $\mathsf{QAC}^0$ circuits. Our construction can be seen as compiling the Learning with Errors (LWE)-based single-round proof of quantumness of Arabadjieva et al. (2025) to very low depth. The price paid for this compilation is the reliance on less standard, though well-motivated, assumptions: in addition to the lattice knowledge assumption used by Arabadjieva et al. (2025), we require a strengthened variant of the adaptive-hardcore-bit property of LWE, for which we provide supporting evidence. Unlike previous low-depth proofs of quantumness, the quantum computation here requires no mid-circuit measurements or feed-forward: it consists only of running a shallow circuit and sampling from its output distribution. This shows that shallow quantum circuits have sufficient structure to solve certain classically hard tasks whose solutions can be verified efficiently.

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arXiv2026

Factorized Boolean representations for efficient quantum synthesis

Quantum algorithms promise advantages beyond classical reach, but running them on error-corrected hardware requires translating Boolean specifications into reversible circuits, and the resources that translation demands determine what is executable. Established methods minimize a Boolean expression and map it to a circuit, assuming the minimized form is best. Here we show that minimized expressions retain algebraic structure minimization cannot reach, arising from containment and complementary-polarity relationships among their terms, and that extracting it yields circuits cheaper to execute despite having more operations. The decisive quantity is not a circuit's operation count but the control count of its widest operation, a superlinear cost; extracting shared factors trades a few wide operations for many narrow ones and reduces qubit count. Across benchmarks and oracles from quantum search and factoring algorithms, at the representation level the transformation never increases either cost measure, a guarantee from its construction. Translation to an executable circuit returns part of that advantage, since auxiliary lines must be uncomputed, yet the factorized circuit still left a leading circuit-level optimizer reaching lower final counts, and faster, than unaided. The representation of a computation is therefore itself a resource, optimizable before compilation and distinct from both logic minimization and circuit-level optimization.

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arXiv2026

Edge-Local and Qubit-Efficient Quantum Graph Learning for the NISQ Era

Graph neural networks (GNNs) are a powerful framework for learning representations from graph-structured data, but their direct implementation on near-term quantum hardware remains challenging due to circuit depth, multi-qubit interactions, and qubit scalability constraints. In this work, we introduce a hybrid quantum graph learning architecture designed explicitly for unsupervised learning in the noisy intermediate-scale quantum (NISQ) regime. Our approach combines a variational quantum feature extraction layer with an edge-local and qubit-efficient quantum message-passing mechanism inspired by the Quantum Alternating Operator Ansatz (QAOA) framework. The message-passing operation is decomposed into pairwise interactions along graph edges using standard single- and two-qubit gates. For a graph with $N$ nodes and $n$-qubit feature registers, this reduces the number of qubits required at one time from $Nn$ to at most $2n$. We train the model using the Deep Graph Infomax objective to perform unsupervised node representation learning. The external class labels are not used during graph construction or training and are used only to evaluate the learned embeddings. Experiments on the Cora citation network and the Phase 3 release of the 1000 Genomes Project show that the quantum edge interaction contributes to the quality of the learned node representations.

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arXiv2026

Constrained minimax approximation for quantum signal processing

Quantum signal processing (QSP) provides a simple and efficient framework for implementing polynomial transformations using quantum circuits. Its classical design stage leads to a constrained minimax approximation problem: find a polynomial of prescribed parity that approximates a target function uniformly on a fitting set while remaining bounded in magnitude by one on the domain $[0,1]$, which can be viewed as a semi-infinite constraint. Discretization converts the problem into a linear program, but feasibility at a set of finitely many sampled points does not ensure feasibility on the whole domain, especially when an optimal approximant reaches the boundary of the feasible set. We investigate two approaches to address this difficulty. A Remez exchange method combined with active-set constraint enforcement is efficient on many tested instances, but its stability depends on the target and problem geometry. We then introduce nonlinear Fourier retraction, which uses QSP completion and phase synthesis to turn a nearly feasible polynomial into phase factors for a feasible QSP polynomial without increasing the degree. Across representative problems, retraction largely preserves approximation accuracy and remains effective on instances where the Remez heuristic is unstable. The resulting workflow connects classical minimax approximation and semi-infinite optimization with nonlinear Fourier analysis, and is implemented in the qsppack software package.

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arXiv2026

Mixed-dimensional quantum MacWilliams identity: Bounds for codes and absolutely maximally entangled states in heterogeneous systems

As emerging quantum architectures evolve into heterogeneous networks combining different physical substrates, such as qubits for logic and higher-dimensional qudits for robust communication, the traditional scalar metrics of quantum error correction become insufficient. To address this, we introduce a mathematical framework based on dimension multisets to characterize quantum error-correcting codes (QECC) and absolutely maximally entangled (AME) states in mixed-dimensional Hilbert spaces. By replacing scalar weights with multisets, we accurately capture the exact physical composition of error supports across these diverse systems. Our central result is the mixed-dimensional quantum MacWilliams identity, which establishes the formal algebraic relationship between Shor-Laflamme enumerators and unitary weight enumerators. From this foundation, we deduce the mixed-dimensional shadow identity and derive rigorous, generalized constraints on code parameters, explicitly formulating the mixed-dimensional quantum Hamming, Singleton and Scott bounds, and developing a linear program to systematically evaluate code viability. For the Singleton bound, a tighter bound that has no homogeneous analogue is derived for pure mixed-dimensional codes. Finally, we deploy this enumerator machinery to thoroughly analyze AME states, utilizing shadow inequalities to constrain their existence and introducing a combinatorial grid method for the explicit construction of mixed-dimensional tripartite AME states.

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arXiv2026

Quantum SEDONet: Spectrally-Embedded Quantum Deep Operator Networks for Partial Differential Equations

Quantum DeepONet accelerates neural-operator inference by evaluating an orthogonally parameterized network on a quantum computer, reproducing in ideal simulation the accuracy of its classical counterpart at asymptotically lower inference cost. Its trunk network, however, receives query coordinates with limited spectral structure, requiring the network to learn oscillatory features through its nonlinearities. We propose Quantum SEDONet (Spectral-Embedded Deep Operator Network), which assigns each trunk coordinate a spectral basis according to its boundary condition: Fourier features for periodic coordinates and Chebyshev features for bounded, non-periodic coordinates. The basis is selected per coordinate rather than per problem, allowing both representations within a single problem. Under unary amplitude encoding, the embedding incurs no additional qubits or circuit depth when its dimension remains within the network width, while increasing the parameter count by only a few percent. Across four benchmarks, Quantum SEDONet reduces the mean relative L2 error by 54.1% for the antiderivative, 49.6% for advection, 36.0% for Burgers, and 36.2% for a mixed-boundary channel Poisson problem. Quantum and classical evaluation paths agree to within 10^-8 throughout. The channel Poisson problem simultaneously uses Fourier features in the periodic direction and Chebyshev features in the bounded direction, demonstrating coordinate-wise boundary-matched spectral embedding without additional quantum-resource cost.

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arXiv2026

A Backend-Agnostic MWIS Kernel for Stochastic Unit Commitment with Neutral-Atom Hardware Validation

Quantum hardware is beginning to address structured combinatorial optimisation, but two steps still block practical use: mapping real operational models onto hardware-compatible instances, and converting noisy hardware output back into feasible decisions. Here we introduce a backend-agnostic computational interface that compiles the discrete decision layer of stochastic unit commitment into a move-based maximum-weight independent set (MWIS) problem, while retaining continuous dispatch and feasibility recovery in the classical computational layer. We validate the approach in a green hydrogen scheduling setting and deploy it on the QuEra Aquila neutral-atom quantum processor. This is the first end-to-end industrial scheduling workflow that connects real operational decisions to programmable neutral-atom hardware through a solver-agnostic MWIS representation. Across a 15-day hardware campaign on 50-node instances, hardware-generated solutions after classical refinement match or exceed the dispatch margins obtained from exact MWIS on every day. When scaling to 144 nodes, encoding quality remains stable, while the probability that the full atom array survives, rather than graph embedding, emerges as the dominant bottleneck to further scaling. Together, these results establish a hardware-compatible computational pathway toward larger problem scales, and lay the groundwork for exploring regimes in which exact classical optimisation may no longer scale efficiently.

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arXiv2026

GadIR: A Spatial-Topology Preserving Compiler for Quantum Many-Body Systems Simulation

Simulating quantum many-body systems has been one of the most important applications of quantum computation. For simulation, the Hamiltonian of a physical system is compiled into quantum programs with native instructions for quantum hardware. In previous works, the Hamiltonian is represented as Pauli strings, then compiled and optimized based on the quantum circuit model. Such representation paradigm neglects the spatial topology of original physical models, which is vital information to reducing the overhead of compiling many-body systems Hamiltonians. To address such neglect, we introduce a spatial-topology preserving compiler for quantum many-body simulation. Using Pauli gadgets as the representations of the Hamiltonian, we introduce our intermediate representation -- GadIR, to preserve the spatial-topology information of original physical models. Our compiler frontend performs the group reduction algorithm based on Pauli gadget model, which is a hardware-independent optimization. Our compiler backend performs trotterization and scheduling on Pauli gadgets, then synthesizes the Pauli gadgets into hardware-native quantum programs. We evaluate our compiler on all the canonical quantum many-body system models, while achieving a significant reduction on compilation overhead regarding four major quantum architectures. Overall, our spatial-topology preserving IR exploits the compilation optimization space for quantum many-body systems Hamiltonian.

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arXiv2026

Construction of Quantum Rank-Metric Codes Using Hermitian Orthogonality

Stacked quantum memory is an architecture in which multiple layers of qubits are stacked. Quantum rank-metric codes are effective for error correction in stacked quantum memories. However, the previously proposed quantum Gabidulin codes based on the CSS construction had a problem: due to algebraic constraints, the applicable memory layouts were strictly limited to square shapes of odd length. In this paper, we first propose a framework for constructing quantum rank-metric codes from classical linear codes with symplectic self-orthogonality. Building upon this, we propose a new construction method for quantum Gabidulin codes by combining the Hermitian self-orthogonality of classical Gabidulin codes--utilizing the self-dual basis that exists when the extension degree of the finite field is even--with the quantum code construction method using Hermitian orthogonality by Matsumoto and Uyematsu. The proposed method succeeds in approximately doubling the ratio of the minimum rank distance to the number of physical qubits while maintaining the code rate. Furthermore, it eliminates the restriction of the conventional method that requires the number of cells and layers of the stacked memory to be odd, realizing the construction of quantum rank-metric codes applicable to memories with an even number of cells and layers. This construction improves the relative error correction capability of the stacked quantum memory architecture and increases the degree of freedom in design while preserving the code rate.

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arXiv2026

Logical Neural Belief Propagation for Linear-Complexity Decoding of Surface Codes

Quantum error correction (QEC) requires decoders that achieve high logical accuracy while scaling efficiently with the code length. Belief propagation (BP) is attractive for its linear decoding complexity, but conventional BP decoders often fail to reach sufficient logical accuracy on surface codes. We propose Logical Neural Belief Propagation (L-NBP), a BP-based neural decoder that redirects the decoding objective from physical-level decoding to logical-level decoding. L-NBP first runs a neural BP (NBP) module that produces posterior beliefs, and a logical classifier then transforms these beliefs into a continuous-valued soft syndrome and predicts the logical operator. Because all components in L-NBP are trainable by backpropagation, L-NBP is trained end-to-end, so that the NBP module learns to extract soft syndromes that are favorable for logical classification. On surface codes, L-NBP matches or outperforms the BP with ordered-statistics decoding (BP-OSD) and minimum-weight perfect matching (MWPM) while retaining the linear complexity of BP, and achieves a threshold of $17.5\%$ under depolarizing noise. Moreover, under circuit-level noise, L-NBP matches the accuracy of BP-OSD on the distance-$9$ surface code while requiring only $0.2\%$ of its complexity. These results show that combining BP, neural weights, and logical-level decoding enables scalable and high-accuracy quantum decoding.

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arXiv2026

Universal recovery in approximate quantum error correction

Universal recovery -- the existence of a single recovery map that corrects an entire family of error channels -- is a central feature of quantum error correction (QEC). In exact QEC, linearity guarantees that a code correcting a given error set also corrects every channel whose Kraus operators lie in its linear span, and that a single recovery map suffices for all such channels. Approximate quantum error correction (AQEC), which relaxes perfect recovery to recovery with controlled error, has traditionally lacked this structure. In a recent paper (arXiv:2607.22995), we developed a theory of approximate quantum error correction showing that a restricted form of linearity persists in the approximate setting, yielding uniform AQEC guarantees for the family of channels controlled by a given error set. In this work, we complete the picture by establishing the second half of universal recovery in the approximate setting: a single recovery map can simultaneously correct every channel controlled by a given error set. The error-set theory we proposed quantifies approximate correctability through two parameters: the environment-leakage distance, governing worst-case performance, and the Knill--Laflamme Hellinger distance, governing average-case performance. We show here that both quantities also control universal decoding. We further study the Petz map naturally associated with an error set as an explicit universal recovery, and obtain uniform average- and worst-case guarantees across the entire family of channels.

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arXiv2026

An End-to-End Hybrid Quantum--Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study

Sampling from discrete Markov random fields (MRFs) is a hard problem. We study amplitude-encoded i.i.d. sampling for small MRFs where $2^n$ target probabilities are precomputed classically. This removes quantum exponential speedup but allows a clean comparison against classical MCMC based on independent circuit samples ($τ\approx 1$). Across 60 instances spanning five graph families (1k-step burn-in, 3k retained samples), the mean ESS ratios of Quantum to Single-Site Gibbs, Block Gibbs, Tuned-Block, and Parallel Tempering are $16.35$, $7.29$, $1.82$, and $1.79$, showing modern classical samplers substantially close this gap. Amortizing $O(2^n)$ preprocessing into wall-clock time, exact inverse-CDF sampling yields $17.7\text{M}$ ESS/s versus $488\text{K}$ ESS/s for the quantum sampler ($36\times$ mean rate, $153\times$ per-instance), confirming no wall-clock advantage. We characterize MCMC autocorrelation costs and benchmark amplitude-encoded state preparation at $n \in \{8,10,12\}$. An MPS scaling study ($n \le 40$) shows bond dimension $χ=32$ achieves $F=0.721\pm0.059$ at $n=40$. Finally, a matched-budget VQC vs. MPS comparison at $n \in \{8,10,12\}$ shows VQC fidelities fall far below MPS: $(F_{\mathrm{VQC}}, F_{\mathrm{MPS}}) = (0.31, 0.99), (0.21, 0.96), (0.17, 0.88)$ at compressions $10.7\times$, $34.1\times$, and $113.8\times$.

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arXiv2026

Plateau-Constrained Selection of Commuting Phase-Term Orderings Under a Fixed Maintained-Parity Compiler Contract

Ordering objectives for commuting phase terms can have many equal optima, yet prior methods do not characterize or exploit those ties. We use a classical two-stage permutation search under fixed placement and maintained-parity quantum lowering: Stage 1 certifies the primary support optimum, and Stage 2 samples equal-cost tours and selects by a frozen routed score. On synthetic 16-qubit assignment-Ising instances, exact counting through 20 terms establishes instance-dependent multiplicity; when the support lower bound is attained, the reversal-reduced width equals the number of undirected Hamiltonian paths of the support line graph. A revised engineering analysis found 9.14% fewer routed controlled-NOT gates than unoptimized order, while the registered comparison found 11.10% fewer than prior stochastic search. Among 24 sampled minimum-support-cost orders at 36 terms, direct-depth selection reduced opposite-SABRE-seed depth by 12.83% in all 20 aggregates, whereas a matched 24-restart control changed depth by only -0.41% (unresolved). Candidate rankings persisted across SABRE routing seeds, explaining why selection survived routing re-randomization. The depth benefit transferred to a second generator and to 48 terms, but reversed under BasicSwap. On a prospective IBM Heron panel, raw generator error shifted by -0.0025 (-0.59%); fixed-panel shot uncertainty excluded zero, but term-seed inference remained unresolved. Equal-primary-cost tours are a useful router-conditioned compiler freedom, not a guaranteed hardware benefit.

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