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arXiv:2604.20804

Quantum hardware noise learning via differentiable Kraus representation on tensor networks

Ryo Sakai, Yu Yamashiro

quant-phSubmitted Apr 22, 2026• Announced Apr 23, 2026• 0 citations
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Abstract

We present a method for learning quantum hardware noise from a measurement distribution of a single device experiment. Each noise channel is represented by automatically differentiable Kraus operators obtained from a Stinespring-based parameterization that is completely positive and trace preserving by construction, and circuits are simulated with a matrix product density operator forward model. Independent channels are attached to each native gate type, to each nearest-neighbor crosstalk interaction, and to state preparation and measurement, and all channels are optimized end-to-end against a distance between the simulated and observed measurement distributions. On ibm_fez, a Heron-generation superconducting processor, training on a ripple-carry adder circuit reproduces the device output distribution, and the same learned parameters, applied without retraining, also track the device distribution of an unrelated multiplier circuit, indicating that the method captures intrinsic device characteristics rather than overfitting to the training circuit. A systematic evaluation across a range of benchmark circuits confirms that this generalization is consistent. We further use the learned model to perform an offline feasibility assessment of the quantum approximate optimization algorithm with an error detection scheme, demonstrating the kind of noise-aware prediction the framework is designed to enable.

Comments
12 pages, 9 figures

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We present a method for learning quantum hardware noise from a measurement distribution of a single device experiment. Each noise channel is represented by automatically differentiable Kraus operators obtained from a Stinespring-based parameterization that is completely positive and trace preserving by construction, and circuits are simulated with a matrix product density operator forward model. Independent channels are attached to each native gate type, to each nearest-neighbor crosstalk interaction, and to state preparation and measurement, and all channels are optimized end-to-end against a distance between the simulated and observed measurement distributions. On ibm_fez, a Heron-generation superconducting processor, training on a ripple-carry adder circuit reproduces the device output distribution, and the same learned parameters, applied without retraining, also track the device distribution of an unrelated multiplier circuit, indicating that the method captures intrinsic device characteristics rather than overfitting to the training circuit. A systematic evaluation across a range of benchmark circuits confirms that this generalization is consistent. We further use the learned model to perform an offline feasibility assessment of the quantum approximate optimization algorithm with an error detection scheme, demonstrating the kind of noise-aware prediction the framework is designed to enable.
Maximizing the computational utility of near-term quantum processors requires predictive noise models that inform robust, noise-aware compilation and error mitigation. Conventional models often fail to capture the complex error dynamics of real hardware or require prohibitive characterization overhead. We introduce a data-efficient framework that first constructs a physically motivated, parameterized noise model, and subsequently employs machine-learning-driven Bayesian optimization to identify its parameters. Our approach circumvents costly characterization protocols by estimating algorithm- and hardware-specific error parameters directly from readily available experimental data derived from existing application and benchmark circuit executions. The generality and robustness of the framework are demonstrated across diverse algorithms and superconducting devices, yielding high-fidelity predictions by estimating an independent parameter set tailored to each specific algorithm-hardware context. Crucially, we show that a model calibrated exclusively on small-scale circuits accurately predicts the behavior of larger validation circuits. Our data-efficient approach achieves up to a 65% improvement in model fidelity quantified by the Hellinger distance between predicted and experimental circuit output distributions, compared to standard noise models derived from device properties. This work establishes a practical paradigm for application-aware noise characterization, enabling compilation and error-mitigation strategies tailored to the specific interplay between quantum algorithms and device-specific noise dynamics.
Classical simulation of noisy quantum circuits is essential for validating algorithms, benchmarking hardware, and assessing error-mitigation strategies, but remains limited by the exponential cost of density-matrix methods and the high variance of standard trajectory sampling. We introduce a variance-aware tensor network framework that combines the tensor jump method with local TDVP gate evolution on matrix product states and sparse Pauli-Lindblad hardware noise models. Gates are applied as short variational evolutions on the MPS manifold, while noise is sampled per circuit window from Pauli-Lindblad jump sets with state-independent hazards and dissipative contractions that reduce to irrelevant global factors after renormalization. The method supports correlated multi-qubit Lindblad noise consistent with hardware connectivity, including long-range operators on non-adjacent qubits, enabling direct simulation of crosstalk and other connectivity-induced errors beyond local noise models. We develop two unbiased variance-aware unravelings. An analog unitary-mixture unraveling matches the Lindblad generator exactly under symmetric Gaussian or two-point angle laws, while a projector-jump unraveling yields state-independent hazards and closed-form variance laws. Both retain the standard 1/sqrt(N) Monte Carlo convergence but with reduced prefactors. Empirically, projector sampling strongly reduces trajectory variance and bond-dimension growth across many circuit architectures, whereas analog sampling is most effective at weak noise. We demonstrate accurate, scalable noisy-circuit simulation on a 25-qubit noisy XY quench and IBM's 127-qubit kicked-Ising benchmark with long-range depolarizing noise, achieving reduced Monte Carlo variance and favorable MPS bond-dimension growth compared with standard Kraus-insertion baselines.
Classical simulation of noisy quantum circuits is essential for validating algorithms, bench-marking hardware, and guiding error-mitigation strategies. Yet it remains challenging due to either the exponential memory footprint of density matrix methods or the high variance in trajectories of standard Kraus-insertion approaches. We introduce a variance aware tensor network framework that unifies the tensor jump method (TJM) with a local time-dependent variational principle (TDVP) and a sparse Pauli-Lindblad model (SPLM) of hardware noise. Gates are realized as short variational evolutions on the matrix product state (MPS) manifold, while noise is applied stochastically per circuit window using Pauli-Lindblad jump sets that render the sampling hazard state-independent and the dissipative contraction trivial after renormalization. Strikingly, our method supports arbitrary Lindblad correlated multi-qubit noise channels consistent with hardware connectivity, including long-range noise operators on non-adjacent subsets, enabling direct simulation of crosstalk and other connectivity-induced errors beyond local noise models. Building on prior work that introduced analog unitary unravelings, we adapt this scheme to a framework based on the Lindblad master equation with exact generator matching under discretized angle laws and a parameter choice. This exactly matches the Lindblad generator, while selecting Gaussian or two-point angle laws. In parallel, we introduce an MPS-projector-jump unraveling that yields state-independent hazards and closed-form variance laws. Both schemes are unbiased and inherit the standard 1/√N Monte Carlo convergence, but with substantially smaller constants due to variance reduction. Empirically, projector sampling markedly reduces the required bond dimension per trajectory across many circuit architectures, while analog sampling excels at low noise. We demonstrate accurate, scalable noisy-circuit simulation on a 25-qubit noisy XY quench and IBM’s 127-qubit kicked Ising benchmark with long-range depolarizing noise, achieving substantially reduced Monte Carlo variance and favorable bond dimension growth compared to standard Kraus insertion baselines.
Accurate noise models are essential for high-performance quantum error correction, yet characterizing the noise of a quantum device typically requires dedicated experiments. We present a variational framework that learns the noise model directly from quantum-error-correction syndrome and logical-observable data collected during error-corrected memory experiments. The fault-event probabilities are treated as variational parameters and optimized via gradient descent to minimize the binary cross-entropy between the decoder's predictions and experimental logical-observable outcomes. We prove that this objective is principled rather than ad hoc: a sufficiently expressive noise ansatz attains the information-theoretic minimum logical error rate. We instantiate this framework using a tensor-network decoder, which provides exact maximum-likelihood decoding and analytically differentiable gradients with respect to all noise parameters. Using circuit-level data from Google's Sycamore processor, and starting from an uninformed prior, the optimization recovers noise models whose logical error rates agree to within 2%2\%2% with those of Google's independently characterized detector error model. The mean squared error between the learned and reference noise parameters shows a clear overall decrease throughout training, confirming that the method recovers physically meaningful noise structure, not merely parameters that happen to decode well. We further demonstrate that the optimization can track device drifts in real time via warm-started updates, maintaining near-optimal decoding performance under synthetically evolving noise without the need for re-characterization. The approach is decoder-agnostic in its formulation and naturally extends to correlated noise models.
Quantum computing hardware is prone to decoherence and control errors, which can reduce entanglement and lead to mixed states. Practical quantum algorithms must extract insights from this noisy data. We test the hypothesis that a compact, circuit-based Quantum Generative Adversarial Network (QGAN) trained against a moving, noise-scheduled target can learn the action of a depolarizing channel and generate a family of noisy entangled two-qubit states that match state-level similarity and reproduce entanglement trends. We implement a compact QGAN in PennyLane with TensorFlow and train it against a moving target formed by Bell-pair states passed through a depolarizing channel whose strength is scheduled during training. The generator and discriminator are variational circuits; learning is assessed by state-level similarity (fidelity and trace distance) and by entanglement measures (concurrence and negativity). Our model learns the action of the noise channel and reproduces a family of noisy, entangled two-qubit states. Our results indicate that QGANs can capture hardware-relevant noise while preserving essential structure in the data. Such models can serve as error-aware state preparers, compact surrogates for device noise, and practical tools for quantum data augmentation and benchmarking on near-term quantum computing hardware. To our knowledge, this is the first systematic QGAN evaluation combining dynamic depolarizing noise schedule, finite-shot/readout-noisy training, and entanglement-aware metrics.
Training parameterized quantum circuits requires balancing optimization progress with limited evaluation budgets and the statistical uncertainty of near-term quantum hardware. We present a modular benchmarking framework that separates quantum search-direction estimation from classical parameter-update rules, allowing their interactions and sensitivities to be examined independently. We evaluate a suite of gradient-based, stochastic, and derivative-free optimizers across combinatorial optimization using the Quantum Approximate Optimization Algorithm (QAOA), supervised quantum machine learning using Iris classification and a quantum convolutional neural network (QCNN) for binary MNIST classification, and quantum chemistry using the variational quantum eigensolver (VQE) for molecular hydrogen. By separating objective evaluations from sample-circuit costs under finite-shot simulation and physical execution on a 156-qubit processor, we compare optimizer behavior across workloads with different parameter counts and measurement requirements. Four selected simulator and hardware case studies report terminal and best observed objectives separately, alongside post-training classifier accuracies. The comparisons include selected MaxCut and hydrogen trajectories and illustrate workload-dependent objective changes and evaluation costs, while the simulator benchmark compares both peak and mean performance across three seeds. The hardware runs do not establish an optimizer ranking or isolate a causal effect of device noise.