Abstract Quantum and hybrid quantum-classical workflows repeatedly need to predict how ideal circuit distributions appear as finite-shot noisy hardware histograms, but refitting high-dimensional noise simulators at each calibration point can be costly. We cast this task as finite-shot distribution learning for structured quantum outputs: given ideal distributions and noisy counts, learn a low-dimensional Markov surrogate and evaluate held-out distributional risk. Existing fast closed-form kernels lack identifiability guarantees, while richer physics-motivated simulators fit approximately 20 BO-tuned noise parameters without parameter-identifiability guarantees. We instantiate this middle ground with SA-IBF, a two-parameter closed-form kernel mixing independent bit-flip noise with a Hamming-sector-preserving component. For the support-face regimes induced by symmetry-preserving circuits, we show a support-face bridge and a rank-conditioned local guarantee at fitted operating points; open-interior genericity establishes non-degeneracy of the full-simplex model. We also show a small-q Fisher upper bound in which the Fisher information for alpha conditional on q scales on the order of N times q squared for N shots and per-qubit flip rate q, certified for 2 to 8 qubits, yielding Cramer-Rao divergence as q approaches zero; analytic-Jacobian diagnostics verify the fitted-point rank premise at all seven representative operating points and all 230 panel fits. On an 890-execution IBM Heron hardware dataset spanning four backends, SA-IBF gives a diagnosable accuracy-cost Pareto point: in matched fitted-physics comparisons, it meets the sector-aware 21-parameter Ji-BO Hellinger accuracy budget on three of four molecular qubit settings while reducing refit cost by 231-447 times under matched implementations. The remaining setting flags a uniform-flip-rate boundary where the tested Ji-BO comparator's heterogeneous parameters lower risk. Supporting calibration evidence shows lower held-out Hellinger distance than plain bit-flip noise on all seven primary configurations and throughout a 400-execution cross-backend molecular panel. These results make SA-IBF a lightweight, identifiability-guided learned distribution-level surrogate for repeated quantum noise simulation in symmetry-structured quantum and hybrid quantum-classical workloads, including symmetry-preserving quantum-machine-learning settings.
Abstract Quantum and hybrid quantum-classical workflows repeatedly need to predict how ideal circuit distributions appear as finite-shot noisy hardware histograms, but refitting high-dimensional noise simulators at each calibration point can be costly. We cast this task as finite-shot distribution learning for structured quantum outputs: given ideal distributions and noisy counts, learn a low-dimensional Markov surrogate and evaluate held-out distributional risk. Existing fast closed-form kernels lack identifiability guarantees, while richer physics-motivated simulators fit approximately 20 BO-tuned noise parameters without parameter-identifiability guarantees. We instantiate this middle ground with SA-IBF, a two-parameter closed-form kernel mixing independent bit-flip noise with a Hamming-sector-preserving component. For the support-face regimes induced by symmetry-preserving circuits, we show a support-face bridge and a rank-conditioned local guarantee at fitted operating points; open-interior genericity establishes non-degeneracy of the full-simplex model. We also show a small-q Fisher upper bound in which the Fisher information for alpha conditional on q scales on the order of N times q squared for N shots and per-qubit flip rate q, certified for 2 to 8 qubits, yielding Cramer-Rao divergence as q approaches zero; analytic-Jacobian diagnostics verify the fitted-point rank premise at all seven representative operating points and all 230 panel fits. On an 890-execution IBM Heron hardware dataset spanning four backends, SA-IBF gives a diagnosable accuracy-cost Pareto point: in matched fitted-physics comparisons, it meets the sector-aware 21-parameter Ji-BO Hellinger accuracy budget on three of four molecular qubit settings while reducing refit cost by 231-447 times under matched implementations. The remaining setting flags a uniform-flip-rate boundary where the tested Ji-BO comparator's heterogeneous parameters lower risk. Supporting calibration evidence shows lower held-out Hellinger distance than plain bit-flip noise on all seven primary configurations and throughout a 400-execution cross-backend molecular panel. These results make SA-IBF a lightweight, identifiability-guided learned distribution-level surrogate for repeated quantum noise simulation in symmetry-structured quantum and hybrid quantum-classical workloads, including symmetry-preserving quantum-machine-learning settings.
Abstract Noise models support quantum-circuit simulation and need recalibration as hardware and workloads change. For circuits whose ideal outputs occupy one Hamming-weight sector, independent bit-flip (IBF) models tie leakage from the sector to the flip rate. We introduce SA-IBF, a two-parameter closed-form model whose sector-preserving weight mixes independent bit flips with flips conditioned on the sector to control this leakage separately. For nonzero weights, no mixture of product bit-flip channels reproduces its kernel. Given ideal distributions, we derive local identifiability conditions and a rank diagnostic for each fit. Across two data sets on four IBM Heron processors, SA-IBF predicts test data with lower Hellinger distance than IBF on every execution. On molecular quantum-autoencoder circuits, it matches a 21-parameter noise model fitted by Bayesian optimization to within 0.01 in Hellinger distance at three of four qubit numbers, at over 200-fold lower computational cost. This enables low-cost noise modeling of small symmetry-preserving circuits.
Quantum Phase Estimation (QPE) is a foundational algorithm for molecular ground-state energy estimation, but its deep circuit requirements make direct hardware execution impractical on Noisy Intermediate-Scale Quantum (NISQ) devices. We present an analytically grounded variational surrogate framework in which a shallow Variational Quantum Circuit (VQC) is trained to reproduce the QPE measurement distribution without any quantum circuit simulation. The training target is computed entirely classically via the Dirichlet kernel, evaluated directly from the Full Configuration Interaction (FCI) ground-state energy, the ancilla qubit count, and the time evolution parameter, eliminating the exponentially scaling simulation bottleneck of prior surrogate approaches. We apply this framework to the hydrogen molecule (H2) with a symmetry-tapered Hamiltonian, conducting a four-stage experimental investigation on IBM Quantum hardware. Stage 1 compares linear and full entangler topologies for the RY-RZ-CZ ansatz, with and without XpXm Dynamical Decoupling (DD), across four distributional metrics (Hellinger distance, fidelity error, total variation distance, Jensen-Shannon divergence), identifying the linear entangler as optimal. Stage 2 varies VQC layers (p=1 to 5) for the linear-entangler ansatz, identifying single-layer depth as optimal under hardware noise. Stage 3 applies this configuration to the reduced RY-CZ ansatz, comparing ideal and noisy simulator-trained parameters. A supplementary noise analysis at p∈{8,64} characterizes the depth-dependent interplay between circuit depth and DD effectiveness. The framework enables faithful QPE mimicry using a linearly scaling VQC, recovering the ground-state energy within the chemical accuracy threshold (1 kcal/mol), constituting a scalable, hardware-efficient paradigm for QPE-based molecular energy estimation on NISQ devices.
Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this paper, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bitflip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches RZNE [28], M3 [24], Hammer [35], and QBEEP [33] by1.26x,1.29x,1.47x, and 2.65 x, respectively.
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.
Calibrating a quantum processor means estimating gate-error parameters from data, and a hard-to-estimate parameter is usually assumed to leave a weak signature more repetitions will resolve. Coherent over-rotations break that premise. For commuting single- and two-qubit transverse over-rotations with known support on a computational-basis input, the passive histogram is exactly invariant under a sign group acting on the coherent angles, of order 2n+1 for the complete family with n≥2, so no estimator resolves the signs uniformly at any sample size. A calibration correction applied with the wrong sign doubles the rotation error it should remove. At zero angle the obstruction turns continuous, with a Fisher information singular along every coherent direction and an infinite Cramér-Rao bound. At generic angles the continuous defect clears for 5≤n≤8, the range we compute, while the sign degeneracy persists. Covering the support removes both, and a design resolves the signed angles uniformly exactly when it covers. On ∣ηR∣<π/2, 0≤pR<1/2 coverage is constructive, returning each angle in closed form from a ratio of two measured expectations without knowing the rates. A twirl-free code of ⌈log2(n+1)⌉ added product-Pauli settings covers, and for the complete family none uses fewer. Conditioning then sets the Cramér-Rao cost, and we give its floor explicitly. Exact computation matches the theory, the passive fit stays at chance on the signs at every budget while the closed-form inverse recovers them, and angle magnitudes on two IBM Heron processors follow the conditioning ordering.
Quantum computing promises unparalleled computational power, but its practical implementation is hampered by quantum noise, which affects the reliability of quantum circuits. This paper addresses the critical challenge of noise classification in NISQ ‘Noisy Intermediate-Scale Quantum’ algorithms, focusing on bit flip, phase flip, and depolarising noise. We introduce a novel balanced quantum noise dataset generated through random quantum circuits, ensuring comprehensive coverage of various noise types and intensities. Additionally, we develop a hybrid quantum-classical machine learning model that achieves over 85% accuracy in classifying bit flip and depolarising noise, and perfect accuracy in detecting phase flip noise under our simulation conditions. Our approach builds on a dual quantum architecture, utilising IBM Qiskit for dataset generation and Pennylane for model training. These simulation results indicate potential improvements for noise-aware modelling and error mitigation; however, we emphasise that translating this performance to physical devices requires further validation due to hardware-specific decoherence and calibration effects.