Data-Efficient Quantum Noise Modeling via Machine Learning

TL;DR

This work tackles the challenge of modeling quantum noise on near-term devices without heavy calibration overhead. It introduces a circuit-size-independent, physically motivated parameterized noise description $\mathcal{N}(\boldsymbol{\theta})$ whose 20 parameters are learned via Bayesian optimization to minimize the mean $D_H$ between simulated and experimental distributions. The method achieves up to 65% reduction in $D_H$ across QAOA, VQE, and random circuits on multiple superconducting IBM backends, and demonstrates strong extrapolation from 4–6 to 7–9 qubits. The application-aware calibration, reuse of vendor-calibration priors, and offline, data-efficient workflow enable improved noise-aware compilation and error mitigation without extra calibration experiments.

Abstract

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.

Figures (7)

• Figure 1: Flowchart of the data-efficient quantum noise modeling framework. A parameterized noise model $\mathcal{N}(\boldsymbol{\theta})$ is initially constructed based on calibration data provided by hardware vendors. The device-specific noise model $\mathcal{N}(\boldsymbol{\theta^*})$ is then identified by executing benchmarking circuits on real quantum hardware and aligning experimental results with noisy simulations. This iterative optimization, performed on a classical computer, leverages machine learning (ML)-based Bayesian optimization to update $\boldsymbol{\theta}$. This approach is highly flexible, designed to ingest outcome distributions from diverse preexisting experimental data, including application-specific circuits, avoiding the need for dedicated characterization.
• Figure 2: Hellinger distances between outcomes from simulations using default device noise model ($x$-axis) and our parameterized noise models ($y$-axis) versus real executions on ibmq_kolkata. Blue circles represent models optimized via BO, while orange squares denote those optimized through RS. All points below the dashed diagonal ($y=x$) indicate an improvement in model fidelity over the default model. The percentages shown in the legend represent the average reduction in Hellinger distance achieved by each optimization method relative to the default model. (a) Training phase using QAOA circuits on 4-, 5-, and 6-qubit instances, and (b) predictive performance on 7-, 8-, and 9-qubit circuits. Each circuit size was executed at four distinct times, yielding a total of 12 circuits for both training and prediction sets.
• Figure 3: Optimization landscape of the mean Hellinger distance, projected onto the two most significant noise parameters, as identified by Optuna, with marginalization over other noise model parameters. (a) Bayesian optimization and (b) random search. Each point represents a trial, and the red star marks the optimal configuration yielding the minimum value.
• Figure 4: Comparison of BO and RS for training the parameterized noise model on ibmq_kolkata (Kolkata-RS and Kolkata), alongside BO results on ibmq_mumbai (Mumbai) and ibmq_ehningen (Ehningen). (a) The average percentage reduction in Hellinger distance $D_H$ relative to the default noise model, for both training (blue, left) and prediction (orange, right) sets, evaluated on QAOA circuits with 4--6 qubits (training) and 7--9 qubits (prediction), each executed at four calibration instances. Error bars denote means and standard deviations derived from three independent repetitions across the 12 circuits per set. (b) The convergence of the optimization process corresponding to the training results presented in (a), which displays the best-achieved mean Hellinger distance of the training circuits over iterations.
• Figure 5: Impact of different training dataset sizes on the performance of BO-optimized noise model on ibmq_kolkata. Each training set is denoted by the number of QAOA circuits. The experimental setting is the same as in Fig. \ref{['fig:tra_pre_qpus']}.