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arXiv:2601.14226

Deep Learning Approaches to Quantum Error Mitigation

Leonardo Placidi, Ifan Williams, Enrico Rinaldi, Daniel Mills, Cristina Cîrstoiu, Vanya Eccles, Ross Duncan

quant-phcs.LGSubmitted Jan 20, 2026• Announced Jan 21, 2026• 0 citations
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Abstract

We present a systematic investigation of deep learning methods applied to quantum error mitigation of noisy output probability distributions from measured quantum circuits. We compare different architectures, from fully connected neural networks to transformers, and we test different design/training modalities, identifying sequence-to-sequence, attention-based models as the most effective on our datasets. These models consistently produce mitigated distributions that are closer to the ideal outputs when tested on both simulated and real device data obtained from IBM superconducting quantum processing units (QPU) up to five qubits. Across several different circuit depths, our approach outperforms other baseline error mitigation techniques. We perform a series of ablation studies to examine: how different input features (circuit, device properties, noisy output statistics) affect performance; cross-dataset generalization across circuit families; and transfer learning to a different IBM QPU. We observe that generalization performance across similar devices with the same architecture works effectively, without needing to fully retrain models.

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We present a systematic investigation of deep learning methods applied to quantum error mitigation of noisy output probability distributions from measured quantum circuits. We compare different architectures, from fully connected neural networks to transformers, and we test different design/training modalities, identifying sequence-to-sequence, attention-based models as the most effective on our datasets. These models consistently produce mitigated distributions that are closer to the ideal outputs when tested on both simulated and real device data obtained from IBM superconducting quantum processing units (QPU) up to five qubits. Across several different circuit depths, our approach outperforms other baseline error mitigation techniques. We perform a series of ablation studies to examine: how different input features (circuit, device properties, noisy output statistics) affect performance; cross-dataset generalization across circuit families; and transfer learning to a different IBM QPU. We observe that generalization performance across similar devices with the same architecture works effectively, without needing to fully retrain models.
A quantum error mitigation technique based on machine learning is proposed, which learns how to adjust the probabilities estimated by measurement in the computational basis. Neural networks in two different designs are trained with random quantum circuits consisting of a set of one- and two-qubit unitary gates whose measurement statistics in the ideal (noiseless) and real (noisy) cases are known. Once the neural networks are trained, they infer the amount of probability adjustment to be made on the measurement obtained from executing an unseen quantum circuit to reduce the error. The proposed schemes are tested with two-, three-, five-, and seven-qubit quantum circuits of depth up to 20 by computer simulations with realistic error models and experiments using the IBM quantum cloud platform. In all test cases, the proposed mitigation technique reduces the error effectively. Our method can be used to improve the accuracy of noisy intermediate-scale quantum (NISQ) algorithms without relying on extensive error characterization or quantum error correction.
Quantum computing has gained significant attention in recent years, with numerous algorithms and applications under active development. Limited by the current quantum technology, quantum noise and readout error have become critical issues. Various methods have been proposed to address readout error through error mitigation techniques, typically involving post-processing of measurement data. However, most of these methods increase the quantum hardware overhead, leading to higher computational costs. In this work, we present a machine-learning-based approach that minimizes hardware overhead while improving accuracy of the measurement probability distributions. We employed a convolutional neural network (CNN) autoencoder, commonly used for image denoising, as our baseline model. The datasets were derived from 4-qubit random circuits with depths ranging from 1 to 18, generated using Qiskit backends for target and noisy measurement data. The model was trained using mean squared error (MSE) as the loss function and Adam optimizer over 500 epochs, achieving an average noise reduction by 95% across the validation set, with no signs of overfitting. To validate the model's effectiveness across diverse quantum states, we conducted extensive tests on both typical quantum circuits and algorithms, including Grover's search algorithm, Quantum Fourier Transform, Haar random circuits and Trivial Paramagnet. The results demonstrated consistent and robust denoising in noisy measurement data, indicating that the autoencoder model is well-suited for efficient quantum error mitigation for current noisy quantum computers. This work contributes to the advancement of quantum error mitigation techniques using machine learning.
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Machine Learning-based quantum error mitigation (ML-QEM) has emerged as a promising approach for improving the performance of noisy quantum algorithms. However, existing ML-QEM methods often have restricted applicability to variational circuits and rely on inaccessible noiseless training data. In this work, we propose a practical ML-QEM protocol tailored to variational quantum algorithms, which generates training data by simulating (near-)Clifford circuits. This data is used for model selection and training, producing a mitigation model that can correct variational circuits with arbitrary parameters and transfer across different target Hamiltonians of similar structure. We benchmark the proposed method on the Variational Quantum Eigensolver (VQE) task for the Sherrington-Kirkpatrick Hamiltonian of up to n=12n=12n=12 qubits under various noise models, analyzing its effect on trainability and comparing its performance against standard Zero-Noise Extrapolation (ZNE). The results demonstrate consistent several-fold error suppression across all tested settings and superior performance over ZNE in the high-noise regime, providing evidence for the applicability of the proposed protocol to present-day NISQ processors.
Supervised approaches to quantum error mitigation learn a map from noisy circuit outputs to ideal ones, and therefore require the ideal outputs. Producing those ideal outputs demands noiseless classical simulation, whose cost grows exponentially with system size, so supervision is unavailable in exactly the regime where mitigation matters most. We ask whether cheap, individually unreliable signals drawn from circuit structure and hardware calibration can take the place of ideal labels. We assemble sixteen heuristic labeling functions (stabilizer and parity constraints, relaxation and readout characteristics, local depth, gate counts, and neighboring activity), reconcile their disagreements with a probabilistic label model, and read the resulting per-qubit error probabilities as a readout channel whose inverse mitigates the measured distribution. No ideal output enters the training path. On 147,000147{,}000147,000 five-qubit circuits executed on two IBM devices, the method removes 24.3%24.3\%24.3% (Algiers) and 28.8%28.8\%28.8% (Hanoi) of the Kullback-Leibler divergence to the ideal distribution, against 15.4%15.4\%15.4% and 21.5%21.5\%21.5% for the strongest published analytical baseline, a margin that holds on both devices and lies far outside its bootstrap interval. Supervised neural models trained on ideal distributions remain stronger where such labels exist, and we quantify that gap rather than setting it aside; the method's claim is to the regime where they do not, since the labels they require cannot be computed for the circuits mitigation is needed for. The codes will be released shortly.
We present an approach for a deep-learning compiler of quantum circuits, designed to reduce the output noise of circuits run on a specific device. We train a convolutional neural network on experimental data from a quantum device to learn a hardware-specific noise model. A compiler then uses the trained network as a noise predictor and inserts sequences of gates in circuits so as to minimize expected noise. We tested this approach on the IBM 5-qubit devices and observed a reduction in output noise of 12.3% (95% CI [11.5%, 13.0%]) compared to the circuits obtained by the Qiskit compiler. Moreover, the trained noise model is hardware-specific: applying a noise model trained on one device to another device yields a noise reduction of only 5.2% (95% CI [4.9%, 5.6%]). These results suggest that device-specific compilers using machine learning may yield higher fidelity operations and provide insights for the design of noise models.