Noise is a major obstacle in current quantum computing, and Machine Learning for Quantum Error Mitigation (ML-QEM) promises to address this challenge, enhancing computational accuracy while reducing the sampling overheads of standard QEM methods. Yet, existing models lack physical interpretability and rely heavily on extensive datasets, hindering their scalability in large-scale quantum circuits. To tackle these issues, we introduce the Neural Noise Accumulation Surrogate (NNAS), a physics-inspired neural network for ML-QEM that incorporates the structural characteristics of quantum noise accumulation within multi-layer circuits, endowing the model with physical interpretability. Experimental results demonstrate that NNAS outperforms current methods across a spectrum of metrics, including error mitigation capability, quantum resource consumption, and training dataset size. Notably, for deeper circuits where QEM methods typically struggle, NNAS achieves a remarkable reduction of over half in errors. NNAS also demands substantially fewer training data, reducing dataset reliance by at least an order of magnitude, due to its ability to rapidly capture noise accumulation patterns across circuit layers. This work pioneers the integration of quantum process-derived structural characteristics into neural network architectures, broadly enhancing QEM's performance and applicability, and establishes an integrative paradigm that extends to various quantum-inspired neural network architectures.
Noise is a major obstacle in current quantum computing, and Machine Learning for Quantum Error Mitigation (ML-QEM) promises to address this challenge, enhancing computational accuracy while reducing the sampling overheads of standard QEM methods. Yet, existing models lack physical interpretability and rely heavily on extensive datasets, hindering their scalability in large-scale quantum circuits. To tackle these issues, we introduce the Neural Noise Accumulation Surrogate (NNAS), a physics-inspired neural network for ML-QEM that incorporates the structural characteristics of quantum noise accumulation within multi-layer circuits, endowing the model with physical interpretability. Experimental results demonstrate that NNAS outperforms current methods across a spectrum of metrics, including error mitigation capability, quantum resource consumption, and training dataset size. Notably, for deeper circuits where QEM methods typically struggle, NNAS achieves a remarkable reduction of over half in errors. NNAS also demands substantially fewer training data, reducing dataset reliance by at least an order of magnitude, due to its ability to rapidly capture noise accumulation patterns across circuit layers. This work pioneers the integration of quantum process-derived structural characteristics into neural network architectures, broadly enhancing QEM's performance and applicability, and establishes an integrative paradigm that extends to various quantum-inspired neural network architectures.
Abstract Noise is a major obstacle in current quantum computing, and Machine Learning for Quantum Error Mitigation (ML-QEM) promises to address this challenge, enhancing computational accuracy while reducing the sampling overheads of standard QEM methods. Yet, existing models lack physical interpretability and rely heavily on extensive datasets, hindering their scalability in large-scale quantum circuits. To tackle these issues, we introduce the Neural Noise Accumulation Surrogate (NNAS), a physics-inspired neural network for ML-QEM that incorporates the structural characteristics of quantum noise accumulation within multi-layer circuits, endowing the model with physical interpretability. Experimental results demonstrate that NNAS outperforms current methods across a spectrum of metrics, including error mitigation capability, quantum resource consumption, and training dataset size. Notably, for deeper circuits where QEM methods typically struggle, NNAS achieves a remarkable reduction of over half in errors. NNAS also demands substantially fewer training data, reducing dataset reliance by at least an order of magnitude, due to its ability to rapidly capture noise accumulation patterns across circuit layers. This work pioneers the integration of quantum process-derived structural characteristics into neural network architectures, broadly enhancing QEM's performance and applicability, and establishes an integrative paradigm that extends to various quantum-inspired neural network architectures.
Abstract Quantum computing holds transformative promise, but its realization is hindered by the inherent susceptibility of quantum computers to errors. Quantum error mitigation has proved to be an enabling way to reduce computational error in present noisy intermediate scale quantum computers. This research introduces an innovative approach to quantum error mitigation by leveraging machine learning, specifically employing adaptive neural networks. With experiment and simulations done on 127-qubit IBM superconducting quantum computer, we were able to develop and train a neural network architecture to dynamically adjust output expectation values based on error characteristics. The model leverages a prior classifier module outcome on simulated quantum circuits with errors, and the antecedent neural network regression module adapts its parameters and response to each error characteristics. Results demonstrate the adaptive neural network’s efficacy in mitigating errors across diverse quantum circuits and noise models, showcasing its potential to surpass traditional error mitigation techniques with an accuracy of 99% using the fully adaptive neural network for quantum error mitigation. This work presents a significant application of classical machine learning methods towards enhancing the robustness and reliability of quantum computations, providing a pathway for the practical realization of quantum computing technologies.
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=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.
Noise in quantum hardware is the primary obstacle to realizing the transformative potential of quantum computing. Quantum error mitigation (QEM) offers a promising pathway to enhance computational accuracy on near-term devices, yet existing methods face a difficult trade-off between performance, resource overhead, and theoretical guarantees. In this work, we introduce neighbor-informed learning (NIL), a versatile and scalable QEM framework that unifies and strengthens existing methods such as zero-noise extrapolation (ZNE) and probabilistic error cancellation (PEC), while offering improved flexibility, accuracy, efficiency, and robustness.
NIL learns to predict the ideal output of a target quantum circuit from the noisy outputs of its structurally related ``neighbor'' circuits. A key innovation is our 2-design training method, which generates training data for our machine learning model. In contrast to conventional learning-based QEM protocols that create training circuits by replacing non-Clifford gates with uniformly random Clifford gates, our approach achieves higher accuracy and efficiency, as demonstrated by both theoretical analysis and numerical simulation. Furthermore, we prove that the required size of the training set scales only \emph{logarithmically} with the total number of neighbor circuits, enabling NIL to be applied to problems involving large-scale quantum circuits. Our work establishes a theoretically grounded and practically efficient framework for QEM, paving a viable path toward achieving quantum advantage on noisy hardware.
The pursuit of high-fidelity digital quantum simulation is fundamentally constrained by the inevitable presence of noise in current and near-term quantum processors. While quantum error correction ultimately promises fault-tolerance, its substantial qubit overhead renders it impractical for the noisy intermediate-scale quantum (NISQ) era. This research addresses the critical gap between hardware imperfections and simulation accuracy by designing systematic, resource-efficient machine learning (ML) error-mitigation protocols tailored specifically for digital quantum simulation. Unlike generic error-suppression methods, our approach exploits the unique structural properties of simulated quantum dynamics—including time-translation invariance, locality of interactions, and conserved quantities—to inform the training of lightweight neural networks and Gaussian process regressors. We develop a hybrid framework that combines randomized compiling with data-driven noise-inversion models, enabling real-time estimation and subtraction of both coherent and incoherent errors without exponential sampling overhead. Through extensive numerical benchmarks on spin-chain and Fermi-Hubbard models, we demonstrate that our ML protocols achieve up to an order-of-magnitude reduction in infidelity compared to standard probabilistic error cancellation and zero-noise extrapolation, while requiring fewer calibration circuits. Furthermore, we introduce an adaptive online learning scheme that continuously refines the mitigation model during the simulation runtime, automatically adjusting to time-dependent drift in hardware noise. Our results establish a practical pathway toward scalable, high-accuracy quantum simulations on existing devices, with implications for condensed matter physics, quantum chemistry, and the development of quantum advantage benchmarks.
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.