Abstract Compared with traditional computers, quantum computers can provide exponential acceleration for certain critical fields. However, the coupling of quantum systems with the environment, along with the intrinsic characteristics of quantum systems, has collectively introduced quantum noise, which has emerged as a significant impediment to the development of quantum computing. Quantum error mitigation (QEM) has been proposed as an alternative solution in the noisy intermediate-scale quantum era. In recent years, with the rise of artificial intelligence, machine learning-based QEM technology has received attention from the industry. However, the latest machine learning-based QEM techniques have limitations, especially their inability to mitigate errors in the quantum circuits whose number of qubits exceeds the number of qubits in the training set, and their tendency to amplify noise when constructing feature sets. This paper proposes QEMOS, a novel random forest-based machine learning model that utilizes a new feature dataset incorporating quantum computer backend properties, with feature dimensionality reduction enabling decoupling from the number of qubits. The model is trained and tested using six different simulators from Qiskit and a real quantum computer tianyan-176. It is worth noting that this model overcomes the limitation of sensitivity to the number of qubits, which was the main problem of previous methods. When trained on 5–9 qubit circuits, the model achieves a probability of correct mitigation of 86.38% on 2–13 qubit circuits, though this efficacy is observed primarily for circuits exhibiting high-probability outputs and decreases as all output probabilities approach zero. Compared to the baseline, the model demonstrates a 31.74% error reduction on test sets with more qubits than the training set. On real quantum computer, testing shows an average error reduction of 67.5%.
Abstract Compared with traditional computers, quantum computers can provide exponential acceleration for certain critical fields. However, the coupling of quantum systems with the environment, along with the intrinsic characteristics of quantum systems, has collectively introduced quantum noise, which has emerged as a significant impediment to the development of quantum computing. Quantum error mitigation (QEM) has been proposed as an alternative solution in the noisy intermediate-scale quantum era. In recent years, with the rise of artificial intelligence, machine learning-based QEM technology has received attention from the industry. However, the latest machine learning-based QEM techniques have limitations, especially their inability to mitigate errors in the quantum circuits whose number of qubits exceeds the number of qubits in the training set, and their tendency to amplify noise when constructing feature sets. This paper proposes QEMOS, a novel random forest-based machine learning model that utilizes a new feature dataset incorporating quantum computer backend properties, with feature dimensionality reduction enabling decoupling from the number of qubits. The model is trained and tested using six different simulators from Qiskit and a real quantum computer tianyan-176. It is worth noting that this model overcomes the limitation of sensitivity to the number of qubits, which was the main problem of previous methods. When trained on 5–9 qubit circuits, the model achieves a probability of correct mitigation of 86.38% on 2–13 qubit circuits, though this efficacy is observed primarily for circuits exhibiting high-probability outputs and decreases as all output probabilities approach zero. Compared to the baseline, the model demonstrates a 31.74% error reduction on test sets with more qubits than the training set. On real quantum computer, testing shows an average error reduction of 67.5%.
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.
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 offers exponential advantages for problems in cryptography, optimization, and quantum simulation, yet the practicality of current Noisy Intermediate-Scale Quantum (NISQ) devices is severely constrained by decoherence, gate imperfections, and measurement noise. Conventional quantum error correction (QEC) codes such as Steane and surface codes impose large qubit overheads and require high-fidelity logical operations, making them unsuitable for near-term hardware. To address this gap, this work introduces ML-QEM, an adaptive quantum error mitigation framework that employs machine learning to identify and correct dominant Pauli error patterns in real time using only 3–5 ancillary qubits. By integrating Qiskit Aer noise modeling with a lightweight TensorFlow-based classifier, ML-QEM learns device-specific noise characteristics and applies targeted recovery operations with minimal latency. Evaluations across depolarizing, amplitude damping, and thermal relaxation noise models demonstrate a 28.4% average fidelity improvement, 60–84% lower overhead than Steane and surface codes, and a classical processing delay of only 21.7 ms. ML-QEM thus provides an effective and resource-efficient pathway toward enhancing quantum computation fidelity in the NISQ era.
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.
Quantum computers have the potential to outperform classical computers for some complex computational problems. However, current quantum computers (e.g., from IBM and Google) have inherent noise that results in errors in the outputs of quantum software executing on the quantum computers, affecting the reliability of quantum software development. The industry is increasingly interested in machine learning (ML)-based error mitigation techniques, given their scalability and practicality. However, existing ML-based techniques have limitations, such as only targeting specific noise types or specific quantum circuits. This paper proposes a practical ML-based approach, called Q-LEAR, with a novel feature set, to mitigate noise errors in quantum software outputs. We evaluated Q-LEAR on eight quantum computers and their corresponding noisy simulators, all from IBM, and compared Q-LEAR with a state-of-the-art ML-based approach taken as baseline. Results show that, compared to the baseline, Q-LEAR achieved a 25% average improvement in error mitigation on both real quantum computers and simulators. We also discuss the implications and practicality of Q-LEAR, which, we believe, is valuable for practitioners.
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.