Machine learning provides a scalable solution for quantum error mitigation. However, the selection of appropriate Pauli strings for inclusion in training data remains a challenge. Current methods rely on heuristic or uniform random sampling, requiring data for every Pauli string in the Hamiltonian, a process that scales linearly with measurements and grows with system size. To address this, we introduce quantum error mitigation with prior knowledge of Pauli weights (Pauli weight quantum error mitigation (Pi-QEM)), a systematic framework that selects training observables based on Pauli weight. By leveraging the relationship between variance and locality in parameterized quantum circuits, Pi-QEM trains on a small subset of dominant, low-weight Pauli strings. In numerical simulations of molecular systems on a noisy IBM quantum backend, Pi-QEM reduces ground-state energy estimation error by up to 34.01% using just a single dominant local observable, offering an efficient, scalable pathway for high-precision error mitigation on NISQ devices.
Machine learning provides a scalable solution for quantum error mitigation. However, the selection of appropriate Pauli strings for inclusion in training data remains a challenge. Current methods rely on heuristic or uniform random sampling, requiring data for every Pauli string in the Hamiltonian, a process that scales linearly with measurements and grows with system size. To address this, we introduce quantum error mitigation with prior knowledge of Pauli weights (Pauli weight quantum error mitigation (Pi-QEM)), a systematic framework that selects training observables based on Pauli weight. By leveraging the relationship between variance and locality in parameterized quantum circuits, Pi-QEM trains on a small subset of dominant, low-weight Pauli strings. In numerical simulations of molecular systems on a noisy IBM quantum backend, Pi-QEM reduces ground-state energy estimation error by up to 34.01% using just a single dominant local observable, offering an efficient, scalable pathway for high-precision error mitigation on NISQ devices.
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.
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.
Quantum error mitigation (QEM) is critical for harnessing the potential of near-term quantum devices. Particularly, QEM protocols can be designed based on machine learning, where the mapping between noisy computational outputs and ideal ones can be learned on a training set consisting of Clifford circuits or near-Clifford circuits that contain only a limited number of non-Clifford gates. This learned mapping is then applied to noisy target circuits to estimate the ideal computational output. In this work, we propose a learning-based error mitigation framework called Clifford Perturbation Data Regression (CPDR), which constructs training sets by Clifford circuits with small perturbations. Specifically, these circuits are parameterized quantum circuits, where the rotation angles of the gates are restricted to a narrow range, ensuring that the gates remain close to Clifford gates. This design enables the efficient simulation of the training circuits using the Sparse Pauli Dynamics method. As a result, CPDR is able to utilize training sets with a better diversity to train the model, compared with previous learning-based QEM models that construct training sets with only Clifford or near-Clifford circuits. Numerical simulations on small-scale Ising model circuits demonstrate that the performance of CPDR dramatically outperforms that of existing methods such as Zero-Noise Extrapolation and learning-based Probabilistic Error Cancellation. Furthermore, using the experimental data from IBM's 127-qubit Eagle processor, our findings suggest that CPDR demonstrates improved accuracy compared to the original mitigation results reported in [Nature 618, 500 (2023)].
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 computers, while offering exponential computational advantages, are highly vulnerable to noise-induced errors, particularly during the measurement process. This paper investigates machine learning-based error mitigation strategies with a focus on transfer learning. By initially training a base model on a specific quantum device, we leverage transfer learning to adapt the model for use on different quantum computers. This approach not only achieves superior performance with reduced dataset size and training time but also maintains hardware agnosticism, as demonstrated through tests on various IBM quantum backends. Our method provides a practical solution for enhancing the accuracy and efficiency of noisy intermediate-scale quantum (NISQ) algorithms by improving machine learning-based error mitigation.