Empirical or Simulated? Revisiting Training Data Assumptions in Learning-Based Quantum Error Mitigation

Seyed Mohamad Ali Tousi, Guilherme N. DeSouza

Fadhil Fatih Shiddiq, Darell Timothy Tarigan, Hadyan Luthfan Prihadi +4 more

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.

Zhang, Ruiqi, Yuguo Shao, Fuchuan Wei +3 more

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)].

Jingpeng Zhang, Shengyong Li, Jie Han +3 more

Continuous-variable (CV) quantum systems provide a versatile platform for quantum information processing, in which quantum states can be represented in the quadrature phase space. In realistic implementations, environmental noise, primarily photon loss and dephasing, progressively degrades these states. Machine-learning-based quantum error mitigation (QEM) has recently emerged as a promising approach to suppress such noise; however, existing methods are typically limited to the training horizon and require training data that cover the entire evolution, which is experimentally demanding. Here we introduce a framework for extrapolative quantum error mitigation based on a time-conditioned Swin Transformer. By explicitly embedding the evolution time via adaptive layer normalization, the model learns a correction map that accounts for the continuous accumulation of noise while capturing nonlocal phase-space correlations. Numerical simulations under both Markovian and non-Markovian noise demonstrate accurate state recovery in the long-time regime, where existing approaches deteriorate. Our results establish extrapolative QEM as a practical route to mitigating noise in CV quantum systems without exhaustive training data.

Haoran Liao, Derek S. Wang, Iskandar Sitdikov +3 more

Nikita Korolev, Kirill Lakhmanskiy, Daniil Rabinovich

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.