Error-Mitigated Hamiltonian Simulation: Complexity Analysis and Optimization for Near-Term and Early-Fault-Tolerant Quantum Computers
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911508358758400 |
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| author | Murota, Keisuke Todo, Synge Endo, Suguru |
| author_facet | Murota, Keisuke Todo, Synge Endo, Suguru |
| contents | Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated into performance analysis, despite the non-negligible noise levels in quantum devices. In this work, we analyze noisy Hamiltonian simulation with quantum error mitigation for Trotterized and randomized LCU-based Hamiltonian simulation algorithms. We give an end-to-end comprehensive complexity analysis of error-mitigated Hamiltonian simulation algorithms using the mean-squared error. Because quantum error mitigation incurs an exponential cost with the number of layers in quantum algorithms, there is a trade-off between the sampling cost and the bias in simulation accuracy or the algorithmic sampling overhead. Optimizing this trade-off, we derive an analytic depth-selection rule and characterize the optimal end-to-end scaling as a function of target accuracy and noise parameters. We further quantify the noise-characterization cost required for error mitigation via gate set tomography and the recently proposed space-time noise inversion method, showing that the latter can significantly reduce the characterization overhead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11527 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Error-Mitigated Hamiltonian Simulation: Complexity Analysis and Optimization for Near-Term and Early-Fault-Tolerant Quantum Computers Murota, Keisuke Todo, Synge Endo, Suguru Quantum Physics Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated into performance analysis, despite the non-negligible noise levels in quantum devices. In this work, we analyze noisy Hamiltonian simulation with quantum error mitigation for Trotterized and randomized LCU-based Hamiltonian simulation algorithms. We give an end-to-end comprehensive complexity analysis of error-mitigated Hamiltonian simulation algorithms using the mean-squared error. Because quantum error mitigation incurs an exponential cost with the number of layers in quantum algorithms, there is a trade-off between the sampling cost and the bias in simulation accuracy or the algorithmic sampling overhead. Optimizing this trade-off, we derive an analytic depth-selection rule and characterize the optimal end-to-end scaling as a function of target accuracy and noise parameters. We further quantify the noise-characterization cost required for error mitigation via gate set tomography and the recently proposed space-time noise inversion method, showing that the latter can significantly reduce the characterization overhead. |
| title | Error-Mitigated Hamiltonian Simulation: Complexity Analysis and Optimization for Near-Term and Early-Fault-Tolerant Quantum Computers |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.11527 |