Error-Mitigated Hamiltonian Simulation: Complexity Analysis and Optimization for Near-Term and Early-Fault-Tolerant Quantum Computers

Abstract: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. We analyze noisy Hamiltonian simulation with quantum error mitigation (QEM) for Trotterized and randomized linear-combination-of-unitaries (LCU)-based Hamiltonian simulation algorithms. We give a 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. Importantly, optimizing the depth of randomized-LCU-based Hamiltonian simulation improves the simulation-time dependence of the sampling-overhead exponent from quadratic to linear. 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.

arXiv:2603.11527 [quant-ph]

(or arXiv:2603.11527v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.11527 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.