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Taming Trotter Errors with Quantum Resources
Xiangran Zhang1, Jue Xu1,2, Qi Zhao1
1The University of Hong Kong, QICI Quantum Information and Computation Initiative, School of Computing and Data Science, Pokfulam Road, Hong Kong SAR, China.
Abstract:
Quantum simulation is a cornerstone application of quantum computing, yet how fundamental quantum resources-entanglement and nonstabilizerness-shape simulation fidelity remains an open question. In this Letter, we establish a rigorous connection between these resources and the statistical behavior of algorithmic errors arising in Hamiltonian simulation based on the Trotter-Suzuki formula. By analyzing ensembles of states with fixed entanglement entropy or magic, we make two key discoveries: First, the variance of the Trotter error decreases with increasing entanglement entropy, indicating a stronger concentration of error for entangled states. Moreover, we find that the kurtosis of the error exhibits a negative linear dependence on magic, implying that states with high magic possess lighter-tailed error distributions and thus a reduced probability of large deviations. These findings reveal a subtle phenomenon: quantum resources that obstruct classical emulation may, paradoxically, enhance the intrinsic robustness of quantum simulation, highlighting a constructive interplay between complexity and stability in quantum computation.
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