Taming Trotter Errors with Quantum Resources

TL;DR

This paper explores how quantum resources like entanglement and magic influence the accuracy and error distribution in Hamiltonian simulation, revealing that certain resources can improve robustness.

Contribution

It establishes a rigorous link between quantum resources and error behavior in Trotter-based simulation, showing how entanglement and magic affect error variance and tail distribution.

Findings

Error variance decreases with higher entanglement entropy.

High magic states have lighter-tailed error distributions.

Quantum resources can enhance simulation robustness despite complexity.

Abstract

Quantum simulation is a cornerstone application of quantum computing, yet how fundamental quantum resources--entanglement and non-stabilizerness (``magic")--shape simulation fidelity remains an open question. In this work, 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.