Taming Trotter Errors with Quantum Resources
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917409605025792 |
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| author | Zhang, Xiangran Xu, Jue Zhao, Qi Zhou, You |
| author_facet | Zhang, Xiangran Xu, Jue Zhao, Qi Zhou, You |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13486 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Taming Trotter Errors with Quantum Resources Zhang, Xiangran Xu, Jue Zhao, Qi Zhou, You Quantum Physics 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. |
| title | Taming Trotter Errors with Quantum Resources |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.13486 |