arXiv subjects

Xiangran Zhang

Publications and source records attributed to Xiangran Zhang.

2 recordsLinked to original sources

arXiv2026

Taming Trotter Errors with Quantum Resources

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.

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arXiv2026

Classical Simulation of Noiseless Quantum Dynamics without Randomness

Simulating noiseless quantum dynamics classically faces a fundamental dilemma: tensor-network methods become inefficient as entanglement saturates, while Pauli-truncation approaches typically rely on noise or randomness. To close the gap, we propose the Low-weight Pauli Dynamics (LPD) algorithm that efficiently approximates local observables for short-time dynamics in the absence of noise. We prove that the truncation error admits an average-case bound without assuming randomness, provided that the state is sufficiently entangled. Counterintuitively, entanglement--usually an obstacle for classical simulation--alleviates classical simulation error. We further show that such entangled states can be generated either by tensor-network classical simulation or near-term quantum devices. Our results establish a rigorous synergy between existing classical simulation methods and provide a complementary route to quantum simulation that reduces circuit depth for long-time dynamics, thereby extending the accessible regime of quantum dynamics.

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