使用Trotter与THRIFT哈密顿量模拟方法高效模拟线性化Vlasov-Poisson动力学的量子模拟
Efficient Quantum Simulation of Linearized Vlasov--Poisson Dynamics Using Trotter and THRIFT Hamiltonian Simulation Methods
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中文总结 AI 辅助
本研究将线性化Vlasov-Poisson方程重构为适用于门控量子计算的厄米特哈密顿量，采用Trotter、THRIFT方法结合Richardson外推，系统模拟对比了磁化与非磁化等离子体的动力学，为相关量子模拟提供实用指南。
中文摘要 AI 辅助
Vlasov-Poisson系统为等离子体提供了基础的动力学描述，在理解朗道阻尼、波粒相互作用等集体现象中发挥核心作用。由于相空间的高维性，这类动力学的高效数值模拟仍具挑战性。本研究针对磁化与非磁化等离子体，将离散化后的线性化Vlasov-Poisson方程重构为适用于门控量子计算的厄米特哈密顿量，采用量子模拟框架开展研究。时间演化分别使用一阶、二阶、四阶Trotter-Suzuki乘积公式，以及近期提出的时间分辨相互作用框架（THRIFT）实现。针对磁化与非磁化等离子体模型，通过电场演化、状态保真度、收敛行为、能量守恒、纠缠熵，以及电路深度、两量子比特门复杂度等量子资源需求，系统评估不同模拟方法的性能。为在不增加电路深度的前提下进一步减小有限时间步长误差，引入Richardson外推作为误差缓解技术。研究结果全面对比了Trotter与THRIFT方法，为在门控量子计算机上准确且资源高效地模拟等离子体动力学提供了实用指南。
英文摘要
The Vlasov--Poisson system provides the fundamental kinetic description of plasma and plays a central role in understanding collective phenomena such as Landau damping and wave--particle interactions. Efficient numerical simulation of these dynamics remains challenging because of the high dimensionality of phase space. In this work, we studied magnetized and non-magnetized plasma using a quantum simulation framework for the linearized Vlasov-Poisson equation by reformulating the discretized system as a Hermitian Hamiltonian suitable for gate-based quantum computation. The time evolution is implemented using first, second and fourth-order Trotter--Suzuki product formulas and the recently proposed Time-Resolved Interaction Framework (THRIFT). The performance of the different simulation methods is systematically evaluated through electric field evolution, state fidelity, convergence behavior, energy conservation, entanglement entropy and quantum resource requirements, including circuit depth and two-qubit gate complexity, for both magnetized and non-magnetized plasma models. To further reduce finite time step errors without increasing circuit depth, Richardson extrapolation is incorporated as a error-mitigation technique. The results provide a comprehensive comparison of Trotter and THRIFT approaches and establish practical guidelines for accurate and resource-efficient quantum simulation of plasma dynamics on gate-based quantum computers.
