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arXiv 2601.01550quant-phcs.DS
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低能量子空间中的时间依赖哈密顿量模拟

Time-Dependent Low-Energy Simulation Accelerates Adiabatic State Preparation

CFCS, School of Computer Science, Peking University(北京大学计算机科学与技术学院前沿计算研究中心);IIIS, Tsinghua University(清华大学交叉信息研究院);SEAS, Harvard University(哈佛大学工程与应用科学学院)

Shuo Zhou, Zhaokai Pan, Weiyuan Gong, Tongyang Li

AI总结:

本文提出在低能量子空间中改进时间依赖哈密顿量模拟的算法,并证明了查询复杂度下界。

摘要:

哈密顿量模拟是绝热量子计算、量子控制和量子多体物理中的关键子程序,其中量子动力学通常发生在低能量子空间中。与时间不变的哈密顿量模拟不同,迄今为止,对于在低能量假设下时间依赖哈密顿量的量子模拟算法仍缺乏全面理解。在本文中,我们研究在初始状态支持于低能量子空间的情况下,能够改进标准性能保证的程度。特别是,我们基于乘积公式计算了基于时间依赖自旋哈密顿量的数字量子模拟的 Trotter 数,假设初始状态支持于少量低能量本征态,并展示了在模拟全幺正模拟方面的改进。技术上,我们通过利用绝热扰动理论分析底层哈密顿量的时间变化能量谱,推导出基于乘积公式的低能量模拟误差的交换子缩放。我们进一步讨论了非平衡量子多体动力学模拟和绝热态准备的应用。最后,我们证明了通用时间依赖哈密顿量模拟的查询复杂度下界。

英文摘要:

Hamiltonian simulations are key subroutines in adiabatic quantum computation and quantum many-body physics, where quantum dynamics often happen in the low-energy sector. Previous studies have shown that the low-energy assumption can reduce the resource requirements of standard time-independent Hamiltonian simulation algorithms. However, whether such advantages extend to time-dependent Hamiltonian simulation remains open. In this paper, we consider the adiabatic regime where the relevant low-energy subspace is spanned by a fixed number of low-energy eigenstates and separated from the rest of the spectrum by a gap. We show that, for simulating spin Hamiltonians by product formulas, the explicit system size dependence in the leading commutator-scaling term can be replaced by a low-energy scale up to logarithmic factors. Technically, we derive the low-energy simulation error with commutator scaling for product formulas by leveraging adiabatic perturbation theory to analyze the time-variant energy spectrum of the underlying Hamiltonian. We further conduct numerical experiments on adiabatic state preparation of an illustrative example system to support our theoretical findings. Finally, we prove a lower bound of query complexity for generic time-dependent Hamiltonian simulations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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