Hamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the implementation of exponentials of commutators, which has previously made it unappealing for quantum computing. The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle, at the expense of a lack of provable global numeric error bounds. In this work, we establish one such error bound for CFQM-based time-dependent quantum Hamiltonian simulation by carefully estimating the error of each step involved in their definition. This allows us to compare its cost with the alternatives, and show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude. As a result, we find that CFQMs may be particularly useful to simulate time-dependent Hamiltonians on early fault-tolerant quantum computers.

中文翻译：

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通过无换向器的准 Magnus 算子对瞬态哈密顿量进行量子模拟


哈密顿模拟可以说是量子计算机最基本的应用。Magnus 运算符是计算数学中瞬态哈密顿量模拟的常用方法，但其使用需要实现换向器的指数运算，这在以前使其对量子计算没有吸引力。无换向器的准 Magnus 算子 （CFQM） 的开发绕过了这一障碍，但代价是缺乏可证明的全局数值误差边界。在这项工作中，我们通过仔细估计定义中涉及的每个步骤的误差，为基于 CFQM 的时间相关量子哈密顿模拟建立了一个这样的误差边界。这使我们能够将其成本与替代方案进行比较，并表明 CFQM 通常是可用的最有效的乘积公式技术，其效率高出一个数量级以上。因此，我们发现 CFQM 对于在早期容错量子计算机上模拟瞬态哈密顿量可能特别有用。