Randomizing multi-product formulas for Hamiltonian simulation
Randomizing multi-product formulas for Hamiltonian simulation
复制标题
随机化多乘积公式以进行哈密顿模拟
DOI：
10.22331/q-2022-09-19-806
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发表时间：
2021
期刊：
影响因子：
6.4
通讯作者：
J. Eisert
中科院分区：
文献类型：
--
作者：
Paul K. Faehrmann;M. Steudtner;R. Kueng;M. Kieferová;J. Eisert
量子模拟，即在量子计算机上对量子过程的模拟，为有效模拟凝聚态物理、量子化学和材料科学中的问题提供了一条前进的道路。虽然大多数量子模拟算法都是确定性的，但最近涌现的一些想法表明，随机化可以极大地提高算法的性能。在这项工作中，我们介绍了一种量子模拟方案，该方案一方面结合了随机编译的优点，另一方面结合了高阶多积公式，因为它们用于线性组合-酉（LCU）算法或量子误差缓解。在此过程中，我们提出了一个随机抽样框架，预计将对可编程量子模拟器有用，并提出了两种针对它量身定制的新的多乘积公式算法。我们的框架通过避免使用标准LCU方法实现多积公式所需的遗忘幅度放大来减少电路深度，使其对用于估计量子系统动力学的早期量子计算机特别有用，而不是执行成熟的量子相位估计。我们的算法使仿真误差随电路深度呈指数级缩小。为了证实它们的功能，我们证明了严格的性能界限以及随机抽样过程的浓度。我们证明了该方法在几个物理上有意义的哈密顿例子中的功能，包括费米子系统和Sachdev-Ye-Kitaev模型，该方法在努力中提供了有利的缩放。
Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of quantum simulation algorithms are deterministic, a recent surge of ideas has shown that randomization can greatly benefit algorithmic performance. In this work, we introduce a scheme for quantum simulation that unites the advantages of randomized compiling on the one hand and higher-order multiproduct formulas, as they are used for example in linear-combination-of-unitaries (LCU) algorithms or quantum error mitigation, on the other hand. In doing so, we propose a framework of randomized sampling that is expected to be useful for programmable quantum simulators and present two new multi-product formula algorithms tailored to it. Our framework reduces the circuit depth by circumventing the need for oblivious amplitude amplification required by the implementation of multi-product formulas using standard LCU methods, rendering it especially useful for early quantum computers used to estimate the dynamics of quantum systems instead of performing full-fledged quantum phase estimation. Our algorithms achieve a simulation error that shrinks exponentially with the circuit depth. To corroborate their functioning, we prove rigorous performance bounds as well as the concentration of the randomized sampling procedure. We demonstrate the functioning of the approach for several physically meaningful examples of Hamiltonians, including fermionic systems and the Sachdev–Ye–Kitaev model, for which the method provides a favorable scaling in the effort.
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影响因子：
6.7
作者：
McClean, Jarrod R.;Rubin, Nicholas C.;Babbush, Ryan
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Babbush, Ryan
影响因子：
6.4
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影响因子：
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通讯作者：
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影响因子：
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Preskill, John
影响因子：
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作者：
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通讯作者：
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