Quantum localization bounds Trotter errors in digital quantum simulation
Quantum localization bounds Trotter errors in digital quantum simulation
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DOI：
10.1126/sciadv.aau8342
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发表时间：
2018-06
期刊：
影响因子：
13.6
通讯作者：
M. Heyl;P. Hauke;P. Zoller
中科院分区：
文献类型：
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作者：
M. Heyl;P. Hauke;P. Zoller
多体局域化现象提高了量子计算机上数字量子模拟的准确性。数字量子模拟（DQS）的一个根本挑战是控制固有误差，该误差在将量子多体系统的时间演化离散化为量子门序列时出现，称为特洛特化。在这里，我们表明，量子局域化，通过量子干涉约束的时间演化，强烈约束这些本地观测误差，导致独立于系统大小和模拟时间的误差。因此，DQS本质上比全局多体波函数的已知误差界限所建议的更鲁棒。这种鲁棒性的特征在于作为Trotter步长的函数的尖锐阈值，其将具有可控Trotter误差的局部区域与量子混沌制度分离。我们的研究结果表明，DQS与比较大的特罗特步骤可以保留控制误差的本地观测。因此，可以减少忠实地表示期望的时间演变所需的门操作的数量。
A many-body localization phenomenon boosts the accuracy of digital quantum simulation on quantum computers. A fundamental challenge in digital quantum simulation (DQS) is the control of an inherent error, which appears when discretizing the time evolution of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization-by constraining the time evolution through quantum interference-strongly bounds these errors for local observables, leading to an error independent of system size and simulation time. DQS is thus intrinsically much more robust than suggested by known error bounds on the global many-body wave function. This robustness is characterized by a sharp threshold as a function of the Trotter step size, which separates a localized region with controllable Trotter errors from a quantum chaotic regime. Our findings show that DQS with comparatively large Trotter steps can retain controlled errors for local observables. It is thus possible to reduce the number of gate operations required to represent the desired time evolution faithfully.