Heyl Markus, Hauke Philipp, Zoller Peter
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany.
Kirchhoff-Institute for Physics, Heidelberg University, 69120 Heidelberg, Germany.
Sci Adv. 2019 Apr 12;5(4):eaau8342. doi: 10.1126/sciadv.aau8342. eCollection 2019 Apr.
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.
数字量子模拟（DQS）中的一个基本挑战是控制固有误差，这种误差在将量子多体系统的时间演化离散化为一系列量子门（称为 Trotter 化）时出现。在此，我们表明，通过量子干涉来约束时间演化的量子局域化，对于局部可观测量能强烈地限制这些误差，从而导致误差与系统大小和模拟时间无关。因此，DQS 在本质上比全局多体波函数的已知误差界限所表明的要稳健得多。这种稳健性的特征是作为 Trotter 步长函数的一个尖锐阈值，它将具有可控 Trotter 误差的局域化区域与量子混沌区域区分开来。我们的研究结果表明，具有相对较大 Trotter 步长的 DQS 对于局部可观测量可以保持可控误差。因此，有可能减少忠实地表示所需时间演化所需的门操作数量。
