Mainz 2017 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 55: Quantum Computing II
Q 55.2: Talk
Friday, March 10, 2017, 14:45–15:00, P 2
Energy localization ensures robustness of digital quantum simulation — •Philipp Hauke1,2, Markus Heyl3, and Peter Zoller1,2 — 1Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck — 2Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck — 3Max-Planck-Institut fuer Physik komplexer Systeme, D-01187 Dresden
Following Lloyds seminal work from 1996, the Trotter error of digital quantum simulation (DQSs) is usually assumed to diverge with simulated time and particle number. This is true if one is interested in the correctness of the full time-evolution operator. In quantum simulation, however, the quantities of interest are typically few-body observables. Understanding the DQS as a periodically driven system, we demonstrate that, once the Trotter step is sufficiently small, the error of few-body observables remains bounded even for large systems and for arbitrarily long times. This is ensured for all systems that display energy localization. In that case, a sharp transition exists into a regime where Trotter errors in local observables become perturbative. Even in systems where energy localization does not exist, we argue that the DQS deteriorates only logarithmically with time. As these findings show, digital quantum simulation can be exponentially better than usually stated, as long as one is concerned with few-body observables.