PT - JOURNAL ARTICLE
AU - Heyl, Markus
AU - Hauke, Philipp
AU - Zoller, Peter
TI - Quantum localization bounds Trotter errors in digital quantum simulation
AID - 10.1126/sciadv.aau8342
DP - 2019 Apr 01
TA - Science Advances
PG - eaau8342
VI - 5
IP - 4
4099 - http://advances.sciencemag.org/content/5/4/eaau8342.short
4100 - http://advances.sciencemag.org/content/5/4/eaau8342.full
SO - Sci Adv2019 Apr 01; 5
AB - 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.