Quantum localization bounds Trotter errors in digital quantum simulation
Abstract
A fundamental challenge in digital quantum simulation (DQS) is the control of inherent errors. These appear when discretizing the time evolution generated by the Hamiltonian of a quantum manybody system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localizationby constraining the time evolution through quantum interferencestrongly bounds these errors for local observables. Consequently, for generic quantum manybody Hamiltonians, Trotter errors can become independent of system size and total simulation time. For local observables, DQS is thus intrinsically much more robust than what one might expect from known error bounds on the global manybody wave function. This robustness is characterized by a sharp threshold as a function of the Trotter step size. The threshold separates a regular region with controllable Trotter errors, where the system exhibits localization in the space of eigenstates of the timeevolution operator, from a quantum chaotic regime where the trajectory is quickly scrambled throughout the entire Hilbert space. Our findings show that DQS with comparatively large Trotter steps can retain controlled Trotter errors for local observables. It is thus possible to reduce the number of quantum gate operations required to represent the desired time evolution faithfully, thereby mitigating the effects of imperfect individual gate operations
 Publication:

Science Advances
 Pub Date:
 April 2019
 DOI:
 10.1126/sciadv.aau8342
 arXiv:
 arXiv:1806.11123
 Bibcode:
 2019SciA....5.8342H
 Keywords:

 Quantum Physics;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Statistical Mechanics
 EPrint:
 13 pages, 6 figures (including supplementary material), corrected typos