Reliability of analog quantum simulation

Mohan Sarovar, Jun Zhang, Lishan Zeng

Published 2016-03-30Version 1

Analog quantum simulators (AQS) will likely be the first nontrivial application of quantum technology for predictive simulation. However, there remain questions regarding the degree of confidence that can be placed in the results of AQS since they do not naturally incorporate error correction. Specifically, how do we know whether an analog simulation of a quantum model will produce predictions that agree with the ideal model in the presence of inevitable imperfections? At the same time there is a widely held expectation that certain quantum simulation questions will be robust to errors and perturbations in the underlying hardware. Resolving these two points of view is a critical step in making the most of this promising technology. In this work we formalize the notion of AQS reliability by determining sensitivity of AQS outputs to underlying parameters, and formulate conditions for robust simulation. Our approach naturally reveals the importance of model symmetries in dictating the robust properties of a quantum simulation. To demonstrate the approach, we present analytical and numerical results that characterize the robust features of several quantum many-body models, including the transverse field Ising model and the Fermi-Hubbard model.