Describing Trotterized Time Evolutions on Noisy Quantum Computers via Static Effective Lindbladians

Abstract

We consider the extent to which a Trotterized time evolution implemented on a quantum computer is altered by the presence of decoherence. Given a specific set of assumptions regarding the manner in which noise processes acting on such a device can be modeled at the circuit level, we show how the effects of noise can be reinterpreted as a shift to the dynamics of the original system being simulated. In particular, we find that this shift can be described through the use of static Lindblad noise terms, which act in addition to the original unitary dynamics. The form of these noise terms depends not only on the underlying noise processes occurring on the device, but also on the original unitary dynamics, as well as the manner in which these dynamics are simulated on the device, i.e., the choice of quantum algorithm. We call this effectively simulated open quantum system the noisy algorithm model. Our results are confirmed through numerical analysis.

15 pages, 11 figures main text; 3 pages, 2 figures appendix. This third version is a result of the peer review process with the journal Quantum, which has accepted this article. This is the final arXiv version which will be published in Quantum. The majority of the changes are minor clarifying edits to the text, in order to aide in understanding. We have also expanded the number of references