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arXiv · 1704.04405

Classical simulation of quantum circuits by dynamical localization: analytic results for Pauli-observable scrambling in time-dependent disorder

Adrian Chapman·Akimasa Miyake
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Abstract

We extend the concept of Anderson localization, the confinement of quantum information in a spatially irregular potential, to quantum circuits. Considering matchgate circuits, generated by time-dependent spin-1/2 XY Hamiltonians, we give an analytic formula for the out-of-time-ordered correlator of a local observable, and show that it can be efficiently evaluated by a classical computer even when the explicit Heisenberg time evolution cannot. Because this quantity bounds the average error incurred by truncating the evolution to a spatially limited region, we demonstrate dynamical localization as a means for classically simulating quantum computation and give examples of localized phases under certain spatio-temporal disordered Hamiltonians.

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Adrian Chapman, Akimasa Miyake. 2017-04-14. Classical simulation of quantum circuits by dynamical localization: analytic results for Pauli-observable scrambling in time-dependent disorder. https://doi.org/10.1103/physreva.98.012309

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