Optimal Trotterization in universal quantum simulators under faulty control

George C. Knee and William J. Munro
Phys. Rev. A 91, 052327 – Published 26 May 2015

Abstract

Universal quantum simulation may provide insights into those many-body systems that cannot be described classically and that cannot be efficiently simulated with current technology. The Trotter formula, which decomposes a desired unitary time evolution of the simulator into a stroboscopic sequence of repeated elementary evolutions, is a key algorithmic component which makes quantum simulation of dynamics tractable. The Trotter number n sets the time scale on which a computer running this algorithm is switched from one elementary evolution to another. In the ideal case, the precision of the simulation can be arbitrarily controlled by increasing n. We study a more realistic scenario where each gate is applied imperfectly. The resultant trade-off in errors leads to an ultimate limit on the precision of the simulation. We calculate the optimum Trotter number n* that achieves this limit, which is the minimum statistical distance from the actual simulation to the ideal one.

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  • Received 10 March 2015

DOI:https://doi.org/10.1103/PhysRevA.91.052327

©2015 American Physical Society

Authors & Affiliations

George C. Knee* and William J. Munro

  • NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan

  • *gk@physics.org

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Issue

Vol. 91, Iss. 5 — May 2015

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