Destructive Error Interference in Product-Formula Lattice Simulation

Minh C. Tran, Su-Kuan Chu, Yuan Su, Andrew M. Childs, and Alexey V. Gorshkov
Phys. Rev. Lett. 124, 220502 – Published 4 June 2020
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Abstract

Quantum computers can efficiently simulate the dynamics of quantum systems. In this Letter, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product-formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of n sites for time t using the first-order product formula with r time slices is O(nt/r+nt3/r2) when nt2/r is less than a small constant. Given an error tolerance ϵ, the error bound yields an estimate of max{O(n2t/ϵ),O(n2t3/2/ϵ1/2)} for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [Proc. Natl. Acad. Sci. U.S.A. 115, 9456 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.

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  • Received 22 January 2020
  • Accepted 6 May 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.220502

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Minh C. Tran1,2,3, Su-Kuan Chu1,2, Yuan Su1,4,5, Andrew M. Childs1,4,5, and Alexey V. Gorshkov1,2,3

  • 1Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
  • 2Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
  • 3Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
  • 4Department of Computer Science, University of Maryland, College Park, Maryland 20742, USA
  • 5Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland 20742, USA

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Issue

Vol. 124, Iss. 22 — 5 June 2020

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