Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers

Daniel C. Hackett, Kiel Howe, Ciaran Hughes, William Jay, Ethan T. Neil, and James N. Simone
Phys. Rev. A 99, 062341 – Published 28 June 2019

Abstract

In the near-future noisy intermediate-scale quantum era of quantum computing technology, applications of quantum computing will be limited to calculations of very modest scales in terms of the number of qubits used. The need to represent numeric quantities using limited resources leads to digitization errors which must be taken into account. As a first step towards quantum simulations of realistic high-energy physics problems, we use ensembles of SU(2) lattice gauge fields generated with standard classical computing to explore the effects of digitizing elements of the gauge group to a finite set. We consider several methods for digitizing the group, finding the best performance from an action-preserving projection onto a mesh. Working in (3+1) dimensions, we find that using 7 (qu)bits to represent each SU(2) gauge link induces a digitization error of the order of 10% in short-distance observables and 2% in long-distance observables. Promisingly, our results indicate that each SU(2) gauge link can be represented by O(10) (qu)bits, from which we estimate that a 163SU(2) lattice could be simulated with no more than O(105) (qu)bits. Our results on digitization are also of interest as a form of lossy compression that could be used in high-performance classical computing to alleviate communications bottlenecks.

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  • Received 23 November 2018

DOI:https://doi.org/10.1103/PhysRevA.99.062341

©2019 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsQuantum Information, Science & Technology

Authors & Affiliations

Daniel C. Hackett1,*, Kiel Howe2,†, Ciaran Hughes2,‡, William Jay1,2,§, Ethan T. Neil1,3,∥, and James N. Simone2,¶

  • 1Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
  • 2Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
  • 3RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA

  • *daniel.hackett@colorado.edu
  • khowe@fnal.gov
  • chughes@fnal.gov
  • §wjay@fnal.gov
  • ethan.neil@colorado.edu
  • simone@fnal.gov

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Vol. 99, Iss. 6 — June 2019

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