Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers
Abstract
We report that in the nearfuture noisy intermediatescale quantum (NISQ) 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 highenergy physics problems, we explore classically the effects of digitizing elements of the $$\mathrm{SU}(2)$$ gauge group to a finite set. We consider several methods for digitizing the group, finding the best performance from an actionpreserving projection onto a mesh. Working in (3+1) dimensions, we find that using $$\sim 7$$ (qu)bits to represent each $$\mathrm{SU}(2)$$ gauge link induces a digitization error on the order of $$10\%$$ in shortdistance observables and $$2\%$$ in longdistance observables. Promisingly, our results indicate that each $$\mathrm{SU}(2)$$ gauge link can be represented by $$\mathcal{O}(10)$$ (qu)bits, from which we estimate that a $16^3$ $$\mathrm{SU}(2)$$ lattice could be simulated with no more than $$\mathcal{O}(10^5)$$ (qu)bits. Lastly, our results on digitization are also of interest as a form of lossy compression that could be used in highperformance classical computing to alleviate communications bottlenecks.
 Authors:

 Univ. of Colorado, Boulder, CO (United States)
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Univ. of Colorado, Boulder, CO (United States); Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Univ. of Colorado, Boulder, CO (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
 Publication Date:
 Research Org.:
 Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP)
 OSTI Identifier:
 1488593
 Alternate Identifier(s):
 OSTI ID: 1546279
 Report Number(s):
 arXiv:1811.03629; FERMILABPUB18615T
Journal ID: ISSN 24699926; PLRAAN; 1702968
 Grant/Contract Number:
 AC0207CH11359; SC0010005; SC0012704
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review A
 Additional Journal Information:
 Journal Volume: 99; Journal Issue: 6; Journal ID: ISSN 24699926
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Hackett, Daniel C., Howe, Kiel, Hughes, Ciaran, Jay, William, Neil, Ethan T., and Simone, James N. Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers. United States: N. p., 2019.
Web. doi:10.1103/PhysRevA.99.062341.
Hackett, Daniel C., Howe, Kiel, Hughes, Ciaran, Jay, William, Neil, Ethan T., & Simone, James N. Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers. United States. doi:10.1103/PhysRevA.99.062341.
Hackett, Daniel C., Howe, Kiel, Hughes, Ciaran, Jay, William, Neil, Ethan T., and Simone, James N. Fri .
"Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers". United States. doi:10.1103/PhysRevA.99.062341. https://www.osti.gov/servlets/purl/1488593.
@article{osti_1488593,
title = {Digitizing gauge fields: Lattice Monte Carlo results for future quantum computers},
author = {Hackett, Daniel C. and Howe, Kiel and Hughes, Ciaran and Jay, William and Neil, Ethan T. and Simone, James N.},
abstractNote = {We report that in the nearfuture noisy intermediatescale quantum (NISQ) 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 highenergy physics problems, we explore classically the effects of digitizing elements of the $\mathrm{SU}(2)$ gauge group to a finite set. We consider several methods for digitizing the group, finding the best performance from an actionpreserving projection onto a mesh. Working in (3+1) dimensions, we find that using $\sim 7$ (qu)bits to represent each $\mathrm{SU}(2)$ gauge link induces a digitization error on the order of $10\%$ in shortdistance observables and $2\%$ in longdistance observables. Promisingly, our results indicate that each $\mathrm{SU}(2)$ gauge link can be represented by $\mathcal{O}(10)$ (qu)bits, from which we estimate that a $16^3$ $\mathrm{SU}(2)$ lattice could be simulated with no more than $\mathcal{O}(10^5)$ (qu)bits. Lastly, our results on digitization are also of interest as a form of lossy compression that could be used in highperformance classical computing to alleviate communications bottlenecks.},
doi = {10.1103/PhysRevA.99.062341},
journal = {Physical Review A},
issn = {24699926},
number = 6,
volume = 99,
place = {United States},
year = {2019},
month = {6}
}
Web of Science
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