Gluon field digitization for quantum computers

Andrei Alexandru (Department of Physics, The George Washington University, Washington, D.C. 20052, USA; Department of Physics, University of Maryland, College Park, Maryland 20742, USA) ; Paulo F. Bedaque (Department of Physics, University of Maryland, College Park, Maryland 20742, USA) ; Siddhartha Harmalkar (Department of Physics, University of Maryland, College Park, Maryland 20742, USA) ; Henry Lamm (Department of Physics, University of Maryland, College Park, Maryland 20742, USA) ; Scott Lawrence (Department of Physics, University of Maryland, College Park, Maryland 20742, USA) ; et al. - Show all 6 authors

Simulations of gauge theories on quantum computers require the digitization of continuous field variables. Digitization schemes that use the minimum amount of qubits are desirable. We present a practical scheme for digitizing SU(3) gauge theories via its discrete subgroup S(1080). The S(1080) standard Wilson action cannot be used since a phase transition occurs as the coupling is decreased, well before the scaling regime. We propose a modified action that allows simulations in the scaling window and carry out classical Monte Carlo calculations down to lattice spacings of order a0.08 fm. We compute a set of observables with subpercent precision at multiple lattice spacings and show that the continuum extrapolated value agrees with the full SU(3) results. This suggests that this digitization scheme provides sufficient precision for noisy intermediate-scale quantum era QCD simulations.

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      "value": "Simulations of gauge theories on quantum computers require the digitization of continuous field variables. Digitization schemes that use the minimum amount of qubits are desirable. We present a practical scheme for digitizing <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> gauge theories via its discrete subgroup <math><mi>S</mi><mo>(</mo><mn>1080</mn><mo>)</mo></math>. The <math><mi>S</mi><mo>(</mo><mn>1080</mn><mo>)</mo></math> standard Wilson action cannot be used since a phase transition occurs as the coupling is decreased, well before the scaling regime. We propose a modified action that allows simulations in the scaling window and carry out classical Monte Carlo calculations down to lattice spacings of order <math><mi>a</mi><mo>\u2248</mo><mn>0.08</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></math>. We compute a set of observables with subpercent precision at multiple lattice spacings and show that the continuum extrapolated value agrees with the full <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> results. This suggests that this digitization scheme provides sufficient precision for noisy intermediate-scale quantum era QCD simulations."
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Published on:
03 December 2019
Publisher:
APS
Published in:
Physical Review D , Volume 100 (2019)
Issue 11
DOI:
https://doi.org/10.1103/PhysRevD.100.114501
arXiv:
1906.11213
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: