In our previous studies [<a href="http://dx.doi.org/10.1103/PhysRevD.108.074501">Phys. Rev. D 108, 074501 (2023)</a>., Proc. Sci. LATTICE2023 (2024) 219 [<a href="http://arXiv.org/abs/2311.07209">arXiv:2311.07209</a>].], we confirmed that a quantum annealer can be used for importance sampling of gauge theories. In this paper, we extend the previous results to larger 2-dimensional and 4-dimensional lattices to generate ensembles for U(3) gauge theory in the strong coupling limit. We make use of the D-Wave quantum annealer to generate histograms for sublattices, and use the Metropolis-Hastings algorithm to determine thermodynamic observables and their dependence on the physical parameters on large volumes. We benchmark our results to those obtained from classical Monte Carlo simulations.

Germany

South Korea

Jangho Kim

Thomas Luu

Wolfgang Unger

Quantum sampling on a quantum annealer for large volumes in the strong coupling limit for gauge group U(3)

Lattice QCD in the strong coupling regime can be formulated in dual variables, which are integer-valued. It can be efficiently simulated for modest finite temperatures and finite densities via the worm algorithm, circumventing the finite density sign problem in this regime. However, the low temperature regime is more expensive to address. As the partition function is solely expressed in terms of integers, it can be cast as a combinatorial optimization problem that can be solved on a quantum annealer. We will first explain the setup of the system we want to study and then present its reformulation suitable for a quantum annealer, and in particular the D wave. As a proof of concept, we present first results obtained on D wave for gauge group U(1) and U(3), and outline the next steps towards gauge groups <math><mrow><mi>SU</mi></mrow><mo>(</mo><mn>3</mn><mo>)</mo></math>. We find that in addition, histogram reweighting greatly improves the accuracy of our observables when compared to analytic results.

<math><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> gauge theory in the strong coupling limit on a quantum annealer

Anisotropic lattice spacings are mandatory to reach the high temperatures where chiral symmetry is restored in the strong-coupling limit of lattice QCD. Here, we propose a simple criterion for the nonperturbative renormalization of the anisotropy coupling in strongly coupled <math><mrow><mi>SU</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo></mrow></math> or <math><mrow><mi>U</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo></mrow></math> lattice QCD with massless staggered fermions. We then compute the renormalized anisotropy, and the strong-coupling analogue of Karsch’s coefficients (the running anisotropy), for <math><msub><mi>N</mi><mi>c</mi></msub><mo>=</mo><mn>3</mn></math>. We achieve high precision by combining diagrammatic Monte Carlo and multihistogram reweighting techniques. We observe that the mean field prediction in the continuous time limit captures the nonperturbative scaling, but receives a large, previously neglected correction on the unit prefactor. Using our nonperturbative prescription in place of the mean field result, we observe large corrections of the same magnitude to the continuous time limit of the static baryon mass and of the location of the phase boundary associated with chiral symmetry restoration. In particular, the phase boundary, evaluated on different finite lattices, has a dramatically smaller dependence on the lattice time extent. We also estimate, as a byproduct, the pion decay constant and the chiral condensate of massless SU(3) QCD in the strong-coupling limit at zero temperature.