Gluon field digitization for quantum computers

Abstract

Simulations of gauge theories on quantum computers require the digitization of continuous field variables. Digitization schemes that uses 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 proposed a modified action that allows simulations in the scaling window and carry out classical Monte Carlo calculations down to lattice spacings of order a ≈ 0.08 fm. We compute a set of observables with sub-percent 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 NISQ-era QCD simulations.

Simulating lattice gauge theories within quantum technologies

“…The possibility to simulate a LGT in a quantum computer was first considered in [75], which estimated the required resources to perform a digital quantum simulation of U(1), SU(2) and SU (3) theories. See also other recent works on quantum computation [76][77][78][79][80][81][82][83], on superconducting quantum simulation [84,85], on atomic quantum simulation [41,[86][87][88][89][90][91][92][93][94][95], on classical simulation [96,97], or on Hamiltonian formulation [98,99] of lattice gauge theories, and for a general review on quantum simulation [6].…”

Loop, string, and hadron dynamics in SU(2) Hamiltonian lattice gauge theories

“…Using the available tensors, the complete set of nonvanishing singlets is listed below in (34)- (38):…”

“…Such simulations are instructive, but generalizing to non-Abelian gauge groups and multidimensional space is necessary to address the important problems where classical computers fall short. Work on these generalizations is underway [30][31][32][33][34][35][36][37][38][39] (see also Refs. [17,22] and references therein), but the state of these studies is even less mature due to the significant practical complications involved with non-Abelian interactions.…”

Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories

“…The discrete nature of TFT formulations makes it a generic tool to set up quantum computing protocols. It provides an alternative to field discretization [65][66][67]. Motivations for quantum computing include doing ab initio real-time calculations relevant to fragmentation processes and parton distribution functions [68].…”

“…Note also that it is possible to construct models where the approximations Eqs. (59) and (66) are exact. The questions of topological configurations and duality are discussed for Abelian gauge models of this type in various dimensions in Refs.…”