Quantum Annealer

Lattice gauge theory is an essential tool for strongly interacting non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. Recent studies suggest that quantum computers could extend the reach of lattice gauge theory in dramatic ways, but the usefulness of quantum annealing hardware for lattice gauge theory has not yet been explored. In this work, we implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition. Numerical results are obtained from calculations on D-Wave Advantage hardware for eigenvalues, eigenvectors, vacuum expectation values, and time evolution. The success of this initial exploration indicates that the quantum annealer might become a useful hardware platform for some aspects of lattice gauge theories.

This paper investigates the possibility of using an analog quantum computer as commercialized by D-Wave to solve large QUBO problems by means of a single invocation of the quantum annealer. Indeed this machine solves a spin glass problem with programmable coefficients but subject to quite strong topology restrictions on the set of non-zero coefficients. Rather than mapping problem variables onto multiple qbits, an approach which requires many invocations of the annealer to solve small size problems, it is tempting to investigate the existence of sparse relaxations compliant with the qbits interconnection topology of the machine, hence solvable in one invocation of the annealing oracle, but still providing good-quality solutions to the original problem. This paper provides an experimental setup which aims to determine whether or not such convenient relaxations do exist or, rather, are easy to find. Our
experiments suggest that it is not the case and, therefore, that solving even moderate size arbitrary problems with a single call to a quantum annealer is not possible at least within the constraints of the so-called Chimera topology. We conclude the paper with a number of perspectives that this results imply on the design of heuristics taking profit of a quantum annealing oracle to solve large scale problems.

Lattice gauge theory is an essential tool for strongly interacting non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. Recent studies suggest that quantum computers could extend the reach of lattice gauge theory in dramatic ways, but the usefulness of quantum annealing hardware for lattice gauge theory has not yet been explored. In this work, we implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition. These plaquettes are in two spatial dimensions and calculations use the Hamiltonian formulation where time is not discretized. Numerical results are obtained from calculations on D-Wave Advantage hardware for eigenvalues, eigenvectors, vacuum expectation values, and time evolution. The success of this initial exploration indicates that the quantum annealer might become a useful hardware platform for some aspects of lattice gauge theories.