SU(2) lattice gauge theory on a 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.Comment: 19 pages, 10 figure

Time-evolution of SU(2) lattice gauge theory on a quantum computer

Lattice Gauge Theory is a mathematical tool used to study the forces of nature, like Quantum Electrodynamics and Quantum Chromodynamics. Quantum computers offer an alternative to classical computers in studying these forces. In my thesis, a gate-based quantum computer was used to perform calculations of the propagation of an excitation in real-time. A new error mitigation method was developed to greatly extend the range of comprehensible data over time by using the physics circuits to estimate the accumulated error. I also developed the theoretical foundation for higher energy systems, as well as higher dimensional geometry

Self-mitigating Trotter circuits for SU(2) lattice gauge theory on a quantum computer

Quantum computers offer the possibility to implement lattice gauge theory in Minkowski rather than Euclidean spacetime, thus allowing calculations of processes that evolve in real time. In this work, calculations within SU(2) pure gauge theory are able to show the motion of an excitation traveling across a spatial lattice in real time. This is accomplished by using a simple yet powerful method for error mitigation, where the original circuit is used both forward and backward in time. For a two-plaquette lattice, meaningful results are obtained from a circuit containing hundreds of CNOT gates. The same method is used for a five-plaquette lattice, where calculations show that residual systematic effects can be reduced through follow-up mitigation.Comment: 10 pages, 7 figure