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

Abstract

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.