Implementation of VQE for SU(3) Lattice Gauge Theory on IBM's Quantum Devices

Implementation of Lattice QCD (LQCD) on a quantum computer is beginning to be feasible for simple systems, such as one-dimensional gauge theory with fermions. The Variational Quantum Eigensolver (VQE) is a hybrid classical-quantum optimizer. It is resilient to noise, and in the context of quantum simulation is useful for eigendecomposition and state-preparation. A circuit design for finding the ground state of the one-dimensional three-color lattice using VQE is implemented on two of IBM's 7-qubit quantum devices and their simulators. The devices have a limited runtime, so symmetries and separation of the circuit into static and parameter-dependent components are used to minimize the number of quantum circuit elements needed. This study provides a framework for use of VQE in quantum lattice gauge theory in the near future, which has the potential to advance LQCD's ability to provide both ab initio results for physical quantities needed for nuclear and particle physics experiments and efficiently reproduce relevant states.