Quantum computational representation of gauge field theory

Abstract

Presented is a quantum computing model of a quantum field theory for a system of fermions interacting via a massive gauge field. The model describes a relativistic superconducting fluid and uses a metric tensor field to both encode the fermion's intrinsic spin in the torsion of curved space and encode the coupling of fermions via a massive 4-potential field. The quantum computing model is a lattice model whose cell size is a deformation parameter: the equivalent lattice and curved-space gauge field theory models both reduce to quantum field theory in flat Minkowski space at zero cell size. The low-energy expansions of the lattice model and Euler-Lagrange equations of the curved-space gauge field theory are the same equations of motion. The fermion and gauge fields obey the Dirac and Proca equations, and the gauge field strength is determined by the fermion field.