A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge
  Theory in the Local Multiplet Basis
Maintaining local interactions in the quantum simulation of gauge field
theories relegates most states in the Hilbert space to be unphysical --
theoretically benign, but experimentally difficult to avoid. Reformulations of
the gauge fields can modify the ratio of physical to gauge-variant states often
through classically preprocessing the Hilbert space and modifying the
representation of the field on qubit degrees of freedom. This paper considers
the implications of representing SU(3) Yang-Mills gauge theory on a lattice of
irreducible representations in both a global basis of projected global quantum
numbers and a local basis in which controlled-plaquette operators support
efficient time evolution. Classically integrating over the internal gauge space
at each vertex (e.g., color isospin and color hypercharge) significantly
reduces both the qubit requirements and the dimensionality of the unphysical
Hilbert space. Initiating tuning procedures that may inform future calculations
at scale, the time evolution of one- and two-plaquettes are implemented on one
of IBM's superconducting quantum devices, and early benchmark quantities are
identified. The potential advantages of qudit environments, with either
constrained 2D hexagonal or 1D nearest-neighbor internal state connectivity,
are discussed for future large-scale calculations.
Anthony Ciavarella Natalie Klco Martin J. Savage