Solving Gauss's law on digital quantum computers with loop-string-hadron digitization

Abstract

We show that using the loop-string-hadron (LSH) formulation of SU(2) lattice gauge theory (I. Raychowdhury and J. R. Stryker, Phys. Rev. D 101, 114502 (2020)10.1103/PhysRevD.101.114502) as a basis for digital quantum computation easily solves an important problem of fundamental interest: Implementing gauge invariance (or Gauss's law) exactly. We first discuss the structure of the LSH Hilbert space in d spatial dimensions, its truncation, and its digitization with qubits. Error detection and mitigation in gauge theory simulations would benefit from physicality "oracles,"so we decompose circuits that flag gauge-invariant wave functions. We then analyze the logical qubit costs and entangling gate counts involved with the protocols. The LSH basis could save or cost more qubits than a Kogut-Susskind-type representation basis, depending on how the bases are digitized as well as the spatial dimension. The numerous other clear benefits encourage future studies into applying this framework.