Physics

Qubit

Mathematics

Lattice gauge theory

Gauge theory

Digitization

Gauge fixing

Theoretical physics

Gauge boson

Computer science

Quantum computer

Quantum mechanics

Theoretical computer science

Hilbert space

Telecommunications

Quantum

Physical Review Research

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)) 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.2 MoreReceived 22 April 2020Accepted 4 June 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033039Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLattice gauge theoryNon-Abelian gauge theoriesQuantum algorithmsQuantum computationQuantum error correctionQuantum simulationQuantum InformationParticles & Fields

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