Quantum Gate Sets for Lattice QCD in the strong coupling limit: $N_f=1$

TL;DR

This paper develops specific quantum gate sets to simulate lattice QCD in the strong-coupling limit with one flavor, enabling quantum simulations without bosonic Hilbert space truncation and facilitating studies at non-zero density.

Contribution

It introduces primitive quantum gate sets tailored for lattice QCD in the strong-coupling limit, leveraging color-singlet degrees of freedom to avoid bosonic truncation.

Findings

Gate sets enable simulation of mesonic dynamics with two qubits per site.

Baryons are static and decouple in continuous time limit.

Controlled gate implementations facilitate baryon dynamics simulation.

Abstract

We derive the primitive quantum gate sets to simulate lattice quantum chromodynamics (LQCD) in the strong-coupling limit with one flavor of massless staggered quarks. This theory is of interest for studies at non-zero density as the sign problem can be overcome using Monte Carlo methods. In this work, we use it as a testing ground for quantum simulations. The key point is that no truncation of the bosonic Hilbert space is necessary as the theory is formulated in terms of color-singlet degrees of freedom (``baryons'' and ``mesons''). The baryons become static in the limit of continuous time and decouple, whereas the dynamics of the mesonic theory involves two qubits per lattice site. Lending dynamics also to the ``baryons'' simply requires to use the derived gate set in its controlled version.