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

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.