Lattice Quantum Chromodynamics for Quantum Simulations

Abstract:We develop a framework for quantum simulations of lattice SU($N_c$) gauge theory with quarks. Staggered and Wilson lattice fermions are considered in two and three spatial dimensions and a theta angle is included in three dimensions. The physical, gauge-invariant Hilbert space is formulated in a representation basis, where gauge and fermionic degrees of freedom are encoded by irreducible representations of SU($N_c$) that tensor at each lattice site to contain a singlet. We discuss algorithms for simulating time evolution on quantum computers and carry out noiseless simulations of lattice quantum chromodynamics ($N_c=3$) on small lattices with up to 32 qubits, showcasing theta angle effects, hadronic states, string dynamics, and a baryon chemical potential for the first time in three spatial dimensions.

arXiv:2607.26445 [quant-ph]

(or arXiv:2607.26445v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.26445 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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