Lattice Quantum Chromodynamics and Electrodynamics on a Universal Quantum Computer

Lattice gauge theories form a cornerstone of computational particle physics. Here we present explicit quantum algorithms down to gate-by-gate level circuits for simulating quantum electrodynamics and chromodynamics. The algorithms include every element of the Kogut-Susskind Hamiltonian for U(1), SU(2), and SU(3) theories, and are extensible to SU(N) theories. Furthermore, we provide concrete estimates of the fault-tolerant computational resources required for simulations of lattice gauge theories in any dimension and lattice size. Future improvements based on our results will one day bring about new discoveries in particle and nuclear physics via quantum simulations.