Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques

Understand

We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2) and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension.

• We provide explicit circuit constructions as well as T-gate counts and logical qubit counts for Hamiltonian simulation.
• We find up to 25 orders of magnitude reduction in space-time volume over Trotter methods for simulations of non-Abelian lattice gauge theories relevant to the standard model.
• This improvement results from our algorithm having polynomial scaling with the number of colors in the gauge theory, achieved by utilizing oracle constructions relying on the sparsity of physical operators, in contrast to the exponential scaling seen in state-of-the-art Trotter methods which employ explicit mappings onto Pauli operators.