A universal framework for the quantum simulation of Yang–Mills theory
Abstract
Quantum computers promise to simulate complex quantum field theories that are intractable for classical computers, potentially revealing new physics in strongly interacting systems. Current approaches for simulating Yang-Mills gauge theories face significant technical barriers due to complex group structures and complicated truncation schemes that vary drastically between different theories. Here we show that the orbifold lattice formulation provides a universal framework for quantum simulation of Yang-Mills theories with arbitrary gauge groups and dimensions. Our approach reduces all theories to the same simple Hamiltonian form, enabling implementation with standard quantum gates regardless of system complexity. We demonstrate explicit quantum circuits using only controlled-NOT and single-qubit operations, with concrete resource estimates for time evolution algorithms. This universal framework simplifies quantum simulation of gauge theories and enables systematic scaling to larger systems on fault-tolerant quantum computers. The quantum simulation of lattice gauge theories is anticipated to be an important scientific application of future quantum computing capabilities. This work elaborates on a formulation of lattice gauge theory quantum simulation that aims to require quantum computing techniques akin to those for simulating ϕ4 scalar field theory by utilizing non-compact continuous variable quantum degrees of freedom.
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