Quantum simulation of non-Abelian lattice gauge theories: A variational approach to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">D</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:math> with dynamic

Quantum simulation of lattice gauge theories (LGTs) provides a powerful framework for understanding nonperturbative phenomena. However, to realize the hope of answering challenging physics questions on near-term devices it is crucial to develop resource-efficient formulations, in particular for non-Abelian LGTs and beyond (1+1) dimensions. In this work, we address this issue by focusing on the difficulty of simulating fermionic degrees of freedom and on mitigating the Hilbert space redundancy, i.e., the presence of exponentially many nonphysical states that do not obey gauge invariance. First, we show a procedure that removes the matter and improves the hardware-resource efficiency. We demonstrate it for the simplest non-Abelian group addressable with this procedure, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi mathvariant="double-struck">D</a:mi><a:mn>8</a:mn></a:msub></a:math>, in the cases of both one and two spatial dimensions. Then, with the objective of running a variational quantum simulation on real quantum hardware, we map the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi mathvariant="double-struck">D</c:mi><c:mn>8</c:mn></c:msub></c:math> LGT onto qudit systems with local interactions. We propose a variational scheme for the qudit system with a local Hamiltonian, which can be implemented on a universal qudit quantum device. Our results show the effectiveness of the matter-removing procedure, solving the redundancy problem, and reducing the amount of quantum resources. This approach can serve as a way of simulating LGTs in high spatial dimensions, with non-Abelian gauge groups, and including dynamical fermions.