Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to ${\mathbb{D}}_8$

Abstract

In this work, we address the problem of a resource-efficient formulation of non-Abelian LGTs by focusing on the difficulty of simulating fermionic degrees of freedom and the Hilbert space redundancy. First, we show a procedure that removes the matter and improves the efficiency of the hardware resources. We demonstrate it for the simplest non-Abelian group addressable with this procedure, ${\mathbb{D}}_8$, both in the cases of one (1D) and two (2D) spatial dimensions. Then, with the objective of running a variational quantum simulation on real quantum hardware, we map the ${\mathbb{D}}_8$ lattice gauge theory 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 as the one developed in $\text{href}$. Our results show the effectiveness of the matter-removing procedure, solving the redundancy problem and reducing the amount of quantum resources. This can serve as a way of simulating lattice gauge theories in high spatial dimensions, with non-Abelian gauge groups, and including dynamical fermions.

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Cited by in corpus (3)

• Robust Control and Entanglement of Qudits in Neutral Atom Arrays
• Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection
• Phase structure of the one-dimensional ${\mathbb{Z}}_2$ lattice gauge theory with second nearest-neighbor interactions