Primitive Quantum Gates for an $SU(2)$ Discrete Subgroup: Binary Octahedral

TL;DR

This paper develops a set of quantum gates to simulate the binary octahedral group, a nonabelian subgroup of SU(2), improving the approximation of SU(2) lattice gauge theories with a modest increase in qubits.

Contribution

It introduces a primitive gate set for the binary octahedral group, enhancing quantum simulation accuracy of SU(2) gauge theories over previous methods.

Findings

Enhanced approximation of SU(2) lattice gauge theory.

Requires one additional qubit per gauge link.

Provides a complete set of primitive gates for the binary octahedral group.

Abstract

We construct a primitive gate set for the digital quantum simulation of the 48-element binary octahedral ($\mathbb{BO}$) group. This nonabelian discrete group better approximates $SU(2)$ lattice gauge theory than previous work on the binary tetrahedral group at the cost of one additional qubit -- for a total of six -- per gauge link. The necessary primitives are the inversion gate, the group multiplication gate, the trace gate, and the $\mathbb{BO}$ Fourier transform.