Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT

TL;DR

This paper develops a set of quantum gates for simulating the binary tetrahedral group, an approximation to SU(2) lattice gauge theory, and benchmarks some gates on IBM quantum hardware.

Contribution

It introduces primitive quantum gates for the $ ext{BT}$ group and demonstrates their experimental implementation on a real quantum device.

Findings

Inversion and trace gates achieved fidelities between 14-55%.

The gate set enables digital quantum simulation of $ ext{BT}$ group.

The approach approximates SU(2) lattice gauge theory with minimal qubits.

Abstract

We construct a primitive gate set for the digital quantum simulation of the binary tetrahedral ($\mathbb{BT}$) group on two quantum architectures. This nonabelian discrete group serves as a crude approximation to $SU(2)$ lattice gauge theory while requiring five qubits or one quicosotetrit per gauge link. The necessary basic primitives are the inversion gate, the group multiplication gate, the trace gate, and the $\mathbb{BT}$ Fourier transform over $\mathbb{BT}$. We experimentally benchmark the inversion and trace gates on ibm nairobi, with estimated fidelities between $14-55\%$, depending on the input state.