Classical simulation of Yang-Baxter gates

TL;DR

This paper presents a classical simulation method for quantum circuits generated by certain Yang-Baxter gates, including all qubit solutions, enabling efficient classical computation of these topological quantum circuits.

Contribution

It introduces a probabilistic classical algorithm to simulate a broad class of Yang-Baxter-based quantum circuits, including all qubit solutions and some higher-dimensional cases.

Findings

Classical simulation is possible for all qubit Yang-Baxter solutions.

The algorithm extends to some higher-dimensional solutions.

Efficient simulation may impact understanding of topological quantum computation.

Abstract

A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantum-computational gate, then topological braiding corresponds to a quantum circuit. A basic question is when such a representation affords universal quantum computation. In this work, we show how to classically simulate these circuits when the gate in question belongs to certain families of solutions to the Yang-Baxter equation. These include all of the qubit (i.e., $d = 2$) solutions, and some simple families that include solutions for arbitrary $d \ge 2$. Our main tool is a probabilistic classical algorithm for efficient simulation of a more general class of quantum circuits. This algorithm may be of use outside the present setting.