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Classical simulation of Yang-Baxter gates

Published

Author(s)

Stephen P. Jordan, Gorjan Alagic, Aniruddha Bapat

Abstract

A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group Bn for every n ≥ 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 ≥ 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.
Proceedings Title
9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)
Conference Dates
May 21-23, 2014
Conference Location
Singapore

Keywords

algorithms, quantum computing, topology

Citation

Jordan, S. , Alagic, G. and Bapat, A. (2014), Classical simulation of Yang-Baxter gates, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014), Singapore, -1 (Accessed July 19, 2024)

Issues

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Created November 3, 2014, Updated June 2, 2021