Quantum simulation of non-unitary operators generated by R-matrices in the Yang-Baxter equation

¹ School of Energy Storage Science and Engineering, North China University of Technology Beijing 100144, China
² Beijing Key Laboratory of Information Metamaterials - Beijing 100144, China
³ Shenzhen SpinQ Technology Co Ltd. - Shenzhen 518000, China

Received: 7 April 2026
Accepted: 21 May 2026

Abstract

As a type of non-Abelian anyons, Yang-Lee anyons have topological quantum computing potential comparable to that of Fibonacci anyons, and their non-unitary braiding property is conducive to the construction of non-unitary quantum gates. Any braiding process of Yang-Lee anyons can be realized by combining two basic braiding matrices, which are generated by the R-matrix of the Yang-Baxter equation. However, one of the basic braiding matrices of the braiding process of Yang-Lee anyons is difficult to be simulated directly because of its non-unitary property. To address this challenge, we propose, using the linear combination of unitaries (LCU) framework, the first probabilistic simulation scheme for the three-dimensional non-unitary matrix associated with Yang-Lee anyon braiding. We design two feasible quantum circuits in a qubit-qutrit hybrid system and in a pure-qubit system. Both schemes achieve simulation through controlled operations and ancillary qubit measurements, and the success probability is jointly determined by the input state, the dimensions of the total Hilbert space and the normalization factor. This work presents an approach to simulating the three-dimensional non-unitary matrix associated with Yang-Lee anyon braiding, which can serve as a building block for non-unitary quantum information processing.