The Yang-Baxter equation, Quantum computing and Quantum entanglement

Abstract

We present a method to construct infinite families of entangling $2$-qudit gates, and amongst them entangling $2$-qudit gates which satisfy the Yang-Baxter equation. We show that, given $2$-qudit gates $c$ and $d$, if $c$ or $d$ is entangling, then their Tracy-Singh product $c⊠d$ is also entangling and we can provide non-entangled states which become entangled after the application of $c⊠d$.

arXiv commentchanges and some additions have been made

References in corpus (16)

• Skew braces and the Yang-Baxter equation
• Braiding Operators are Universal Quantum Gates
• Comparing Quantum Entanglement and Topological Entanglement
• A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation
• Optical Simulation of Yang-Baxter Equation
• On structure groups of set-theoretic solutions to the Yang-Baxter equation
• Garside groups and Yang-Baxter equation
• Entanglement Criteria - Quantum and Topological
• Set theoretic Yang-Baxter & reflection equations and quantum group symmetries
• Quantum time dynamics of 1D-Heisenberg models employing the Yang-Baxter equation for circuit compression
• Finite quotients of groups of I-type
• Experimental realization of the Yang-Baxter Equation via NMR interferometry
• Conserved charges in the quantum simulation of integrable spin chains
• Yang-Baxter operators need quantum entanglement to distinguish knots
• Cyclic groups and quantum logic gates
• Solutions to the constant Yang-Baxter equation in all dimensions