Optimal realization of Yang-Baxter gate on quantum computers

TL;DR

This paper develops optimal methods for implementing Yang-Baxter gates on quantum computers, compares their fidelities, and demonstrates their use in simulating the Yang-Baxter equation, advancing quantum simulation of integrable systems.

Contribution

It introduces geometrically motivated optimal realizations of Yang-Baxter gates and systematic pulse control methods, improving fidelity in quantum simulations of integrable systems.

Findings

Pulse realizations outperform CNOT/$R_{zz}$ implementations in fidelity.

Optimal realizations reduce gate complexity for Yang-Baxter gates.

Successful demonstration of Yang-Baxter equation simulation on IBM quantum computers.

Abstract

Quantum computers provide a promising method to study the dynamics of many-body systems beyond classical simulation. On the other hand, the analytical methods developed and results obtained from the integrable systems provide deep insights on the many-body system. Quantum simulation of the integrable system not only provides a valid benchmark for quantum computers but is also the first step in studying integrable-breaking systems. The building block for the simulation of an integrable system is the Yang-Baxter gate. It is vital to know how to optimally realize the Yang-Baxter gates on quantum computers. Based on the geometric picture of the Yang-Baxter gates, we present the optimal realizations of two types of Yang-Baxter gates with a minimal number of CNOT or $R_{zz}$ gates. We also show how to systematically realize the Yang-Baxter gates via the pulse control. We test and compare the different realizations on IBM quantum computers. We find that the pulse realizations of the Yang-Baxter gates always have a higher gate fidelity compared to the optimal CNOT or $R_{zz}$ realizations. On the basis of the above optimal realizations, we demonstrate the simulation of the Yang-Baxter equation on quantum computers. Our results provide a guideline and standard for further experimental studies based on the Yang-Baxter gate.