Yang-Baxter gates and integrable circuit

Abstract: Brickwork circuits composed of the Yang-Baxter gates are integrable. It becomes an important tool to study the quantum many-body system out of equilibrium. I will talk about the properties of Yang-Baxter gates via the quantum information theory. We find that only certain two-qubit gates can be converted to the Yang-Baxter gates via the single-qubit gate operations. I will also talk about some possible extensions of the integrable circuits. Numerical analysis suggests that there is a broad class of circuits that are integrable, which are beyond the standard algebraic Bethe ansatz method.

Reference: [1] K. Zhang, K. Hao, K. Yu, V. Korepin, and W.-L. Yang, Geometric representations of braid and Yang-Baxter gates, J. Phys. A: Math. Theor. 57 445303, arXiv:2406.08320 (2024).

[2] K. Zhang, K. Yu, K. Hao, and V. Korepin, Optimal realization of Yang-Baxter gate on quantum computers, Adv. Quantum Technol. 2024, 2300345, arXiv:2307.16781 (2024).

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( slides | video )

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BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

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