Lifting quantum Markov dynamics to speed up mixing

We generalize the concept of non-reversible lifts for reversible diffusion processes initiated by Eberle and Lorler (2024) to quantum Markov dynamics. The lifting operation, which naturally results in hypocoercive processes, can be formally interpreted as, though not restricted to, the reverse of the overdamped limit. We prove that the L^2 convergence rate of the lifted process is bounded above by the square root of the spectral gap of its overdamped dynamics, indicating that the lifting approach can at most achieve a transition from diffusive to ballistic mixing speeds. Further, using the variational hypocoercivity framework based on space-time Poincare inequalities, we derive a lower bound for the convergence rate of the lifted dynamics. These findings offer quantitative convergence.

Speaker

Bowen Li 李博文

City University of Hong Kong

Time

Fri., 14:00-15:00, May 23, 2025

Venue

B626, Shuangqing Complex Building A

About the speaker

Dr. Bowen Li received his BSc in Mathematics from Wuhan University in 2017. He obtained his PhD in Mathematics from The Chinese University of Hong Kong in 2021. From 2021 to 2024, he was a Phillip Griffiths Research Assistant Professor in Duke University. Dr. Bowen Li joined City University of Hong Kong in 2024.

See more details on the homepage:

https://bwlimath.github.io/