We propose a polynomial-time algorithm for preparing the Gibbs state of the two-dimensional toric code Hamiltonian at any temperature, starting from any initial condition, significantly improving upon prior estimates that suggested exponential scaling with inverse temperature. Our approach combines the Lindblad dynamics using a local Davies generator with simple global jump operators to enable efficient transitions between logical sectors. We also prove that the Lindblad dynamics with a digitally implemented low temperature local Davies generator is able to efficiently drive the quantum state towards the ground state manifold. Despite this progress, we explain why protecting quantum information in the 2D toric code with passive dynamics remains challenging.

报告人简介：Dr. Bowen Li joined City University of Hong Kong as an Assistant Professor since 2024 Fall. 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. His recent research interests are quantum information and computing, quantum many-body problems, and mathematical material science.