Abstract

This talk focuses on the simulation of fermionic systems on arbitrary graphs, including two-dimensional lattices. We start by examining the one-dimensional Jordan-Wigner transformation and its expansion to two-dimensional exact bosonization. This method is crucial for simulating fermions using emergent fermions in the ℤ2 toric code. We then discuss how fermionic observables and Pauli matrices can be interconnected through locality-preserving mappings. We show that all fermion-to-qubit mappings are achievable from the two-dimensional exact bosonization by applying Clifford circuits. Furthermore, our exploration includes ℤ2 lattice gauge theories and Pauli stabilizer codes, where we propose new methods to improve the code distances of stabilizer codes in fermion simulations on a two-dimensional lattice without decreasing the fermionic code rate. We modify the Bravyi-Kitaev Superfast simulation (BKSF) and demonstrate its error-correcting properties on various two-dimensional lattices. This talk provides a detailed and accessible overview of the current state of fermion simulation, bosonization techniques, and quantum error correction, demonstrating their importance in quantum computing.

Speaker Intro

陈昱安，北京大学物理学院量子材料科学中心助理教授。2015 年 6 月毕业于美国麻省理工学院，获得数学、物理学学士学位；2020 年 6 月毕业于美国加州理工学院，获得物理学博士学位。曾任谷歌公司量子人工智能（Quantum AI）研究团队研究科学家。2020 年 9月至 2023 年 6 月期间，在美国马里兰大学帕克分校联合量子研究所（JQI）博士后研究员 。2023 年 7 月加入北京大学物理学院。2009年和2010年分别获第40届国际物理奥林匹克竞赛（IPhO）金牌和第51届国际数学奥林匹克竞赛铜牌。