Title: Complexity and order in approximate quantum error-correcting codes

报告人: 刘子文（丘成桐数学科学中心）

时间地点：11月28日（周二）下午 2:00pm，静斋105

Abstract: Quantum codes achieving approximate quantum error correction (AQEC) are useful, often fundamentally important, from both practical and physical perspectives but lack a systematic understanding. In this work, we establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) properties, covering both all-to-all and geometric scenarios including lattice systems. To this end, we introduce a type of code parameter that we call “subsystem variance”, which is closely related to the optimal AQEC precision. Our key finding is that if the subsystem variance is below an O(k/n) critical threshold then any state in the code subspace must obey certain circuit complexity lower bounds, which identify nontrivial “phases” of codes. Our theory of AQEC provides a versatile framework for understanding the quantum complexity and order of many-body quantum systems, offering new insights for wide-ranging physical scenarios, in particular, topological order and critical quantum systems/CFT, which are of outstanding importance in many-body and high energy physics. Ref: arXiv:2310.04710.

Bio: Zi-Wen Liu joined the faculty of Yau Mathematical Sciences Center, Tsinghua University in Fall 2023. Prior to this, he was a 5-Year Senior Postdoctoral Fellow at Perimeter Institute for Theoretical Physics. He obtained his PhD in Physics at MIT. Lately he has been most interested in the interactions between quantum information/computation and physics and mathematics.