Quantum error correction (QEC) protects quantum information from decoherence and enables large-scale quantum computation. The surface code has long been considered a leading error-correcting code due to its simple structure and high threshold. However, it suffers from two significant drawbacks: the high cost of implementing non-Clifford gates and a very low encoding rate. The first drawback can, in principle, be addressed in a fault-tolerant manner using three-dimensional codes. Nevertheless, the thresholds of such codes under realistic noise models are often unknown. The second drawback may be mitigated by employing quantum low-density parity-check (qLDPC) codes, although constructing such codes typically eludes important constraints of practical quantum hardware. This talk contains two parts. First, I will discuss the threshold of the 3D toric code under imperfect measurements, based on statistical-mechanical mapping and a duality method. Our results show a reasonably high phenomenological threshold of 2%, reduced from 3.3% in the case of perfect measurements. The second part of the talk focuses on a class of qLDPC codes known as bivariate bicycle codes, which are particularly suited for practical quantum processors. We establish their topological nature and propose an efficient approach to classify and construct such codes. Additionally, we assess their performance and potential for superconducting and neutral-atom quantum computers.

Biography

Dr. Ke Liu received his PhD from Leiden University in 2016 and worked as a postdoc at the University of Munich until 2023. Then, he joined USTC for a faculty position to lead a theory subgroup of quantum error correction. His research area lies in the frontiers of condensed matter theory and quantum computing, with a particular emphasis on the many-body and fault-tolerant properties of unconventional topological codes.

Inviter

Hao Song