Description
Quantum error correction (QEC) protects quantum information by adding redundancies that help detect and correct errors. Understanding the limitations of QEC under different noise sources is crucial for the development of fault-tolerant quantum computers. In this talk, I will address the challenge of determining the fundamental (optimal) error correction thresholds of QEC codes using the coherent information (CI) of the mixed-state density matrix associated with these codes. This new approach allows us to obtain accurate optimal thresholds from small-sized codes (PRR L042014, 2024), uncover new connections between decoding phase transitions and fermionic topological phases of matter (arXiv:2412.12279), and study optimal thresholds under erasure errors and computational errors together in a rigorous manner (arXiv:2412.16727). I will also discuss how this approach to fundamental thresholds has led to new insights at the interface of quantum information, condensed matter physics, and statistical mechanics.
Links:
