Improving Parameters of Asymptotically Good Quantum LDPC Codes via Stronger Product Expansion

Citation

Cai, Yiyi (2025) Improving Parameters of Asymptotically Good Quantum LDPC Codes via Stronger Product Expansion. Senior thesis (Major), California Institute of Technology. doi:10.7907/665j-dr37. https://resolver.caltech.edu/CaltechTHESIS:06062025-083109104

Abstract

Quantum low-density parity-check (qLDPC) codes are a promising path toward scalable, fault-tolerant quantum computation. This thesis focuses on improving the relative distance of asymptotically good qLDPC codes, with a particular emphasis on quantum Tanner codes. We present a refined analysis of product expansion in tensor codes and introduce a stronger form of the expansion property that leads to improved lower bounds on code distance. Numerical results further illustrate how our method enables improved trade-offs between code parameters under practical constraints. While our analysis is framed in the quantum Tanner code setting, the techniques are broadly applicable to other constructions whose local codes are based on tensor product decompositions. Our work contributes to closing the gap between asymptotic constructions and realizable quantum codes.

Thesis Files