Asymptotically Good Quantum and Locally Testable Classical LDPC Codes

Constructs the first asymptotically good quantum LDPC codes: families of $[[n,k,d]]$ codes with $k=\Theta (n)$ and $d=\Theta (n)$ while maintaining constant stabilizer weight. Resolves a 25-year-old open problem in quantum error correction and opens the path to constant-overhead fault tolerance.

Key Results

• First quantum codes with linear rate AND linear distance AND constant check weight
• Encoding rate: k/n → constant as n → ∞
• Distance: d = Θ(n) (optimal scaling)
• Based on balanced product of classical LDPC codes over suitable groups

Links

• Journal: Proceedings of the 54th ACM STOC
• arXiv: 2111.03654

Zoo Links

• qldpc-codes
• surface-code-logical-qubit