Quantum LDPC Codes With Positive Rate and Minimum Distance Proportional to the Square Root of the Blocklength

The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with a fixed non-zero rate is logarithmic in the blocklength. We propose a construction of quantum LDPC codes with fixed non-zero rate and prove that the minimum distance grows proportionally to the square root of the blocklength.