Fiber Bundle Codes: Breaking the $N^{1/2} operatorname{polylog}(N)$ Barrier for Quantum LDPC Codes

We present a quantum LDPC code family that has distance $Omega(N^{3/5}/operatorname{polylog}(N))$ and $tildeTheta(N^{3/5})$ logical qubits. This is the first quantum LDPC code construction which achieves distance greater than $N^{1/2} operatorname{polylog}(N)$. The construction is based on generalizing the homological product of codes to a fiber bundle.