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 $\tilde\Theta(N^{3/5})$ 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.