Fiber Bundle Codes: Breaking the $N^1/2øperatornamepolylog(N)$ Barrier for Quantum LDPC Codes

Abstract

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