Fiber Bundle Codes: Breaking the $N^{1/2}\mathrm{polylog}(N)$ 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.

39 pages, 2 figures; v2 gives self-contained presentation of weight reduction using weight reduction for classical base code. Also contains explanation of relation between codes in terms of homotopy equivalence of chain complexes

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