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

References in corpus (1)

• Quantum LDPC Codes with Almost Linear Minimum Distance

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