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We provide $poly\log$ sparse quantum codes for correcting the erasure channelarbitrarily close to the capacity. Specifically, we provide $[[n, k, d]]$quantum stabilizer codes that correct for the erasure channel arbitrarily closeto the capacity if the erasure probability is at least $0.33$, and with agenerating set $\langle S_1, S_2, ... S_{n-k} \rangle$ such that $|S_i|\leq\log^{2+\zeta}(n)$ for all $i$ and for any $\zeta > 0$ with high probability.In this work we show that the result of Delfosse et al. is tight: one canconstruct capacity approaching codes with weight almost $O(1)$.

polylog-LDPC Capacity Achieving Codes for the Noisy Quantum Erasure Channel