Concatenating surface codes with quantum Hamming codes achieves high error thresholds up to the surface code limit and suppresses logical errors more effectively than surface codes with comparable overhead for intermediate-scale quantum memories.
Denote the syn- dromes of the n-th block at level l as S(n) l = {si | i ∈ [0, kl − 1]}, where kl = l + 3 is the number of stabi- lizer generators
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Quantum memory based on concatenating surface codes and quantum Hamming codes
Concatenating surface codes with quantum Hamming codes achieves high error thresholds up to the surface code limit and suppresses logical errors more effectively than surface codes with comparable overhead for intermediate-scale quantum memories.