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.
The decoding algorithm runs on each block in O(kl) time, implying that decoding at each level also requires O(kl) time with parallel execution
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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.