Reducing resource overheads for fault-tolerant quantum computing with many-hypercube codes

Last year, I proposed "many-hypercube codes" as concatenated [[6,4,2]] quantum error-detecting codes [1]. The advantage of this code family is its high encoding rates given by (4/6)^L (L is the concatenation level). For example, the encoding rate is about 30% (20%) for code distance 8 (16). However, fault-tolerant preparation of logical states encoded with the many-hypercube codes requires considerably large numbers of ancilla qubits. In this work, I reduce the overheads by introducing more efficient error-detection methods. I also investigate the smallest many-hypercube codes, namely, concatenated [[4,2,2]] quantum error-detecting codes, which have some advantages over the original ones because of their small sizes.

[1] H. Goto, Sci. Adv. 10, eadp6388 (2024).