Fast surgery on homological product codes for constant time fault-tolerant quantum computation

Generalized code surgery is a versatile and low-overhead technique for performing fault-tolerant computation on encoded quantum information. While the time overhead of surgery operations has been a bottleneck to their performance, recent works [BBC25, CHWY25] have delineated conditions that enable surgery operations to be performed in amortized constant time. However, these conditions are challenging to satisfy for generic qLDPC codes without incurring significant space overheads. In this work, we construct fast surgery systems for homological product codes, including the toric code, which are promising candidates for practical quantum error correction. Our gadgets perform flexible parallel logical computation with (near-)constant space and constant time overhead, which are comparable to the overheads of transversal gates and are amenable to near-term experimental realization. These results showcase new possibilities in the design of fast logical computation gadgets which are vital for practical fault-tolerant quantum computation.