Constant-Time Surgery on 2D Hypergraph Product Codes with Near-Constant Space Overhead

Understand

Generalized code surgery is a versatile and low-overhead technique for performing fault-tolerant computation on quantum low-density parity-check (qLDPC) codes.

• In many settings, surgery exhibits practical space overheads, while its time overhead remains a bottleneck at $O(d)$ syndrome rounds per operation.
• In this work, we construct surgery gadgets that perform parallel logical measurements on 2D hypergraph product codes in constant time overhead ($O(1)$) and near-constant space overhead ($\tilde{O}(1)$).
• The reduced time overhead is a result of amortization, as we show, following the formulation by Cowtan et al.