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

TL;DR

This paper introduces constant-time, low-overhead gadgets for performing fault-tolerant logical measurements on 2D hypergraph product codes, enabling faster quantum computations with minimal space costs.

Contribution

It constructs parallel logical measurement gadgets with constant time and near-constant space overhead for 2D hypergraph product codes, improving fault-tolerant quantum operations.

Findings

Achieves $O(1)$ time overhead for logical measurements

Demonstrates near-constant space overhead ($ ilde{O}(1)$)

Shows fault-tolerance for $d$ operations in $O(d)$ time

Abstract

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. (arXiv:2510.14895), that performing $d$ surgery operations in $O(d)$ time is fault tolerant. Our gadgets combine the strengths of different approaches to fault-tolerant logical operations: they partially retain the flexibility of surgery while achieving overheads comparable to transversal gates. Consequently, they are well-suited for near-term experimental realization and demonstrate new possibilities in the design of gadgets for fast logical computation.