Fast surgery for quantum LDPC codes
Nouédyn Baspin, Lucas Berent, Lawrence Z. Cohen
TL;DR
The paper tackles the high temporal overhead of fault-tolerant processing with quantum LDPC codes by introducing a fast generalized surgery protocol that uses a constant number of syndrome-measurement rounds. The approach builds a merged code from a base code and an ancilla via a total complex constructed from a homomorphic chain map, and it proves distance preservation and fault-tolerance under expansion assumptions. A concrete expansion-boosting technique using a repetition code is developed, and the authors demonstrate the method on Abelian multi-cycle codes with numerical evidence that single-round fast surgery can rival multi-round standard approaches. This work advances practical, low-overhead fault-tolerant quantum computation with LDPC codes and points to extensions to non-CSS codes and larger codes.
Abstract
Quantum LDPC codes promise significant reductions in physical qubit overhead compared with topological codes. However, many existing constructions for performing logical operations come with distance-dependent temporal overheads. We introduce a scheme for performing generalized surgery on quantum LDPC codes using a constant number of rounds of syndrome measurement. The merged code in our scheme is constructed by taking the total complex of the base code and a suitably chosen homomorphic chain complex. We demonstrate the applicability of our scheme on an example multi-cycle code and assess the performance under a phenomenological noise model, showing that fast surgery performs comparably to standard generalized surgery with multiple rounds. Our results pave the way towards fault-tolerant quantum computing with LDPC codes with both low spatial and temporal overheads.