Fusion-based implementation of qLDPC codes with quantum emitters

Abstract: Quantum low-density parity check (qLDPC) codes offer higher encoding rate than topological codes, e.g. surface codes, making them favourable for practical, fault-tolerant quantum computing with low overhead. These codes are particularly well-suited for fusion-based photonic implementations as this platform readily supports non-local connections. We propose a method to implement any Calderbank-Shor-Steane (CSS) qLDPC code with fusions and photonic resource states, which can be deterministically produced by quantum emitters. We use this framework to perform a case study on small exemplary Bivariate Bicycle qLDPC codes. We analyse the performance of our constructions under relevant physical noise mechanisms, including erasures due to fusion failure or photon loss as well as Pauli errors. We obtain performances comparable with topological architectures despite the significantly higher encoding rate.