Fusion-based implementation of qLDPC codes with quantum emitters

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 an architecture specifically tailored to quantum emitters which can implement any Calderbank-Shor-Steane (CSS) qLDPC code. In this architecture, the photonic resource states are deterministically produced via quantum emitters and a conditional repeat-until-success strategy is incorporated to achieve high photon loss tolerance. We simulate small exemplary Bivariate Bicycle qLDPC codes and 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 though with significantly higher encoding rates.