Photonic Implementation of Quantum Relay and Encoders/Decoders for Sparse-Graph Quantum Codes Based on Optical Hybrid

We show that any family of deterministic universal quantum gates can be implemented in integrated optics. We further show how to implement Pauli gates, needed in quantum-error correction, using the same technology. Two basic circuits required in quantum teleportation systems are Bell states and quantum relay. We describe how to implement them in integrated optics. Finally, we study the implementation of sparse-graph (SG) quantum codes in integrated optics. We demonstrate that entanglement assisted SG codes significantly outperform corresponding dual-containing quantum codes.