On the Photonic Implementation of Universal Quantum Gates, Bell States Preparation Circuit, Quantum Relay and Quantum LDPC Encoders and Decoders

We show that any family of universal quantum gates can be implemented based on a single optical hybrid/Mach-Zehnder interferometer (MZI)/directional coupler (DC) and either a highly nonlinear optical fiber or a tap coupler with an avalanche photodiode. We further show how to implement Pauli gates, which are needed in quantum error correction, using the same technology. The use of Bell states in quantum teleportation is essential. We also show how to implement the Bell states preparation circuit. To extend the transmission distance of quantum teleportation systems, the use of quantum relays is necessary. We show how to implement the quantum relay in integrated optics as well. We further study the implementation of encoders/decoders for sparse-graph quantum codes and show that the encoder/decoder for arbitrary quantum sparse-graph code can be implemented in integrated optics as well. We also study the performance of sparse-graph codes and demonstrate that entanglement-assisted sparse-graph codes from balanced incomplete block designs significantly outperform the corresponding dual-containing quantum codes. Finally, we provide several theorems that can be used in the design of entanglement-assisted (EA) quantum codes that require only one qubit to be shared between the source and the destination.