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Abstract
Quantum networks promise to generate shared entanglement between distant users, which can support applications such as quantum key distribution, distributed quantum computing and distributed quantum sensing. A quantum network is made up of nodes known as quantum repeaters. A quantum repeater protects quantum information using error-corrected physical quantum memories or quantum error-correcting codes made up of photonic entangled states. This dissertation examines both varieties of quantum repeaters. It begins with an all-inclusive guidebook to the stabilizer formalism and linear optics, which is utilized extensively throughout the dissertation. In the first part of the dissertation, we present protocols for quantum memory-based repeaters, which govern the quantum operations performed at the quantum repeater. Two-qubit Bell state measurement is the most commonly used operation for quantum repeater protocols. The entanglement generation rate of the protocols that utilize Bell state measurements decays exponentially with the distance between users. Our first protocol achieves an entanglement rate that does not scale with distance by performing multi-qubit joint projective measurements, such as projections onto GHZ states. The second protocol we present explores distilling noisy Bell states using quantum error correcting codes to generate entanglement along a chain of quantum repeaters. We analyze the effect of the code's properties on the entanglement rate and the fidelity delivered to the end user nodes, and the number of quantum memories used per repeater node.
The second part of the dissertation investigates the architectures for all-photonic quantum repeaters, which utilizes a particular class of dual-rail photonic entangled states -- known as the repeater graph state (RGS) -- as a quantum error correcting code to store quantum information. The quality of an RGS is characterized by two factors: (1) the entanglement rate attained and (2) the single photon sources required to prepare the RGS. We enhance both factors by designing an RGS that achieves a higher entanglement rate with fewer qubits and photon sources. By employing quantum emitters as single photon sources and modifying the allowed operations between emitters and photons, we have devised three schemes to prepare photonic entangled states : (1) a linear optics-based scheme that recycles states from failed linear optical circuits, reducing the number of quantum emitters needed by half, (2) a deterministic scheme using only a handful of emitters but with an increased qubit loss probability in the generated state, and (3) a hybrid scheme combining the benefits of the two schemes above. We evaluate the rate-vs.-distance performance of our all-photonic repeater protocol using our optimized emitter-based and the hybrid RGS-preparation schemes, and show orders of magnitude improvement in the number of emitters needed at repeater nodes, compared with previously-known schemes.