Quantum Network Protocols and Architectures

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 advances the state of the art for both varieties of quantum repeaters. It begins with an all-inclusive guidebook to the stabilizer formalism and linear optics---interspersed with new results and insights on graphical rules for arbitrary Clifford manipulations of stabilizer states---which is used extensively throughout the dissertation. In the first part of the dissertation, we present protocols for quantum-memory-based repeaters, the quantum logic and measurement capabilities of which govern the quantum operations performed at the repeater node. The two-qubit Bell state measurement (BSM) is the most commonly used operation by a quantum repeater to lengthen the reach of entanglement to more than one link connecting nearest network nodes. The entanglement generation rate of the protocols that utilize only BSMs decays exponentially with the distance between users. Our first protocol achieves an entanglement rate that does not scale with distance between end users. It uses multi-qubit joint projective measurements, such as projections onto maximally-entangled 3-qubit GHZ states. The second protocol we present performs BSMs and distills noisy Bell states using quantum error correcting codes, across optimized hop lengths, to generate entanglement along a repeater chain. We show that the choice of the code, and hence its distance properties and error correcting abilities, can enable trading between the entanglement rate versus the fidelity delivered to the end users.The second part of the dissertation investigates architectures for all-photonic quantum repeaters, which utilize a particular class of dual-rail photonic-qubit entangled states, known as the repeater graph state (RGS), as a quantum error correcting code to store quantum information. The RGS acts as a quantum memory by error correcting against photon loss on its locally-held photonic qubits (while photonic qubits entangled with the RGS fly to the neighboring nodes to seek nearest-neighbor entanglement). The same RGS also allows for multiplexed BSMs and GHZ projections only via single-qubit measurements on its photons, once the success-failure outcomes of the remote entanglement attempts to the neighboring nodes come back, using the principles of measurement based quantum computing. The quality of an RGS is therefore characterized by two factors: (1) the amount of error correction it can provide for a given RGS size, which translates into the end-to-end entanglement rate, and (2) the number of single photon sources required to prepare the RGS near-deterministically at every clock cycle, which turns into the major resource requirement for all-photonic repeaters. We dramatically improve both of the above by designing an RGS that achieves a higher entanglement rate compared with previously-known RGS geometries and associated protocols, but with fewer qubits in it, and can be prepared using fewer photon sources. By employing quantum emitters as single photon sources and allowing for simple quantum logic operations between emitters and photons that have been experimentally demonstrated, we devised three schemes to prepare photonic entangled states: (1) a linear-optics-based scheme that recycles graph states from failed fusion attempts, thereby reducing the number of quantum emitters needed by about a half, (2) a deterministic scheme using only a handful of emitters but with an increased qubit loss probability accrued in the generated photonic graph 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 each repeater node, compared with previously-known schemes.