Scheduling teleportation in noisy memories

The decoherence of qubits in noisy memories is a major obstacle in implementing a quantum network. In this study, we investigate the effects of decoherence on the fidelity of a quantum network node that handles continuous teleportation requests. To create a teleportation channel, an EPR pair is distributed, which is a probabilistic process that causes delays at the node. This delay causes decoherence in the information as it has to be stored in noisy memory until a teleportation channel is established. We model the memory platform as a buffer that stores incoming qubits waiting for a teleportation channel. The buffer is parameterized by decoherence time, buffer size, and EPR generation rate. We provide a framework that enables us to obtain a probability density function for fidelity loss incurred by a qubit entering this system, and we provide closed-form solutions for calculating average fidelity. We explore the effects of scheduling decisions on fidelity and prove that serving the youngest qubit first and removing the oldest qubits/requests when new ones arrive when the buffer is full maximizes average fidelity. We discuss the trade-offs between throughput and fidelity. Lastly, we use this framework to model a single repeater node and calculate the average fidelity of the end-to-end entanglement produced.