Scheduling Quantum Teleportation with Noisy Memories

TL;DR

This paper models how decoherence in noisy quantum memories affects the fidelity of quantum teleportation channels, providing a framework to optimize buffer management and improve quantum network reliability.

Contribution

It introduces a mathematical model for fidelity decay in noisy quantum memories and proves LIFO serving order as optimal for fidelity preservation.

Findings

Fidelity decays exponentially with storage time, depending on decoherence rate.

LIFO buffer management with pushout is optimal for fidelity.

The model enables efficient computation of average fidelity based on system parameters.

Abstract

Quantum teleportation channels can overcome the effects of photonic loss, a major challenge in the implementation of a quantum network over fiber. Teleportation channels are created by distributing an entangled state between two nodes which is a probabilistic process requiring classical communication. This causes critical delays that can cause information loss as quantum data suffers from decoherence when stored in memory. In this work, we quantify the effect of decoherence on fidelity at a node in a quantum network due to the storage of qubits in noisy memory platforms. We model the memory platform as a buffer that stores incoming qubits waiting for the creation of a teleportation channel. Memory platforms are parameterized with decoherence rate and buffer size, in addition to the order in which the incoming qubits are served. We show that fidelity at a node is a linear sum of terms, exponentially decaying with time, where the decay rate depends on the decoherence rate of the memory platform. This allows us to utilize Laplace Transforms to derive efficiently computable functions of average fidelity with respect to the load, buffer size, and decoherence rate of the memory platform. We prove that serving qubits in a Last In First Out order with pushout for buffer overflow management is optimal in terms of average fidelity. Lastly, we apply this framework to model a single repeater node to calculate the average fidelity of the teleportation channels created by this repeater assuming perfect gate operations.