Q-REACH: Quantum information Repetition, Error Analysis and Correction using Caching Network

Abstract

Quantum repeaters incorporating quantum memory play a pivotal role in mitigating loss in transmitted quantum information (photons) due to link attenuation over a long-distance quantum communication network. However, limited availability of available storage in such quantum repeaters and the impact on the time spent within the memory unit presents a trade-off between quantum information fidelity (a metric that quantifies the degree of similarity between a pair of quantum states) and qubit transmission rate. Thus, effective management of storage time for qubits becomes a key consideration in multi-hop quantum networks. To address these challenges, we propose Q-REACH, which leverages queuing theory in caching networks to tune qubit transmission rate while considering fidelity as the cost metric. Our contributions in this work include (i) utilizing a method of repetition that encodes and broadcasts multiple qubits through different quantum paths, (ii) analytically estimating the time spent by these emitted qubits as a function of the number of paths and repeaters, as well as memory units within a repeater, and (iii) formulating optimization problem that leverages this analysis to correct the transmitted logic qubit and select the optimum repetition rate at the transmitter.