Quantum outage probability for time-varying quantum channels

TL;DR

This paper introduces quantum outage probability concepts for time-varying quantum channels, analyzing how parameter fluctuations impact quantum error correction performance and emphasizing the importance of parameter stability.

Contribution

It develops closed-form expressions for quantum outage probabilities in time-varying amplitude damping channels and highlights the significance of decoherence parameter stability.

Findings

Quantum outage probability quantifies error rates over fluctuating channels.

Parameter fluctuations significantly degrade quantum error correction performance.

Stability of decoherence parameters is crucial for maintaining high quantum channel fidelity.

Abstract

Recent experimental studies have shown that the relaxation time, $T_1$, and the dephasing time, $T_2$, of superconducting qubits fluctuate considerably over time. Time-varying quantum channel (TVQC) models have been proposed in order to consider the time varying nature of the parameters that define qubit decoherence. This dynamic nature of quantum channels causes a degradation of the performance of quantum error correction codes (QECC) that is portrayed as a flattening of their error rate curves. In this article, we introduce the concepts of quantum outage probability and quantum hashing outage probability as asymptotically achievable error rates by a QECC with quantum rate $R_Q$ operating over a TVQC. We derive closed-form expressions for the family of time-varying amplitude damping channels (TVAD) and study their behaviour for different scenarios. We quantify the impact of time-variation as a function of the relative variation of $T_1$ around its mean. We conclude that the performance of QECCs is limited in many cases by the inherent fluctuations of their decoherence parameters and corroborate that parameter stability is crucial to maintain the excellent performance observed over static quantum channels.