Reliability Dynamics in a Two-Site Dissipative Quantum Spin Chain

TL;DR

This paper models the reliability of a quantum spin chain device under environmental influence using Lindblad dynamics, deriving analytical reliability formulas and proposing an experimental assessment protocol.

Contribution

It introduces an analytical framework for quantum device reliability using classical theory and provides exact formulas for a two-site spin chain.

Findings

Derived closed-form reliability expressions for a two-site quantum spin chain.

Identified overdamped-underdamped transition in the dynamics.

Proposed an experimental protocol based on first-passage time statistics.

Abstract

As a key index for applications of a device, the device's reliability is its ability to survive (function normally over time) under the influence of some environment. In this paper we present a quantum energy-storing device model with a quantum spin chain, whose environment influence is described by the Lindblad master equation. Here the device survives if the spin system stays in the state with nonzero excitations; otherwise, it fails. Because the Lindblad dynamics enforces one-way energy decay and strict irreversibility of the failure state, we can investigate the reliability of the quantum device directly using classical reliability theory. Focusing on the minimal nontrivial case -- a two-site spin-1/2 chain -- we derive closed-form expressions for the reliability and the hazard rate. The dynamics exhibit an overdamped-underdamped crossover controlled by the competition between coherent exchange and dissipation inhomogeneity. The exact analytical formulas are in excellent agreement with numerical simulations. More importantly, we establish an experimentally accessible protocol for assessing reliability based on first-passage time statistics.