Derivation of Interacting Two-Qubit Dynamics from Spin-Boson Model

TL;DR

This paper derives equations for two-qubit spin dynamics from a spin-boson model, revealing how entanglement and correlations evolve and persist despite dissipation, with implications for quantum computing stability.

Contribution

We develop a Caldeira-Leggett approach for two-qubit systems, deriving damping equations that incorporate entanglement dynamics from the spin-boson model.

Findings

Total spin relaxation follows a quantum Landau-Lifshitz-Gilbert equation.

Two-spin composite modes sustain oscillations after total spin relaxation.

Two-spin correlations remain stable against dissipation due to composite modes.

Abstract

We derive damping equations of motion for interacting two-spin states from a spin-boson model in order to examine qubit dynamics in quantum computers. On the basis of the composite operator method, we develop the Caldeira-Leggett approach for open quantum systems so that the entanglement dynamics originated from the two-spin correlation can be taken. We demonstrate numerical results for time dependence on the two-spin dynamics. We find that the relaxation of the total spin is described by a quantum version of the Landau-Lifshitz-Gilbert equation for magnetic materials. We also find that a two-spin composite mode keeps oscillation even after the total spin has been fully relaxed. We thus conclude that the two-spin correlation due to the presence of the composite mode is stable against dissipation. We consider the mechanism of why the correlation is maintained.