Quantum Decomposition Algorithm For Master Equations of Stochastic Processes: The Damped Spin Case

TL;DR

This paper presents a quantum decomposition algorithm that efficiently simulates damped spin systems using quantum harmonic oscillators, providing a novel approach to solving master equations in stochastic processes.

Contribution

The paper introduces a new quantum decomposition algorithm (QDA) capable of simulating damped spin systems via quantum harmonic oscillators, advancing computational methods for stochastic master equations.

Findings

Successfully applied QDA to undriven qubit with spontaneous emission and dephasing.

Demonstrated the algorithm's ability to decompose eigenvalue problems into phase-space variables.

Showed potential for simulating complex damped quantum systems.

Abstract

We introduce a quantum decomposition algorithm (QDA) that decomposes the problem $\frac{\partial \rho}{\partial t}=\mathcal{L}\rho=\lambda \rho$ into a summation of eigenvalues times phase-space variables. One interesting feature of QDA stems from its ability to simulate damped spin systems by means of pure quantum harmonic oscillators adjusted with the eigenvalues of the original eigenvalue problem. We test the proposed algorithm in the case of undriven qubit with spontaneous emission and dephasing.