Variational quantum simulation of a nonadditive relaxation dynamics in a qubit coupled to a finite-temperature bath

TL;DR

This paper demonstrates the use of variational quantum simulation to model nonadditive relaxation dynamics of a qubit interacting with a finite-temperature bath, capturing dissipative effects with high fidelity on near-term quantum hardware.

Contribution

It introduces a novel nonadditive relaxation-time model within the VQS framework to simulate realistic thermal bath interactions and explores the effects of drive smoothness on simulation accuracy.

Findings

VQS accurately models nonunitary amplitude damping.

Nonadditive parameters reduce high frequency errors.

Variational manifold maintains fidelity despite increased sensitivity.

Abstract

In this paper, we present an application of the variational quantum simulation (VQS) framework to capture finite-temperature open-system dynamics on near-term quantum hardware. By embedding the generalized amplitude-damping channel into the VQS algorithm, we modeled the energy exchange with a thermal bath through its Lindblad representation and thereby simulated realistic dissipative effects. To explore a wide range of activation behaviors, we introduce a nonadditive relaxation-time model using a generalized form of the Arrhenius law, based on the phenomenological parameter q. We compare our method on a driven qubit subject to both static and composite time-dependent fields, comparing population evolution and trace distance errors against exact solutions. Our results demonstrate that (i) VQS accurately maps the effective nonunitary generator under generalized amplitude damping, (ii) smoother drive envelopes induced by nonaddtive parameters suppress high frequency components and yield lower simulation errors, and (iii) the variational manifold exhibits dynamical selectivity, maintaining mapping fidelity even as the exact solution's sensitivity to q increases. Our results demonstrate that (i) VQS accurately maps the effective nonunitary generator under generalized amplitude damping, (ii) smoother drive envelopes induced by nonaddtive parameters suppress high frequency components and yield lower simulation errors, and (iii) the variational manifold exhibits dynamical selectivity, maintaining mapping fidelity even as the exact solution's sensitivity to q increases.