Reaction coordinate approach to non-Markovian dynamics in the spin-boson model

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Title: Reaction coordinate approach to non-Markovian dynamics in the spin-boson model
Author: Kaupinmäki, Santeri
Contributor: University of Helsinki, Faculty of Science, Department of Physics
Publisher: Helsingin yliopisto
Date: 2018
Language: eng
Thesis level: master's thesis
Discipline: Theoretical Physics
Teoreettinen fysiikka
Teoretisk fysik
Abstract: The fundamental building blocks of quantum computers, called qubits, can be physically realized through any quantum system that is restricted to two possible states. The power of qubits arises from their ability to be in a superposition of these two states, allowing for the development of quantum algorithms that are impossible for classical computers. However, interactions with the surrounding environment destroy the superposition in a process called decoherence, which makes it important to find ways to model these interactions and mitigate them. In this thesis we derive a non-Markovian master equation for the spin-boson model, with a time-dependent two-level system, using the reaction coordinate representation. We show numerically that in the superconducting qubit regime this master equation maintains the positivity of the density operator for relevant parameter ranges, and is able to model non-Markovian effects between the system and the environment. We also compare the reaction coordinate master equation to a Markovian master equation with parameters taken from real superconducting qubits. We demonstrate that the Markovian master equation fails to capture the system–bath correlations for short times, and in many cases overestimates relaxation and coherence times. Finally, we test how a time-dependent bias affects the evolution of the two-level system. The bias is assumed to be constant with an additive term arising from an externally applied time-dependent plane wave control field. We show that an amplitude, angular frequency, and phase shift for the plane wave can be chosen such that the control field improves the coherence time of the two-level system.

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