Quasi non-Markovian approach to the study of decoherence of a controlled-not quantum gate in a chain of few nuclear spins quantum computer

TL;DR

This paper introduces a quasi-non-Markovian master equation to analyze decoherence in a CNOT gate within a three-nuclear-spin quantum computer, highlighting differences from Markovian models at various dissipation rates and temperatures.

Contribution

It presents a novel quasi-non-Markovian approach to study decoherence in quantum gates, extending beyond traditional Markovian models for nuclear spin systems.

Findings

At low dissipation, minimal difference between Markovian and quasi-non-Markovian models.

At high dissipation, significant differences are observable at all temperatures.

The approach improves understanding of decoherence mechanisms in nuclear spin quantum computers.

Abstract

We develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At low dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperature which is unlikely to be measured, and at high dissipation there is a difference which is likely to be measured at any temperature.