Four-level systems and a universal quantum gate

TL;DR

This paper proposes a method to implement a universal quantum XOR gate using two coupled quantum dots under external magnetic fields, analyzing different field configurations and deriving conditions for gate operation.

Contribution

It introduces a theoretical framework for realizing a quantum XOR gate with coupled quantum dots, including exact solutions and parameter adjustments for different magnetic field configurations.

Findings

Exact solutions for spin dynamics under different field configurations.

Conditions for external field parameters to realize XOR gate.

Relations between spin interaction, inter-dot distance, and external fields.

Abstract

We discuss a possibility of implementing a universal quantum XOR gate, by using two coupled quantum dots subjected to external magnetic fields that are parallel and slightly different. We consider this system in two different field configurations. In the first case, parallel external fields with the intensity difference at each spin being proportional to the time-dependent interaction between the spins. General exact solution describing this system is presented and analyzed to adjust parameters of the field. Then we consider parallel fields with intensity difference at each spin being constant and the interaction between the spins switching on and off adiabatically. In both cases we adjust characteristics of the external fields (their intensities and duration) in order to have the parallel pulse adequate for constructing the XOR gate. In order to provide a complete theoretical description of all the cases, we derive relations between the spin interaction, the inter-dot distance, and the external field.