Effective Hamiltonian for the hybrid double quantum dot qubit

TL;DR

This paper derives an effective Hamiltonian for a hybrid double quantum dot qubit, simplifying the understanding of its dynamics and aiding in quantum logic gate implementation in solid-state systems.

Contribution

It introduces a Schrieffer-Wolff based effective Hamiltonian combining Hubbard-like models with projector methods for hybrid quantum dot qubits.

Findings

Derived a simple effective Hamiltonian in terms of exchange interactions.

Analyzed the qubit's dynamical behavior and eigenstates on the Bloch sphere.

Discussed realistic implementation in silicon and coupling with detectors.

Abstract

Quantum dot hybrid qubits formed from three electrons in double quantum dots represent a promising compromise between high speed and simple fabrication for solid state implementations of single qubit and two qubits quantum logic ports. We derive the Schrieffer-Wolff effective Hamiltonian that describes in a simple and intuitive way the qubit by combining a Hubbard-like model with a projector operator method. As a result, the Hubbard-like Hamiltonian is transformed in an equivalent expression in terms of the exchange coupling interactions between pairs of electrons. The effective Hamiltonian is exploited to derive the dynamical behaviour of the system and its eigenstates on the Bloch sphere to generate qubits operation for quantum logic ports. A realistic implementation in silicon and the coupling of the qubit with a detector are discussed.