Valence holes as Luttinger spinor based qubits in quantum dots

TL;DR

This paper develops a theoretical framework for using valence holes in quantum dots as qubits, leveraging Luttinger spinor formalism, and explores single and double qubit operations with magnetic fields and dot orientation.

Contribution

It introduces a novel qubit scheme based on valence holes as Luttinger spinors in quantum dots, detailing control methods and the impact of dot orientation on qubit interactions.

Findings

Single qubit operations via static magnetic fields are feasible.

Qubit coupling is sensitive to quantum dot orientation.

An optimal qubit separation exists for voltage-controlled interactions.

Abstract

We present a theory of valence holes as Luttinger spinor based qubits in p-doped self-assembled quantum dots within the 4-band $k\cdot p$ formalism. The two qubit levels are identified with the two chiralities of the doubly degenerate ground state. We show that single qubit operations can be implemented with static magnetic field applied along the $z$ and $x$ directions, acting analogously to the $\hat{\sigma}_z$ and $\hat{\sigma}_x$ operators in the qubit subspace respectively. The coupling of two dots and hence the double qubit operations are shown to be sensitive to the orientation of the two quantum dots. For vertical qubit arrays, there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.