Exchange Interaction Between Three and Four Coupled Quantum Dots: Theory and Applications to Quantum Computing

TL;DR

This paper analyzes how exchange interactions among multiple coupled quantum dots affect quantum computing, highlighting the importance of considering these effects in qubit gate design.

Contribution

It provides a detailed theoretical analysis of exchange interactions in multi-quantum-dot systems, emphasizing their impact on quantum computer implementations.

Findings

Exchange interactions can change dramatically with multiple spins involved.

Qualitative and quantitative differences in interaction strength are shown.

Heitler-London and Hund-Mulliken models support these findings.

Abstract

Several prominent proposals have suggested that spins of localized electrons could serve as quantum computer qubits. The exchange interaction has been invoked as a means of implementing two qubit gates. In this paper, we analyze the strength and form of the exchange interaction under relevant conditions. We find that, when several spins are engaged in mutual interactions, the quantitative strengths or even qualitative forms of the interactions can change. It is shown that the changes can be dramatic within a Heitler-London model. Hund-Mulliken calculations are also presented, and support the qualititative conclusions from the Heitler-London model. The effects need to be considered in spin-based quantum computer designs, either as a source of gate error to be overcome or a new interaction to be exploited.