The Exchange Gate in Solid State Spin Quantum Computation: The Applicability of the Heisenberg Model

TL;DR

This paper investigates the validity of the Heisenberg model for exchange interactions in solid state spin quantum computing, highlighting corrections at high magnetic fields and in looped spin arrays.

Contribution

It provides a detailed analysis of the limitations of the Heisenberg model in certain regimes and geometries, using exact diagonalization methods.

Findings

Heisenberg model validity range identified

Qualitative corrections at high magnetic fields

Flux-dependent multi-spin terms in looped geometries

Abstract

Solid state quantum computing proposals rely on adiabatic operations of the exchange gate among localized spins in nanostructures. We study corrections to the Heisenberg interaction between lateral semiconductor quantum dots in an external magnetic field. Using exact diagonalization we obtain the regime of validity of the adiabatic approximation. We also find qualitative corrections to the Heisenberg model at high magnetic fields and in looped arrays of spins. Looped geometries of localized spins generate flux dependent, multi-spin terms which go beyond the basic Heisenberg model.