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We consider two typical approximations that are used in the microscopiccalculations of double-quantum dot spin qubits, namely, the Heitler-London (HL)and the Hund-Mulliken (HM) approximations, which use linear combinations ofFock-Darwin states to approximate the two-electron states under the double-wellconfinement potential. We compared these results to a case in which thesolution to a one-dimensional Schr\"odinger equation was exactly known andfound that typical microscopic calculations based on Fock-Darwin statessubstantially underestimate the value of the exchange interaction, which is thekey parameter that controls the quantum dot spin qubits. This underestimationoriginates from the lack of tunneling of Fock-Darwin states, which is accurateonly in the case with a single potential well. Our results suggest that theaccuracies of the current two-dimensional molecular-orbit-theoreticalcalculations based on Fock-Darwin states should be revisited sinceunderestimation could only deteriorate in dimensions that are higher than one.

On the validity of microscopic calculations of double-quantum-dot spin qubits based on Fock-Darwin states