基于Fock-Darwin态的双量子点自旋量子比特微观计算的有效性
On the validity of microscopic calculations of double-quantum-dot spin qubits based on Fock-Darwin states
摘要：
考虑了两种典型的双量子点自旋量子比特微观计算的近似方法，即Heitler-London（HL）和Hund-Mulliken（HM）近似，它们利用Fock-Darwin态的线性组合来近似双阱势下的双电子态.我们将这些结果与一维薛定谔方程的解完全已知的情况进行了比较，发现基于福克-达尔文态的典型微观计算大大低估了交换相互作用的值，交换相互作用是控制量子点自旋量子比特的关键参数。这种低估源于缺乏Fock-Darwin态的隧穿，这只在单势阱的情况下是准确的。我们的研究结果表明，目前的二维分子轨道理论计算的Fock-Darwin状态的基础上的准确性应该重新审视，因为低估只能恶化的尺寸是高于一个。
英文摘要：
We consider two typical approximations that are used in the microscopic calculations of double-quantum dot spin qubits, namely, the Heitler-London (HL) and the Hund-Mulliken (HM) approximations, which use linear combinations of Fock-Darwin states to approximate the two-electron states under the double-well confinement potential. We compared these results to a case in which the solution to a one-dimensional Schrödinger equation was exactly known and found that typical microscopic calculations based on Fock-Darwin states substantially underestimate the value of the exchange interaction, which is the key parameter that controls the quantum dot spin qubits. This underestimation originates from the lack of tunneling of Fock-Darwin states, which is accurate only in the case with a single potential well. Our results suggest that the accuracies of the current two-dimensional molecular-orbit-theoretical calculations based on Fock-Darwin states should be revisited since underestimation could only deteriorate in dimensions that are higher than one.
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