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arXiv quant-ph/9911080quant-phcond-mat.mes-hall
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固态量子计算机的Hilbert空间结构:双量子点人工分子的双电子态

Hilbert space structure of a solid state quantum computer: two-electron states of a double quantum dot artificial molecule

Xuedong Hu, S. Das Sarma

摘要:

我们从理论上研究了GaAs导带中的双量子点氢分子作为量子计算机的基本门,量子点中的电子自旋作为量子比特。这样的两点系统提供了量子计算所需的必要的两量子比特纠缠。我们测量了两个水平耦合量子点的激发光谱,并研究了它对外加磁场的依赖性。特别是,我们专注于最低的单重态和三重态的分裂,最低状态的双占据概率,以及这些状态的相对能量标度。我们指出,在零磁场,它是很难有一个消失的双占用概率为小的错误率和一个相当大的交换耦合快速门控。另一方面,有限磁场可以为具有小误差的量子计算机操作提供有限交换耦合。我们批判性地讨论了包络函数方法在当前方案中的适用性以及各种量子化学方法在处理量子点中的少电子问题时的优点,如Hartree-Fock自洽场方法,分子轨道方法,海森堡模型和哈伯德模型。我们还讨论了量子点量子计算中的一些相关问题,如所需的设计公差,自旋退相干,绝热跃迁,磁场控制,和错误校正。

英文摘要:

We study theoretically a double quantum dot hydrogen molecule in the GaAs conduction band as the basic elementary gate for a quantum computer with the electron spins in the dots serving as qubits. Such a two-dot system provides the necessary two-qubit entanglement required for quantum computation. We determine the excitation spectrum of two horizontally coupled quantum dots with two confined electrons, and study its dependence on an external magnetic field. In particular, we focus on the splitting of the lowest singlet and triplet states, the double occupation probability of the lowest states, and the relative energy scales of these states. We point out that at zero magnetic field it is difficult to have both a vanishing double occupation probability for a small error rate and a sizable exchange coupling for fast gating. On the other hand, finite magnetic fields may provide finite exchange coupling for quantum computer operations with small errors. We critically discuss the applicability of the envelope function approach in the current scheme and also the merits of various quantum chemical approaches in dealing with few-electron problems in quantum dots, such as the Hartree-Fock self-consistent field method, the molecular orbital method, the Heisenberg model, and the Hubbard model. We also discuss a number of relevant issues in quantum dot quantum computing in the context of our calculations, such as the required design tolerance, spin decoherence, adiabatic transitions, magnetic field control, and error correction.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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