dorsal/arxiv
View SchemaHilbert space structure of a solid state quantum computer: two-electron states of a double quantum dot artificial molecule
| Authors | Xuedong Hu, S. Das Sarma |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9911080 |
| URL | https://arxiv.org/abs/quant-ph/9911080 |
| DOI | 10.1103/PhysRevA.61.062301 |
| Journal | Phys. Rev. A 61, 062301 (2000) |
Abstract
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.
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"abstract": "We study theoretically a double quantum dot hydrogen molecule in the GaAs\nconduction band as the basic elementary gate for a quantum computer with the\nelectron spins in the dots serving as qubits. Such a two-dot system provides\nthe necessary two-qubit entanglement required for quantum computation. We\ndetermine the excitation spectrum of two horizontally coupled quantum dots with\ntwo confined electrons, and study its dependence on an external magnetic field.\nIn particular, we focus on the splitting of the lowest singlet and triplet\nstates, the double occupation probability of the lowest states, and the\nrelative energy scales of these states. We point out that at zero magnetic\nfield it is difficult to have both a vanishing double occupation probability\nfor a small error rate and a sizable exchange coupling for fast gating. On the\nother hand, finite magnetic fields may provide finite exchange coupling for\nquantum computer operations with small errors. We critically discuss the\napplicability of the envelope function approach in the current scheme and also\nthe merits of various quantum chemical approaches in dealing with few-electron\nproblems in quantum dots, such as the Hartree-Fock self-consistent field\nmethod, the molecular orbital method, the Heisenberg model, and the Hubbard\nmodel. We also discuss a number of relevant issues in quantum dot quantum\ncomputing in the context of our calculations, such as the required design\ntolerance, spin decoherence, adiabatic transitions, magnetic field control, and\nerror correction.",
"arxiv_id": "quant-ph/9911080",
"authors": [
"Xuedong Hu",
"S. Das Sarma"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall"
],
"doi": "10.1103/PhysRevA.61.062301",
"journal_ref": "Phys. Rev. A 61, 062301 (2000)",
"title": "Hilbert space structure of a solid state quantum computer: two-electron states of a double quantum dot artificial molecule",
"url": "https://arxiv.org/abs/quant-ph/9911080"
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