We study theoretically a double quantum dot hydrogen molecule in the GaAsconduction band as the basic elementary gate for a quantum computer with theelectron spins in the dots serving as qubits. Such a two-dot system providesthe necessary two-qubit entanglement required for quantum computation. Wedetermine the excitation spectrum of two horizontally coupled quantum dots withtwo confined electrons, and study its dependence on an external magnetic field.In particular, we focus on the splitting of the lowest singlet and tripletstates, the double occupation probability of the lowest states, and therelative energy scales of these states. We point out that at zero magneticfield it is difficult to have both a vanishing double occupation probabilityfor a small error rate and a sizable exchange coupling for fast gating. On theother hand, finite magnetic fields may provide finite exchange coupling forquantum computer operations with small errors. We critically discuss theapplicability of the envelope function approach in the current scheme and alsothe merits of various quantum chemical approaches in dealing with few-electronproblems in quantum dots, such as the Hartree-Fock self-consistent fieldmethod, the molecular orbital method, the Heisenberg model, and the Hubbardmodel. We also discuss a number of relevant issues in quantum dot quantumcomputing in the context of our calculations, such as the required designtolerance, spin decoherence, adiabatic transitions, magnetic field control, anderror correction.
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