Electronic structure, entanglement and double occupancy in asymmetric dot molecule quantum gate

Spyridon G. Kosionis

Spyridon G. Kosionis, Emmanuel Paspalakis

Xuedong Hu, S. Das Sarma

We theoretically study 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.

John Schliemann, Daniel Loss, Allan H. MacDonald

Quantum gates that temporarily increase singlet-triplet splitting in order to swap electronic spins in coupled quantum dots lead inevitably to a finite double-occupancy probability for both dots. By solving the time-dependent Schr\"odinger equation for a coupled dot model, we demonstrate that this does not necessarily lead to quantum computation errors. Instead, the coupled dot ground state evolves quasiadiabatically for typical system parameters so that the double-occupancy probability at the completion of swapping is negligibly small. We introduce a measure of entanglement that explicitly takes into account the possibilty of double occupancies and provides a necessary and sufficient criterion for entangled states.

Chi Sun, Jacob Linder

A magnetic field that acts identically on two quantum dots is not expected to move charge between them. Nevertheless, we show that a uniform Zeeman field can strongly reconfigure and even reverse the single-electron charge polarization of an asymmetric open double quantum dot. Using a symmetry-preserving Green's-function equation-of-motion approach, we identify regimes where the preferred dot occupation reverses while the system remains in the single-electron charge sector. Two distinct mechanisms produce this behavior. Unequal gate levels produce different occupation responses because the Zeeman-shifted resonances lie at different positions relative to the reservoir chemical potential, whereas unequal onsite interactions distinguish the dots through their many-body addition spectra. Coulomb blockade stabilizes the single-electron sector, causing the reservoir-mediated response to appear as spatial charge redistribution rather than a change in total occupation. Our results establish a mechanism for magnetic control of charge polarization at fixed electrostatic detuning.