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arXiv:cond-mat/0103410 · Physical Review A

Effect of an inhomogeneous external magnetic field on a quantum-dot quantum computer

Rogério de Sousa, Xuedong Hu, S. Das Sarma

Published Sep 12, 2001• 32 citations
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Abstract

We calculate the effect of an inhomogeneous magnetic field, which is invariably present in an experimental environment, on the exchange energy of a double-quantum-dot artificial molecule, projected to be used as a two-qubit quantum gate in the proposed quantum-dot quantum computer. We use two different theoretical methods to calculate the Hilbert space structure in the presence of the inhomogeneous field: the Heitler-London method, which is carried out analytically, and the molecular orbital method, which is done computationally. Within these approximations we show that the exchange energy J changes slowly when the coupled dots are subject to a magnetic field with a wide range of inhomogeneity, suggesting that swap operations can be performed in such an environment as long as quantum error correction is applied to account for the Zeeman term. We also point out the quantum interference nature of this slow variation in exchange.

DOI
10.1103/physreva.64.042307

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We calculate the effect of an inhomogeneous magnetic field, which is invariably present in an experimental environment, on the exchange energy of a double-quantum-dot artificial molecule, projected to be used as a two-qubit quantum gate in the proposed quantum-dot quantum computer. We use two different theoretical methods to calculate the Hilbert space structure in the presence of the inhomogeneous field: the Heitler-London method, which is carried out analytically, and the molecular orbital method, which is done computationally. Within these approximations we show that the exchange energy J changes slowly when the coupled dots are subject to a magnetic field with a wide range of inhomogeneity, suggesting that swap operations can be performed in such an environment as long as quantum error correction is applied to account for the Zeeman term. We also point out the quantum interference nature of this slow variation in exchange.
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.
We study theoretically the effects of qubit inhomogeneity on the quantum logic gate of qubit swap, which is an integral part of the operations of a quantum computer. Our focus here is to construct a robust pulse sequence for swap operation in the simultaneous presence of Zeeman inhomogeneity for quantum dot trapped electron spins and the finite-time ramp-up of exchange coupling in a double dot. We first present a geometric explanation of spin swap operation, mapping the two-qubit operation onto a single-qubit rotation. We then show that in this geometric picture a square-pulse sequence can be easily designed to perform swap in the presence of Zeeman inhomogeneity. Finally, we investigate how finite ramp-up times for the exchange coupling J negatively affect the performance of the swap gate sequence, and show how to correct the problems numerically.
We present theoretically the Zeeman coupling and exchange induced swap action in spin-based quantum dot quantum computer models in the presence of magnetic field. We study the valence and conduction band states in a double quantum dots made in diluted magnetic semiconductor. The later have been proven to be very useful in building an all-semiconductor platform for spintronics. Due to a strong p–d exchange interaction in diluted magnetic semiconductor (Cd0.57Mn0.43Te), the relative contribution of this components is strongly affected by an external magnetic field, a feature that is absent in non magnetic double quantum dots. We determine the energy spectrum and the swap time as a function of magnetic field and the inter dot distance within the Hund–Mulliken molecular-orbit approach and by including the Coulomb interaction.
We consider a quantum-gate mechanism based on electron spins in coupled semiconductor quantum dots. Such gates provide a general source of spin entanglement and can be used for quantum computers. We determine the exchange coupling JJJ in the effective Heisenberg model as a function of magnetic (B)(B)(B) and electric fields, and of the interdot distance aaa within the Heitler-London approximation of molecular physics. This result is refined by using sp\mathrm{sp}sp hybridization, and by the Hund-Mulliken molecular-orbit approach, which leads to an extended Hubbard description for the two-dot system that shows a remarkable dependence on BBB and aaa due to the long-range Coulomb interaction. We find that the exchange JJJ changes sign at a finite field (leading to a pronounced jump in the magnetization) and then decays exponentially. The magnetization and the spin susceptibilities of the coupled dots are calculated. We show that the dephasing due to nuclear spins in GaAs can be strongly suppressed by dynamical nuclear-spin polarization and/or by magnetic fields.
We report on our recent progress in applying semiconductor quantum dots for spin-based quantum computation, as proposed by Loss and DiVincenzo (1998 Phys. Rev. A 57 120). For the purpose of single-electron spin resonance, we study different types of single quantum dot devices that are designed for the generation of a local ac magnetic field in the vicinity of the dot. We observe photon-assisted tunnelling as well as pumping due to the ac voltage induced by the ac current driven through a wire in the vicinity of the dot, but no evidence for ESR so far. Analogue concepts for a double quantum dot and the hydrogen molecule are discussed in detail. Our experimental results in laterally coupled vertical double quantum dot device show that the Heitler–London model forms a good approximation of the two-electron wavefunction. The exchange coupling constant J is estimated. The relevance of this system for two-qubit gates, in particular the SWAP operation, is discussed. Density functional calculations reveal the importance of the gate electrode geometry in lateral quantum dots for the tunability of J in realistic two-qubit gates.