Quantum computation and communication using electron spins in quantum dots and wires

Abstract

The recent discovery of efficient quantum algorithms for factoring and database search has shown that quantum computing would allow to solve important problems which are intractable with conventional computers. In contrast to the very demanding task of building a large-scale quantum computer, there are quantum communication protocols, e.g. quantum key distribution for cryptography, which—though still difficult—require much less effort and can be implemented with current technology. Apart from the technological motivation, the study of quantum information offers (at least) two additional benefits. First, new insight into fundamental questions on quantum mechanics, e.g. concerning non-locality and entanglement, are gained from an information-theoretical approach. And second, investigating a particular physical implementation of quantum information can give rise to independent physical results. Spintronics, the use of spin as opposed to charge in (classical) electronics is a new field for which some results presented here could be relevant. In this dissertation we investigate several theoretical aspects of the physical implementation of quantum computation and communication in which the fundamental unit of quantum information, the qubit, is represented by the spin of electrons in semiconductor quantum dots. The required coupling between the spins can be obtained by allowing for tunneling of electrons between adjacent dots, leading to a Heisenberg exchange coupling J S1 · S2 between the spins, a scenario which we study for laterally coupled quantum dots in a two-dimensional electron system, and for a three-dimensional setup with vertically coupled quantum dots. Furthermore, an alternative scheme to couple the spins via the interaction with an optical cavity mode is presented. Quantum error correction represents one of the important ingredients for the physical implementation of a quantum computer by protecting it from the e�ects of a noisy environment. As a �rst test for errorcorrection in a solid-state device using spins, we propose an optimized implementation of the most primitive error correction scheme (the threebit code). In this context, we introduce parallel switching, allowing to operate a quantum computer more e�ciently than the usual serial switching. Coupling spins with the exchange interaction J S1 �S2 is not su�cient for quantum computation; the spins also have to be addressed individually using controllable local magnetic �elds or g-factors giBi �Si in order to allow for single-qubit operations. On the one hand, we discuss several schemes for overcoming the di�culty of applying local magnetic �elds (requiring large gradients), e.g. g-factor engineering, which allows for all-electric operation of the device. On the other hand, we show that at the expense of additional devices (spins) and switching operations, single-spin rotations can be dispensed with completely. Addressing the feasibility of quantum communication with entangled electrons in mesoscopic wires, i.e. interacting many-body environments, we propose an interference experiment using a scattering set-up with an entangler and a beam splitter. The current noise for electronic singlet states turns out to be enhanced (bunching), while it is reduced for triplets (antibunching). Due to interactions, the �delity of the entangled singlet and triplet states is reduced by z4F in a conductor described by Fermi liquid theory, zF being the quasiparticle weight factor. Finally, we study the related but more general problem of the noise of the cotunneling current through one or several tunnel-coupled quantum dots in the Coulomb blockade regime. The various regimes of weak and strong, elastic and inelastic cotunneling are analyzed for quantum-dot systems (QDS) with few-level, nearly-degenerate, and continuous electronic spectra. In contrast to sequential tunneling, the noise in inelastic cotunneling can be super-Poissonian. In order to investigate strong cotunneling we develop a microscopic theory of cotunneling based on the density-operator formalism and using the projection operator technique. We have derived the master equation for the QDS and the current and noise in cotunneling in terms of the stationary state of the QDS. These results are then applied to QDS with a nearly degenerate and continuous spectrum.