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Nanotechnology

Coherent charge qubits based on GaAs quantum dots with a built-in barrier

Leonid Evgenevich Fedichkin, Maxim Yanchenko, K. A. Valiev

Published Nov 14, 2000• 105 citations
Publisher

Abstract

We investigated the use of quantum bits (qubits) - semiconductor quantum dots containing one electron and each consisting of two tunnel-connected parts - as basic elements of the quantum computer. The numerical solution of a Schrödinger equation taking account of the Coulomb field of adjacent electrons shows that in such structures the realization of a full set of basic logic operations, which are necessary for fulfillment of quantum computations, is possible. Durations of one- and two-qubit operations versus qubit geometry are obtained. Decoherence rates due to spontaneous emission of phonons and acoustic phonons (both piezoelectric and deformation) are evaluated. Analysis of these rates shows the proposed qubit to be coherent enough to work for an unlimited time.

DOI
10.1088/0957-4484/11/4/339

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We investigated the use of quantum bits (qubits) - semiconductor quantum dots containing one electron and each consisting of two tunnel-connected parts - as basic elements of the quantum computer. The numerical solution of a Schrödinger equation taking account of the Coulomb field of adjacent electrons shows that in such structures the realization of a full set of basic logic operations, which are necessary for fulfillment of quantum computations, is possible. Durations of one- and two-qubit operations versus qubit geometry are obtained. Decoherence rates due to spontaneous emission of phonons and acoustic phonons (both piezoelectric and deformation) are evaluated. Analysis of these rates shows the proposed qubit to be coherent enough to work for an unlimited time.
We investigated using as basic elements of the quantum computer quantum bits (qubits) semiconductor quantum dots containing one electron and consisting each of two tunnel- connected parts. as shown in Fig. I . The numerical solution of a Schrodinger equation with the account of Coulomb field of adjacent electrons shows, that in such structures the realization of a full set of basic logic operations which are necessary for fulfillment Of quantum computations is possible. Decoherence rates due to spontaneous emission of phonons and acoustic phonons (both piezoelectric and deformational) are evaluated. Durations of one- and two-qubit operations versus qubit geometry are obtained.
As basic elements of the quantum computer - quantum bits (qubits) we offer semiconductor quantum dots containing one electron each and consisting each of two tunnel-connected parts. The numerical solution of a Schroedinger equation with the account of Coulomb field of adjacent electrons shows, that in such structures the realization of a full set of basic logic operations which are necessary for fulfillment of quantum computations is possible. Durations of one- and two-qubit operations versus qubit geometry are obtained. Decoherence rates due to spontaneous emission of phonons and acoustic phonons (both piezoelectric and deformation) are evaluated. Analysis of these rates shows the offered qubit to be coherent enough to perform error correction procedures.
The spin of an electron confined into a lateral semiconductor quantum dot has been proposed as a possible physical realization of a qubit. While the spin has the advantage of large decoherence times, operations with more than one qubit will necessarily involve orbital degrees of freedom, namely, charge, which is much more prone to decoherence. There are also alternative quantum dot qubit proposals that are entirely based on charge. We have used a realistic model to quantify the limitations imposed by acoustic phonons on the operation of quantum dot-based qubits. Our treatment includes essential aspects of the setup geometry, wave function profile and materials characteristics. The time dependence of the qubit density matrix is the presence of a phonon bath solved within the Born-Markov approximation. We find that the inclusion of geometric form factors makes the phonon-induced decoherence rates in double dot charge qubits nearly one order of magnitude lower than estimates previously in the literature. Moreover, our theoretical prediction for the quality factor of coherent charge oscillations based on phonon decoherence are higher than the values recently observed experimentally. This allows us to conclude that phonons are not the primary source of decoherence in double quantum dot qubits.
We consider charge qubits based on shallow donor electron states in silicon and coupled quantum dots in GaAs. Specifically, we study the feasibility of P2+{P}_{2}^{+}P2+​ charge qubits in Si, focusing on single qubit properties in terms of tunnel coupling between the two phosphorus donors and qubit decoherence caused by electron-phonon interaction. By taking into consideration the multivalley structure of the Si conduction band, we show that intervalley quantum interference has important consequences for single-qubit operations of P2+{P}_{2}^{+}P2+​ charge qubits. In particular, the valley interference leads to a tunnel-coupling strength distribution centered around zero. On the other hand, we find that the Si band structure does not dramatically affect the electron-phonon coupling and consequently, qubit coherence. We also critically compare charge qubit properties for Si:P2+\mathrm{Si}:{P}_{2}^{+}Si:P2+​ and GaAs double quantum dot quantum computer architectures.
A solid-state implementation of a universal set of gates for quantum computation is proposed and analysed using a time-dependent 2D Schrödinger solver. The qubit is defined as the state of an electron propagating along a couple of quantum wires. The wires are suitably coupled through a potential barrier with variable height and/or width. It is shown how a proper design of the system allows the implementation of any one-qubit transformation. The two-qubit gate is realized through a Coulomb coupler able to entangle the quantum states of two electrons running in two wires of two different qubits. The simulated devices are GaAs—AlGaAs heterostructures that should be on the borderline of present semiconductor technology. An estimate of decoherence effects due to phonon scattering is also presented.
A theoretical investigation is presented into the coherent dynamics of a charge qubit in the form of two tunnel-coupled quantum dots containing a single electron, with the logic states represented by electron orbitals localized at the quantum dots. Analytical expressions are derived for the evolution of a one-or two-qubit system in an applied field. The system and field parameters are evaluated in terms of performing basic one-qubit operations. The possibility is explored for implementing the CNOT operation in a two-qubit system driven by error-free or error-prone control pulses.