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Russian Microelectronics

Perfectly and imperfectly controlled quantum operations on a charge qubit

Alexander V. Tsukanov, K. A. Valiev

Published Mar 1, 2007• 6 citations
Publisher

Abstract

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.

DOI
10.1134/s1063739707020011

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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.
We consider one- and two-qubit operations on charge qubits that represent double quantum dots with one electron in each of them. The dots are formed inside a high-Q semiconductor cavity (disk, toroidal, or spherical) in the antinodes of one of its optical eigenmodes; the frequencies of the transitions between the ground (logic) and excited (auxiliary) states of the discrete electron spectrum in quantum dots are close to the frequency of this mode. The precise tuning of the transition frequency is performed by applying an electric potential on the qubit control gate. Within the model of qubits coherently interacting with a cavity quantum field, a few methods for controlling their states are developed. In particular, we propose different variants for implementing two-qubit CNOT and CZ gates and generating qubit entangled states. By the example of a micro-disk cavity, we calculate the operating characteristics that ensure a high rate of quantum gate implementation.
Quantum operations with a charge solid-state qubit whose logical states are formed by two spatially separated localized states of an electron in the double-dot structure are studied theoretically. We show that it is possible to perform various one-qubit rotations making use of the microwave pulses tuned to the resonances between the localized states and the excited state delocalized over the nanostructure. An explicit analytic expression for the time-dependent electron state vector is derived, and the appropriate pulse parameters are determined.
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.
A crucial requirement for scalable quantum-information processing is the realization of multiple-qubit quantum gates. Universal multiple-qubit gates can be implemented by a set of universal single qubit gates and any one kind of two-qubit gate, such as a controlled-NOT (CNOT) gate. Semiconductor quantum dot qubits are a leading approach for the physical implementation of quantum computation, due to their potential for large-scale integration. Two-qubit gate operations have been so far only demonstrated in individual electron spin-based quantum dot systems. Due to the relatively short de-coherence time, charge qubits in quantum dots are generally considered to be inferior for going beyond single qubit level. Here, we demonstrate the benchmarking CNOT gate in two capacitively coupled charge qubits, each consisting of an electron confined in a GaAs/AlGaAs double quantum dot. Owing to the strong inter-qubit coupling strength, gate operations with a clock speed up to 5GHz has been realized. A processing tomography shows encouragingly that the universal two-qubit gate operations have comparable fidelities to that of spin-based two-qubit gates. Our results suggest that semiconductor charge qubits have a considerable potential for scalable quantum computing and may stimulate the use of long-range Coulomb interaction for coherent quantum control in other devices.
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.
Quantum operations with a charge solid-state qubit whose logical states are formed by two spatially separated localized states of an electron in the double-dot structure are studied theoretically. We show that it is possible to perform various one-qubit rotations making use of the microwave pulses tuned to the resonances between the localized states and the excited state delocalized over the nanostructure. Explicit analytic expression for the time-dependent electron state vector is derived, and the appropriate pulse parameters are determined. PACS Numbers: 03.67.Lx, 73.21.La, 85.35.-p During past decade, quantum computing (QC) or, more generally, quantum information processing, attracted much attention [1]. The reasons for that interest are (i) the existence of quantum algorithms [2] that could perform calculations exponentially faster as compared with classical ones (QC software), and (ii) the rapid development of technology and material science [3] that allowed to realize some prototypes of QC devices (QC hardware). The key elements of the QC hardware are