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Physical Review A

Single qubit from two coupled quantum dots: An approach to semiconductor quantum computations

Xin-Qi Li, Yasuhiko Arakawa

Published Dec 7, 2000• 44 citations
Publisher

Abstract

A scheme to possibly implement the quantum computer is proposed based on the idea to build up the single qubit from two coupled quantum dots. The spatial separation of the two logic states of the qubit can greatly reduce the decoherence time, which allows one to perform the coherent quantum logic operations at a fairly high ratio. Together with the realization of the universal quantum logic gates, and the proper scheme of quantum measurement, the present proposal can satisfy all the essential criteria for quantum computing.

DOI
10.1103/physreva.63.012302

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A scheme to possibly implement the quantum computer is proposed based on the idea to build up the single qubit from two coupled quantum dots. The spatial separation of the two logic states of the qubit can greatly reduce the decoherence time, which allows one to perform the coherent quantum logic operations at a fairly high ratio. Together with the realization of the universal quantum logic gates, and the proper scheme of quantum measurement, the present proposal can satisfy all the essential criteria for quantum computing.
Based on an idea that spatial separation of charge states can enhance quantum coherence, we propose a scheme for a quantum computation with the quantum bit (qubit) constructed from two coupled quantum dots. Quantum information is stored in the electron-hole pair state with the electron and hole located in different dots, which enables the qubit state to be very long-lived. Universal quantum gates involving any pair of qubits are realized by coupling the quantum dots through the cavity photon which is a hopeful candidate for the transfer of long-range information. The operation analysis is carried out by estimating the gate time versus the decoherence time.
The universal quantum computation is obtained when there exists asymmetric anisotropic exchange between electron spins in coupled semiconductor quantum dots. The asymmetric Heisenberg model can be transformed into the isotropic model through the control of two local unitary rotations for the realization of essential quantum gates. The rotations on each qubit are symmetrical and depend on the strength and orientation of asymmetric exchange. The implementation of the axially symmetric local magnetic fields can assist the construction of quantum logic gates in anisotropic coupled quantum dots. This proposal can efficiently use each physical electron spin as a logical qubit in the universal quantum computation.
Since the mid-20th century it has been understood that a general-purpose quan- tum computer would be able to efficiently solve problems that will forever be out-of-reach for conventional computers. Since then, many quantum algorithms have been developed with applications in a wide range of domains including cryptography, simulations, machine learning and data analysis. While this has resulted in substantial attention being paid to the development of quantum com- puters, the best architectures to use in their fabrication is not yet clear. Semiconductor quantum dot devices are a particularly promising candidate for use in quantum computing architectures, as it is anticipated that once the funda- mental building blocks are implemented, they might be massively scalable using the existing lithography techniques of the semiconductor industry. So far, how- ever, it is not yet clear how best to implement the high-fidelity gates required for general-purpose quantum computation. In this thesis, we present and characterise novel theoretical proposals for fast, simple and high-fidelity two-qubit gates using magnetic (exchange) coupling for specific semiconductor quantum dot qubits; namely, the singlet-triplet and resonant-exchange qubits. These two-qubit operations are simple enough that it is feasible for them to be implemented in experiments of the near future. Success- ful implementations would significantly extend the experimentally demonstrable frontier of semi-conductor quantum dot devices as relevant to their use in uni- versal quantum computing architectures. We also develop simple parameter estimation schemes by which it is possible to substantially mitigate the dominant sources of error for our proposed gates; namely, low-frequency charge and magnetic noise. We develop the techniques in the context of pseudo-static magnetic field gradient fluctuations in singlet- triplet qubits, and demonstrate that these techniques lead to a several orders of magnitude improvement in single-qubit coherence times. With minimal effort this could be ported to other qubit architectures.
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.
A quantum computer based on an asymmetric coupled-dot system has been proposed and shown to operate as a controlled-NOT gate. The basic ideas are the following. (1) The electron is localized in one of the asymmetric coupled dots. (2) The electron transfer takes place from one dot to the other when the energy levels of the coupled dots are set to be close. (3) The Coulomb interaction between the coupled dots mutually affects the energy levels of the other coupled dots. The decoherence time of the quantum computation and the measurement time are estimated. The proposed system can be realized by developing the technology of the single-electron memory using Si nanocrystals, and a direct combination of the quantum circuit and the conventional circuit is possible.