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Journal of Modern Optics

Numerical simulation of coherent transport in quantum wires for quantum computing

Andrea Bertoni, Paolo Bordone, ROSSELLA BRUNETTI, Carlo Jacoboni, Susanna Reggiani

Published Jul 1, 2002• 21 citations
Publisher

Abstract

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.

DOI
10.1080/09500340110105948

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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 solid-state implementation of a set of one- and two-qbit gates for quantum computing is proposed. The qbit is defined as the state of an electron running along two quantum wires, suitably coupled through a potential barrier with variable height and/or width. Single-qbit gates are implemented using the coupling between the two wires. The two-qbit gates have been designed using a Coulomb coupler to induce a mutual phase modulation of the two qbits. A number of runs have been performed using a time-dependent 2D Schrodinger solver.
A solid-state implementation of a set of one- and two-qbit gates for quantum computing is proposed. The qbit is defined as the state of an electron running along two quantum wires, suitably coupled through a potential barrier with variable height and/or width. Single-qbit gates are implemented using the coupling between the two wires. The two-qbit gates have been designed using a Coulomb coupler to induce a mutual phase modulation of the two qbits. A number of runs have been performed using a time-dependent 2D Schrodinger solver.
As the key requirement of a quantum computer is the creation and exploitation of entanglement, a detailed study of entangled states has been carried out with reference to a solid-state system based on coupled quantum wires. A brief review of the basic gates is given first, based on preliminary investigations, followed by the analysis of electrons running along coupled quantum wires. The particle dynamics has numerically been simulated by means of a time-dependent Schrodinger solver applied to a two-particle system. Results are reported showing entangled states created by means of suitable quantum-gate networks. Starting from these fundamental results, the complexity of some interesting circuits is addressed, showing both the application of the universal set of quantum gates to complex algorithms and the computational speedup achieved within the proposed implementation.
We present a brief review of the basic requirements for a quantum-computing device based on solid-state technology. An overview covering many prototype implementations and proposals is first presented. Then, the formalism used to describe the quantum transformations is introduced, together with the characteristics that make a set of quantum gates universal. Finally, a simulative analysis of a physical system based on coherent electron propagation in quantum wires shows how such a system meets the requirements for the realization of a universal set of quantum gates.
We propose a new solid state implementation of a quantum computer (quputer) using ballistic single electrons as flying qubits in 1D nanowires. We use a single electron pump (SEP) to prepare the initial state and a single electron transistor (SET) to measure the final state. Single qubit gates are implemented using quantum dots as phase shifters and electron waveguide couplers as beam splitters. A Coulomb coupler acts as a 2-qubit gate, using a mutual phase modulation effect. Since the electron phase coherence length in GaAs/AlGaAs heterostructures is of the order of 30μμμm, several gates (tens) can be implemented before the system decoheres.
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.