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Semiconductor Science and Technology

Entanglement and quantum computing with ballistic electrons

Andrea Bertoni, Susanna Reggiani

Published Mar 3, 2004• 11 citations
Publisher

Abstract

We first present a brief review of the basic requirements, proposals and prototype implementations for quantum computing devices. Then we introduce a specific universal set of quantum gates and describe a physical system, based on coupled quantum wires, that should be able to realize the proposed quantum transformations. Finally, the dynamics of entanglement-creation between two ballistic electrons is analysed for a model system.

DOI
10.1088/0268-1242/19/4/041

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We first present a brief review of the basic requirements, proposals and prototype implementations for quantum computing devices. Then we introduce a specific universal set of quantum gates and describe a physical system, based on coupled quantum wires, that should be able to realize the proposed quantum transformations. Finally, the dynamics of entanglement-creation between two ballistic electrons is analysed for a model system.
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.
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 describe a solid state implementation of a quantum computer using ballistic single electrons as flying qubits in 1D nanowires. We show how to implement all the steps required for universal quantum computation: preparation of the initial state, measurement of the final state and a universal set of quantum gates. An important advantage of this model is the fact that we do not need ultrafast optoelectronics for gate operations. We use cold programming (or pre-programming), i.e. the gates are set before launching the electrons; all programming can be done using static electric fields only.
We present a study of ballistic electron waveguides as used to construct simple quantum computational networks.We begin with an introduction to ballistic electron waveguides, some basic theory of quantum computers, and the possible role of electron waveguides in quantum computation.Following that, our study of various waveguide networks and the physics of the specific components of those networks.We continue with a discussion of shot noise in network elements and its possible role in helping to build good computational gates.Finally we conclude with a summary of research and possible future projects.
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.