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International Conference on Simulation of Semiconductor Processes and Devices

Numerical simulation of a two-particle wave function in quantum wires

Susanna Reggiani, Andrea Bertoni, MASSIMO RUDAN

Published Jun 25, 2003• 0 citations

Abstract

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.

DOI: 10.1109/sispad.2002.1034545

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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.

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.

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.

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.

We present a numerical analysis of the creation of entanglement between an electron freely propagating along a quantum wire and a charged particle bound to a specific site by a harmonic potential. The latter can be considered as a simplified model of an ionized impurity with an internal structure or of a localized phonon mode. Its dynamics is coupled to that of the free electron through a screened Coulomb potential. The time-dependent Schrodinger equation is solved numerically for the two-particle wave function thus describing the coherent evolution of the bipartite system. The two particle are considered distinguishable. As initial condition the product of a minimum uncertainty wave packet and the ground state of the harmonic oscillator are considered.