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Title: Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap

Following a recent proposal of L. Wang and D. Babikov [J. Chem. Phys. 137, 064301 (2012)], we theoretically illustrate the possibility of using the motional states of a Cd{sup +} ion trapped in a slightly anharmonic potential to simulate the single-particle time-dependent Schrödinger equation. The simulated wave packet is discretized on a spatial grid and the grid points are mapped on the ion motional states which define the qubit network. The localization probability at each grid point is obtained from the population in the corresponding motional state. The quantum gate is the elementary evolution operator corresponding to the time-dependent Schrödinger equation of the simulated system. The corresponding matrix can be estimated by any numerical algorithm. The radio-frequency field which is able to drive this unitary transformation among the qubit states of the ion is obtained by multi-target optimal control theory. The ion is assumed to be cooled in the ground motional state, and the preliminary step consists in initializing the qubits with the amplitudes of the initial simulated wave packet. The time evolution of the localization probability at the grids points is then obtained by successive applications of the gate and reading out the motional state population. The gate fieldmore » is always identical for a given simulated potential, only the field preparing the initial wave packet has to be optimized for different simulations. We check the stability of the simulation against decoherence due to fluctuating electric fields in the trap electrodes by applying dissipative Lindblad dynamics.« less
Authors:
;  [1] ;  [2] ;  [2] ;  [3]
  1. Laboratoire de Chimie Quantique et Photophysique, CP 160/09 Université Libre de Bruxelles, B-1050 Brussels (Belgium)
  2. Laboratoire de Chimie Physique, UMR 8000 and CNRS, Université Paris-Sud, F-91405 Orsay (France)
  3. (Belgium)
Publication Date:
OSTI Identifier:
22415608
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 13; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CADMIUM IONS; ELECTRIC FIELDS; GRIDS; OPTIMAL CONTROL; POTENTIALS; PROBABILITY; QUBITS; RADIOWAVE RADIATION; SCHROEDINGER EQUATION; TIME DEPENDENCE; TRANSFORMATIONS; TRAPPING; TRAPS; WAVE PACKETS