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Research of an optimal pulse performing QFT on vibration levels of a trapped ion

par Santos, Ludovic ;Desouter-Lecomte, Michèle;Vaeck, Nathalie
Référence Quantum Chemistry in Belgium meeting (11ème: 23/01/2014: Namur, Belgique)
Publication Non publié, 2014-01-23

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Résumé :

Nowadays, laser pulses can be produced to control populations of molecular and atomic states in order to realise quantum computation. Our aim is to search theoretically a pulse able to realise a quantum Fourier transform (QFT) on a multi qubit system implemented on the vibration levels of a Cadmium ion trapped in an anharmonic potential.We use a basis of B-splines functions to solve the time-independent Schrödinger equation so that we can get the vibration levels and the matrix elements of the transition dipole moment matrix for the trapped Cadmium ion. The group of Babikov have recently worked on a similar system[1].Thanks to the optimal control[2] and using Rabbitz’s algorithm[3], we have maximized two different functionals that have the same goal and the same constraints. One is based on the average transition probability (JP ) and the other on the fidelity (JF ). The goal, which is to modify the vibrational population of the ion according to a QFT, is realized with success for the two functionals. The performance index of the pulses rises, in both cases, to more than 0.99999.An analysis of these optimal pulses was performed by obtaining their constitutive frequen- cies and by applying directly the pulses on some initial populations. This analysis shows the difference of behaviour between the two functionals. On one hand, the pulse obtained with the functionalJP usesessentiallythetransitions∆v±1betweenthevibrationlevels.Ontheother hand, the pulse obtained with the functional JF mainly uses the transitions ∆v ± 1 but also, to a lesser extent, the transitions ∆v ± 3, ±5, ±7.References[1] L. Wang and D. Babikov, “Feasibility of encoding shor’s algorithm into the motional states of an ion in the anharmonic trap,” The Journal of Chemical Physics, vol. 137, p. 064301, 2012.[2] A. Jaouadi, E. Barrez, Y. Justum, and M. Desouter-Lecomte, “Quantum gates in hyperfine levels of ultracold alkali dimers by revisiting constrained-phase optimal control design,” The Journal of chemical physics, vol. 139, no. 1, p. 014310, 2013.[3] W. Zhu, J. Botina, and H. Rabitz, “Rapidly convergent iteration methods for quantum optimal control of population,” The Journal of Chemical Physics, vol. 108, no. 5, pp. 1953– 1963, 1998.