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Quantum dynamics simulator with the motional states of an ion in an anharmonic trap

par Santos, Ludovic ;Justum, Yves;Desouter-Lecomte, Michèle;Vaeck, Nathalie
Référence Quantum Cybernetics & Control (19-23/01/2015: Nottingham, Royaume-Uni)
Publication Non publié, 2015-01-23

Communication à un colloque

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Résumé :

Following a recent proposal[1], we theoretically illustrate the possibility of using the motional states of a Cd+ ion trapped in an anharmonic potential to realize a quantum dynamics simulator of a single-particle Schrödinger equation. The anharmonicity renders the states energetically non equi- distant and allows the control of population transfer between states with an electromagnetic field. The simulated dynamics is discretized on spatial and temporal grids. The gate associated to an ele- mentary evolution is estimated by the Split Operator formalism[2]. The radio-frequency field able to drive the corresponding unitary transformation among the qubit states encoded into the ion motional states is obtained by optimal control theory[3]. The field is unique for a given simulated potential. We also perform the computation of the field for the preparation of the initial simulated wave packet. This one needs to be adapted.The stability of the optimal electric fields driving the elementary evolution is checked by perfor- ming dissipative Lindblad dynamics[4, 5] in order to consider fluctuations in the trap potential due to external fields[6].[1] L. Wang and D. Babikov, "Feasibility of encoding Shor’s algo- rithm into the motional states of an ion in the anharmonic trap", J. Chem. Phys. 137, 064301 (2012).[2] M. D. Feit, Jr J. A. Fleck, and A. Steiger, "Solution of the Schrö- dinger equation by a spectral method", J. Comput. Phys. 47, 412 (1982).[3] W. Zhu, J. Botina and H. Rabitz, "Rapidly convergent iteration methods for quantum optimal control of population", J. Chem. Phys. 108, 1953 (1997).[4] G. Lindblad, "On the generators of quantum dynamical semi-groups", Commun. Math. Phys. 48, 119 (1976).[5] W. Zhu and H. Rabitz, "Closed loop learning control to suppress the effects of quantum decoherence", J. Chem. Phys. 118, 6751 (2003).[6] S. Schneider and G. J. Milburn, "Decoherence and fidelity in ion traps with fluctuating trap parameters", Phys. Rev. A 59, 3766 (1999).