Vibrational computing: Simulation of a full adder by optimal control

[en] Within the context of vibrational molecular quantum computing, we investigate the implementation of a full addition of two binary digits and a carry that provides the sum and the carry out. Four qubits are necessary and they are encoded into four different normal vibrational modes of a molecule. We choose the bromoacetyl chloride molecule because it possesses four bright infrared active modes. The ground and first excited states of each mode form the one-qubit computational basis set. Two approaches are proposed for the realization of the full addition. In the first one, we optimize a pulse that implements directly the entire addition by a single unitary transformation. In the second one, we decompose the full addition in elementary quantum gates, following a scheme proposed by Vedral [Phys. Rev. A 54, 147 (1996)]. Four elementary quantum gates are necessary, two two-qubit CNOT gates (controlled NOT) and two three-qubit TOFFOLI gates (controlled-controlled NOT). All the logic operations consist in one-qubit flip. The logic implementation is therefore quasiclassical and the readout is based on a population analysis of the vibrational modes that does not take the phases into account. The fields are optimized by the multitarget extension of the optimal control theory involving all the transformations among the 2(4) qubit states. A single cycle of addition without considering the preparation or the measure or copy of the result can be carried out in a very competitive time, on a picosecond time scale. (C) 2008 American Institute of Physics.

Disciplines :

Chimie

Auteur, co-auteur :

Bomble, L.

Lauvergnat, D.

Remacle, Françoise ; Université de Liège - ULiège > Département de chimie (sciences) > Laboratoire de chimie physique théorique

Desouter-Lecomte, Michèle ; Université de Liège - ULiège > Département de chimie (sciences) > Laboratoire de chimie physique théorique

Langue du document :

Anglais

Titre :

Vibrational computing: Simulation of a full adder by optimal control

Date de publication/diffusion :

2008

Titre du périodique :

Journal of Chemical Physics

ISSN :

0021-9606

eISSN :

1089-7690

Maison d'édition :

American Institute of Physics (AIP), New York, Etats-Unis - New York

Volume/Tome :

128

Fascicule/Saison :

Peer reviewed :

Peer reviewed vérifié par ORBi

Disponible sur ORBi :

depuis le 05 janvier 2010

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3 (dont 1 ULiège)

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