Statistique de l'interférence quantique et circuits quantiques aléatoires

Ludovic Arnaud 1
1 Information et Chaos Quantiques (LPT)
LPT - Laboratoire de Physique Théorique - IRSAMC
Abstract : This thesis presents different results about two topics in the field of quantum information. The first of these topics concerns the interference present in quantum algorithms, based on a measure recently introduce in the litterature. To do this, two kinds of statistical models of quantum algorithms were used. The first one, which comes from the random matrix theory, is the circular unitary ensemble (CUE) while the second one is a set of quantum circuits, built by random sequences of quantum gates. The analytical and numerical results obtained in this thesis show that {\em on average} any quantum algorithm contain a big amount of interference. The next step was to study the influence of the decoherence created by a thermal bath on the statistics of the interference. Thanks to mathematical methods of integration over the unitary group U(N), it is possible to generalise the previous analytical and numerical results to include the effect of decoherence. The second topic is about the possibility of using quantum algorithms to create efficiently random matrix ensembles. During the works on interference, an equivalence between CUE and the model of random quantum circuits was noticed. One might expect that such random quantum circuits can be used to build random matrix ensembles drawn as CUE. The numerical results of this thesis show that given CUE quantities are well reproduced by the model of random sequences in an efficient way. The efficiency means that the sequences are built with a number of gates which increases as the logarithm of the size of the produced matrices. These results are in agreement with recently published works.
Document type :
Physique mathématique [math-ph]. Université Paul Sabatier - Toulouse III, 2009. Français
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Contributor : Ludovic Arnaud <>
Submitted on : Sunday, June 12, 2011 - 5:46:06 PM
Last modification on : Tuesday, February 3, 2015 - 10:35:33 AM
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Ludovic Arnaud. Statistique de l'interférence quantique et circuits quantiques aléatoires. Physique mathématique [math-ph]. Université Paul Sabatier - Toulouse III, 2009. Français. 〈tel-00599990〉



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