Description
Date depot: 20 février 2019
Titre: Origin of Quantum Superiority, from Discrete to Continuous Models
Directeur de thèse:
Damian MARKHAM (LIP6)
Directrice de thèse:
Elham KASHEFI (LIP6)
Domaine scientifique: Sciences et technologies de l'information et de la communication
Thématique CNRS : Non defini
Resumé:
Following the development of quantum physics, information theory and complexity theory,the study of quantum information as a discipline was born in the 80s and many so-called'classical' results Have seen their quantum analogue be demonstrated recently, as forexample some results on the compression of the information or the transmission of it.Quantum information, however, has unusual properties (superposition of states, entanglement,decoherence) and it can be expected that quantum algorithms also have singular properties.In 1994, Peter Shor developed a quantum algorithm that allows probabilistic factorization ofan integer in polynomial time, which no conventional algorithm is able to do today. Since themost used encryption systems were then based on the supposed impossibility of effectivelyfactorizing an integer, we understand the craze, elicited in particular by this algorithm, for thetheory of quantum information. Examples include the European initiative Quantera, a 34million euro fund deployed in 2017 by the Horizon 2020 research program of the EuropeanUnion to support research projects in quantum technologies.Shor's algorithm is effective in theory, but the experimental reality makes its realizationcomplex, especially because of the phenomenon of decoherence. One of the main challengesof quantum information research is therefore to identify the resource that would allow aquantum computer to outperform its classical counterpart, in order to protect it during anexperimental realization.This will be carried out under the supervision of Damian Markham andElham Kashefi, researchers at the Jussieu Computer Science Laboratory (LIP6) and cofoundersof the Paris Center for Quantum Computing (PCQC). This center brings togetherseveral theoretical and experimental groups in Paris (LTCI, LIP6, LMPQ, LKB amongothers) to be a player in the transition to quantum technology.Thesis director will be Damian Markham and Elham Kashefi will be co-director. Thesetwo researchers are also coordinators of various projects supported by the Quantera initiative,which shows their involvement in the field.The objectives of the thesis are the following:• In a first step, a discrete variable reflection around 'matchgate formalism', originallydeveloped in graph theory, will allow to associate the notion of quantum superiority with thatof remote action in a quantum circuit (arXiv : 0804.4050v2). I will then make the formalisticlink of quasi-probability distributions, in which the notion of quantum superiority isassociated with the negativity of a quasi-probability function, called Glauber-Sudarshan(arXiv: 1511.06526v2).• In a second step, it will be a question of extending this notion of quantum superiority to theformalism of the continuous variable, with the example of 'measurement based quantumcomputation models' (arXiv: 0910.1116v2).• I a third step, I will carry out a more fundamental study to determine which axioms ofquantum physics lead to this superiority.Beyond this guideline, other tracks can be explored as the link with the notion of contextualityor the analogy between quantum computation and phase transition (arXiv: quant-ph /0702020v2).Finally, the theoretical team of Damian Markham and Elham Kashefi is in permanentdialogue, punctuated by regular meetings, with the experimental team of Nicolas Treps(LKB). Thus, the theoretical work carried out during this thesis will be based on intuitionresulting from experience, in the tradition of scientific research.
Doctorant.e: Chabaud Ulysse