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Quantum Information in Time-Frequency Continuous Variables Nicolas Fabre Quantum information in time-frequency continuous variables Nicolas Fabre To cite this version: Nicolas Fabre. Quantum information in time-frequency continuous variables. Physics [physics]. Uni- versité de Paris, 2020. English. NNT : 2020UNIP7044. tel-03191301 HAL Id: tel-03191301 https://tel.archives-ouvertes.fr/tel-03191301 Submitted on 7 Apr 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Université de Paris Ecole doctorale [Physique en Ile de France, ED 564] Laboratoire Matériaux et Phénomènes Quantiques Quantum information in time-frequency continuous variables Par Nicolas Fabre Thèse de doctorat de Physique Dirigée par Perola Milman Et par Arne Keller Présentée et soutenue publiquement le 02/11/2020 Devant un jury composé de : Professeur Olivier Pfister (Univ. Virginia): Président du jury Professeur associé Lorenzo Maccone (Univ. Pavia): Rapporteur Maitre de conf. Valentina Parigi (Univ. Sorbonne): Examinatrice Professeur Marco Liscidini (Univ. Pavia): Examinateur Dir. de recherche Perola Milman (Univ. Paris): Directrice de thèse Professeur Arne Keller (Univ. Paris): Co-directeur de thèse Professeure Sara Ducci (Univ. Paris): Invitée Titre : Information Quantique en variables continues temps-fréquence Résumé : Cette thèse aborde l’encodage de degrés de liberté continus temps- fréquence de photon uniques. Les similitudes mathématiques avec les quadratures du champ électromagnétique amène à généraliser des protocoles exprimées dans ces variables dans notre encodage. On introduit un nouveau type de qubit robuste contre des erreurs du type déplacement dans l’espace des phases temps-fréquence. Un nouvel espace des phases doublement cylindriques est étudié et est une représentation particulièrement adaptée pour des états ayant une symétrie de translation. On étudie également comment construire une distribution de phase fonctionnelle permettant de décrire un état quantique possédant des degrés de libertés continus spectraux et en quadrature. Mots clefs : Photons uniques, Optique quantique, Information quantique, Variables continus, Circuits intégrés, Espace des phases, Variables modulaires Title : Quantum information in time-frequency continuous variables. Abstract : This thesis tackles the time-frequency continuous variables degree of freedom encoding of single photons and examine the formal mathematical analogy with the quadrature continuous variables of the electromagnetic field. We define a new type of qubit which is robust against time-frequency displacement errors. We define a new double-cylinder phase space which is particularly adapted for states which have a translational symmetry. We also study how to build a functional phase space distribution which allows to describe a quantum state with spectral and quadrature continuous variables degrees of freedom. Keywords : Single photons, Quantum optics, Quantum information, Continuous variables, Integrated waveguide circuit, Phase space, Modular variables. Abstract La seconde r´evolution quantique est li´eeau d´eveloppement d'applications de la m´ecaniquequantique o`ula logique quantique joue un r^oleimportant et direct. Ces nouvelles technologies s'´etendent de la m´etrologie, `ala simulation quantique de syst`emescomplexes, jusqu'aux communications quantiques plus s´ecuris´eesen pas- sant par le calcul quantique. Utiliser les propri´et´esde superposition coh´erente et l'intrication de qubits peut per- mettre `aune machine quantique de r´esoudre des probl`emesexponentiellement plus rapide que des algorithmes d´eterministesou probabilistes classiques. L'engouement r´ecent pour le calcul quantique repose sur une plateforme bien particuli`ere,celle des puces supraconductrices. Cela est du `ala premi`ere demonstration de la supr´ematie quantique par l'ordinateur quantique Sycamore de Google poss´edant 53 qubits. Toute- fois, les t^aches r´esolublespar cette machine sont encore bien limit´ees.Celle r´ealis´ee et publi´ee en 2019 consiste `atrouver des agencements dans des nombres al´eatoires produits par les qubits de la machine eux-m^emes. Cette t^ache a ´et´er´esolueen 3 minutes par Sycamore et prendrait 10 000 ans avec un super calculateur clas- sique. Il faut noter, pour les sceptiques, que malgr´ele refroidissement n´ecessaire pour avoir des mat´eriauxdans l'´etatsupraconducteur et donc l'augmentation de la facture d'´electricit´e,la r´esolutionde ces t^aches en un temps record est ´egalement moins gourmande en ´energie. Bien d'autres compagnies ont d´emontr´ecomment r´esoudrecertaines t^aches difficiles pour des ordinateurs classiques avec des machines quantiques du m^emestyle. IBM propose `an'importe quel utilisateur d’effectuer des calculs quantiques sur le cloud sur un arsenal de pr`esde 20 machines, a ´egalement d´evelopp´een 2019 une machine `a53 qubits. Leur expertise porte essentiellement sur la simulation quantique de mol´ecules.La compagnie IonQ propose quant `aelle un ordinateur quantique reposant sur la plateforme d' atomes d'Ytterbium ionis´es pi´eg´es. Cette plateforme est `ace jour celle dont l'erreur par op´erationquantique effectu´eeest la moindre. La scalabilit´ede ces deux plateformes, pour des raisons diff´erentes, est tr`es limit´ee.Il n'est pas possible de d´esignerun candidat id´ealpour le moment. Un ´etatquantique ne peut pas ^etrestock´eind´efiniment et est par na- ture fragile aux interactions avec l'environnement: aucune des machines cit´eesn'est encore pourvue de code correcteur d'erreurs. Les photons uniques ont ´et´ed´esign´ecomme les candidats naturels pour les commu- nications quantiques. Un argument est d'ordre technologique: il est plus facile de d´evelopper une plateforme par rapport `aune autre lorsque celle-ci est d´ej`arobuste. Cela ne signifie pas que des qubits d´efinis`apartir de photons uniques ne pourront jamais ^etreutilis´espour effectuer du calcul quantique, au contraire des qubits supra- conducteurs. Mais la technologie reste `a^etred´evelopp´ee,celle des circuits optiques int´egr´es. Les photons uniques sont des porteurs d'information et ils ont l'avantage d'interagir peu avec l'environnement ce qui garantit d'une bonne coh´erence.Ils sont facilement mesurables et peuvent ^etreproduits `ala demande. N´eanmoins,ils sont difficiles `aintriquer par des op´erationsd´eterministeset sont perdus facilement ce qui les rendent moins aptes pour des t^aches de calculs. Des preuves exp´erimentales d'un avantage quantique, qui est loin d'^etretrivial `ad´efinir,dans des protocoles de calculs quantiques et de communication quantique en encodant de l'information sous forme discr`etedans des photons uniques ont ´et´ed´emontr´es. L'information est encod´ee dans des degr´esde libert´ede photons uniques. On peut nommer la polarisation, le temps d'arriv´eed'un photon unique ou leur fr´equence.La d´emonstrationde proto- cole de QKD (quantum key distribution) en utilisant des qubits en polarisation par des communications satellites-sol par des chercheurs d'universit´eschinoises a ´et´eune impressionnante preuve de l'utilit´ede cette plateforme. Une autre mani`ered'encoder l'information en optique quantique consiste `autiliser les variables continues des quadratures du champ ´electromagn´etique.L'exemple `ace jour le plus d´emonstratif sont les peignes de fr´equencequi sont des ´etatscomprim´es multimodes. La promesse de la production de ces ´etatsgr^ace`ades circuits int´egr´es est port´eepar la compagnie Xanadu. Cette start-up propose depuis septembre 2020, comme IBM, d'utiliser un ordinateur quantique photonique accessible depuis le cloud. La motivation principale est pour le moment le calcul quantique. Cette approche est ´egalement pertinente lorsque les syst`emes`asimuler sont naturellement exprim´es `al'aide de variables continues, comme en th´eoriequantique des champs par exemple. Ce manuscrit de th`eseaborde l'encodage de l'information quantique en utilisant les degr´esde libert´econtinus temps-fr´equencede photons uniques. Cet encodage partage des similitudes math´ematiques avec les variables continues quadrature position-impulsion d'un champ ´electromagn´etiquemonomode. Ces variables sont sensibles au nombre de photons mais leur interpr´etationet utilisation dans des protocoles quantiques sont physiquement tr`esdiff´erentes. Cette ´etude est motiv´eepar les r´ealisationsexp´erimentales de sources de photons uniques avec des circuits int´egr´esfonctionnant en temp´eratureambiante au sein de notre laboratoire Mat´eriauxet Ph´enom`enesQuantiques, dans l'´equipe QITE dirig´ee par Sara Ducci. Deux structures de guide d'onde semi-conductrice en AlGaAs ont ´et´e´elabor´eeset caract´eris´eesproduisant des paires de photons se propageant dans le m^emesens ou dans des sens oppos´es,par un processus de g´en´erationd'´emission spontan´ee(SPDC) de type-II. Les corr´elationsen fr´equencede ces paires de photons peuvent ^etrecontr^ol´eessoit avant leur g´en´erationdans le cas du dispositif dit con- trapropageant, soit apr`esleur g´en´erationdans les deux types de guide d'onde avec les ´el´ements d'optiques habituels. Les circuits int´egr´esposs`edent plusieurs avantages
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