[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-956195","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n \u003Cdiv class=\u0022row\u0022\u003E\n \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n \u003Ch2 class=\u0022h1 text-left\u0022\u003E Quantum Structures\n\u003C\/h2\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n 2.5\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n Semestre 2\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n \u003Cspan\u003E12\u003C\/span\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ETravaux dirig\u00e9s :\u003C\/span\u003E\n \u003Cspan\u003E12\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003EAnglais\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003Enon\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003E\u003Cp\u003ELinear algebra, basic quantum information, and a taste for abstraction. Having followed the P1 course \u201cZX calculus\u201d is a plus but not required.\u003C\/p\u003E\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003E\u003Cp\u003EWhat are the mathematical structures encapsulating the weirdness of quantum theory? How can they be formally pinned down to ease their handling? How, in particular, can the crucial notion of\u0026nbsp;\u003Cem\u003Ecausal structure\u003C\/em\u003E be salvaged within a theory that seems to disregard it in such a careless way? Can one also superpose causal influences? These are the questions that this course will answer. We will show how recently developed mathematics (based in particular on category theory) help us to reformulate quantum theory from the ground up as a\u0026nbsp;\u003Cem\u003Eprocess theory\u003C\/em\u003E, by taking its peculiar properties (first and foremost entanglement) as axioms. This opens to a renewed perspective on the notion of causal structure. Going to\u0026nbsp;\u003Cem\u003Ehigher-order quantum processes\u003C\/em\u003E \u2013 processes that map a quantum evolution to another quantum evolution \u2013, we will discover that even causal structures might be put in a superposition in a quantum computer, leading to new speedups and applications.\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EList of sessions\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003ELecture 1 (2h) \u2013\u0026nbsp; Quantum theory as a process theory, symmetric monoidal categories, daggers, entanglement as cups and caps\u003Cbr\u003E\n\u003Cem\u003Ethen\u003C\/em\u003E TD 1 (1h) \u2013 categories of quantum processes, category of relations. \u0026nbsp;\u003C\/li\u003E\n\u003Cli\u003ELecture 2 (2h) \u2013\u0026nbsp; Classical structures as Frobenius algebras, no-cloning, no-broadcasting, CJ isomorphism, quantum curryfication\u003Cbr\u003E\n\u003Cem\u003Ethen\u003C\/em\u003E TD 2 (1h) \u2013 Markov categories, quantum lambda calculus.\u003C\/li\u003E\n\u003Cli\u003ELecture 3 (2h) \u2013\u0026nbsp; Doubling, discarding, the causality condition, purification\u003Cbr\u003E\n\u003Cem\u003Ethen\u003C\/em\u003E TD 3 (1h) \u2013 purification in the alternative categorical model (rel, )\u003C\/li\u003E\n\u003Cli\u003ETD 4 (3h) \u2013 Categorical axiomatisation of Hilb.\u003C\/li\u003E\n\u003Cli\u003ELecture 5 (2h) \u2013\u0026nbsp; OPTs and re-axiomatisations of quantum theory\u003Cbr\u003E\n\u003Cem\u003Ethen\u003C\/em\u003E TD 5 (1h) \u2013 Local tomography and real quantum theory\u003C\/li\u003E\n\u003Cli\u003ELecture 6 (2h) \u2013\u0026nbsp; Quantum causal models\u003Cbr\u003E\n\u003Cem\u003Ethen\u003C\/em\u003E TD 2 (1h) \u2013 Causal decompositions\u003C\/li\u003E\n\u003Cli\u003ELecture 7 (2h) \u2013\u0026nbsp; Higher-order quantum computation\u003Cbr\u003E\n\u003Cem\u003Ethen\u003C\/em\u003E TD 7 (1h) \u2013 The quantum if\u003C\/li\u003E\n\u003Cli\u003ETD 8 (3h) \u2013 Properties of higher-order maps: purifications, type systems, causal structure\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003Cdiv class=\u0022field-spacing\u0022\u003E\n \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n \u003Cspan\u003EEvaluation Continue non Int\u00e9grale\u003C\/span\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]