[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-956191","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 Complexity Theory\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\u003ESemester:\n          Semestre 1\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\u003ELecture:\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\u003EDirected study:\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, basics of quantum statistical inference, elementary complexity theory.\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\u003EThis course aims to present the rigorous theoretical foundation of the notion of quantum advantage. The main quantum computational models will be introduced in detail as well as the associated quantum complexity classes. We will cover the known theoretical separation between quantum and classical from discrete to continuous variable quantum computing, providing a large panorama of the benefit we can expect from quantum technologies when it comes to theoretical computational complexity.\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EIntroduction to quantum complexity theory:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cp\u003E(Titouan Carette: 6 hours lecture + 6 hours TD)\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EComputational models: Quantum Turing machines and quantum circuits, variations, gate set, approximate universality, Solovay-Kitaev.\u003C\/li\u003E\n\u003Cli\u003EComplexity classes: BQP, QMA, QIP, known inclusions and equalities.\u003C\/li\u003E\n\u003Cli\u003EQuantum query complexity: query model, polynomial bound, adversary bound, separation classical\/quantum.\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003E\u003Cstrong\u003EAnalog model of quantum computation with continuous variable systems:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cp\u003E(Marco Fanizza: 3 hours lecture + 1 TD)\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EStates on separable Hilbert spaces, L^2(R^m), canonical commutation relations, harmonic oscillator, Fock space.\u003C\/li\u003E\n\u003Cli\u003EGaussian states and Gaussian operations, universal gate sets, classical simulability.\u003C\/li\u003E\n\u003Cli\u003ETowards advantage with continuous variables: non-linearities, photon counting\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003E\u003Cstrong\u003EProofs of quantum advantage:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cp\u003E(Cambyse Rouz\u00e9: 6 hours lecture + 2 hours TD)\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EMore on decision problems, the polynomial hierarchy\u0026nbsp;\u003C\/li\u003E\n\u003Cli\u003E\u0026nbsp;Counting problems and the class #P\u003C\/li\u003E\n\u003Cli\u003E\u0026nbsp;Sampling problems and the connection to counting\u003C\/li\u003E\n\u003Cli\u003E\u0026nbsp;Quantum advantage with Boson Sampling\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}]