[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-956199","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  Complex Quantum Systems\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          Annualis\u00e9\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\u003EBasics of quantum statistical inference ; Basics of quantum computing ; Linear algebra\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\u003EMany-body quantum systems are ubiquitous in theoretical and experimental quantum information processing, from the simulation of condensed matter systems to the development of good quantum error-correcting codes. Recent years have seen major developments in our mathematical understanding of these systems\u0027 intricacies. In these lectures, we will explore the complexity of physically motivated models of many-body quantum systems, from ground and thermal states of matter to outputs of short-time quantum evolutions. We will consider two notions of complexity: (i) the computational hardness of simulating properties of the system (a.k.a. forward problem); and (ii) the learnability of classical descriptions of the system from access to samples (a.k.a inverse problem).\u003C\/p\u003E\n\u003Cp\u003EThe course will consist in 26 hours of lectures punctuated with 6 hours of exercises\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EPart 1: Sampling\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003ELecture 1: Simulating real time dynamics, Trotterization, Lieb-Robinson bounds [2h]\u003C\/li\u003E\n\u003Cli\u003ELectures 2-3: The local Hamiltonian problem, QMA hardness of computing the ground state energy, connections to classical optimization [4h]\u003C\/li\u003E\n\u003Cli\u003ELecture 4: Adiabatic and variational quantum algorithms [2h]\u003C\/li\u003E\n\u003Cli\u003ELectures 5-6: Quantum Gibbs sampling and partition function estimation [4h]\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003E\u003Cstrong\u003EPart 2: Learning\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003ELectures 1-2: Learning quantum systems in trace distance: single copy algorithms, Schur- Weyl duality, optimal algorithms [4h]\u003C\/li\u003E\n\u003Cli\u003ELectures 3-4: Learning expectation values of a set of quantum observables: shadow tomography, classical shadows [4h]\u003C\/li\u003E\n\u003Cli\u003ELecture 5: Learning the Hamiltonian of a many-body systems from Gibbs states [2h]\u003C\/li\u003E\n\u003Cli\u003ELectures 6-7: Learning the Hamiltonian of a many-body system from time evolution [2h], Learning tensor networks in 1D [2h]\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}]