[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-956190","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 Unification of Quantum Algorithms\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, basic quantum algorithms (DJ, Grover, Shor). Having followed courses on group theory and representation theory is welcome, but these will in any case be covered at length in the lectures.\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\u003EContrary to what we hear in the media, it is very unlikely that quantum computing unlocks a\u0026nbsp;\u003Cem\u003Euniversal\u003C\/em\u003E computation speedup: it seems there are only specific problems that it solves faster, sometimes dramatically so. Can we identify those problems, and understand why quantum algorithms perform so well on them? This is of course a question of prime importance, both foundational \u2013 for understanding the true power of quantum computing, beyond mere examples \u2013, and practical \u2013 for instance for making sure that our post-quantum cryptography techniques will indeed remain quantum-secure. In this course, we will discover two strikingly different approaches to this question. The first,\u0026nbsp;\u003Cem\u003EQuantum Singular Value Transform\u003C\/em\u003E (QSVT), finds that quantum algorithms are good at polynomial transformations of matrices; the second,\u0026nbsp;\u003Cem\u003EHidden Subgroup Problems\u003C\/em\u003E (HSP), finds that they perform well at spotting group-theoretic regularities. This will also be an occasion to discover some lesser-known quantum algorithms, such as the eigenvalue threshold, HHL, and discrete logarithms. The course will end on open research questions in these highly dynamic research domains.\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EPrerequisites\u003C\/strong\u003E: linear algebra, basic quantum algorithms (DJ, Grover, Shor). Having followed courses on group theory and representation theory is welcome, but these will in any case be covered at length in the lectures.\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EList of sessions\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003ELecture 1 (3h) \u2013\u0026nbsp; Quantum signal processing, amplitude amplification, block encodings, and an application to Grover.\u003C\/li\u003E\n\u003Cli\u003ELecture 2 (3h) \u2013 Quantum Eigenvalue Transforms and the QSVT, applications to the eigenvalue threshold problem and to HHL\u003C\/li\u003E\n\u003Cli\u003ETD 3 (3h) \u2013 Polynomial approximation for the QSVT with Chebyshev polynomials\u0026nbsp;\u003C\/li\u003E\n\u003Cli\u003ELecture 4 (3h) \u2013 Groups and representations\u003C\/li\u003E\n\u003Cli\u003ELecture 5 (3h) \u2013 The regular representation and the Quantum Fourier Transform; HSPs and how they generalise Shor and the discrete logarithm\u003C\/li\u003E\n\u003Cli\u003ELecture 6 (3h) \u2013 Solving the abelian HSP\u003C\/li\u003E\n\u003Cli\u003ETD 7 \u2013 Variations on the abelian HSP\u003C\/li\u003E\n\u003Cli\u003ELecture 8 \u2013 The HSP frontier: results and conjectures on the non-abelian case\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}]