{"id":451,"date":"2022-03-25T10:29:45","date_gmt":"2022-03-25T10:29:45","guid":{"rendered":"https:\/\/projects.ift.uam-csic.es\/qift\/?page_id=451"},"modified":"2022-04-13T17:28:12","modified_gmt":"2022-04-13T17:28:12","slug":"courses","status":"publish","type":"page","link":"https:\/\/projects.ift.uam-csic.es\/qift\/courses\/","title":{"rendered":"Courses and schools"},"content":{"rendered":"\t\t
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Quantum Entanglement and Information
<\/strong>Master of Theoretical Physics at the IFT

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Course contents:<\/p>

1. INTRODUCTION AND OVERVIEW. Information is physical. Quantum information vs. Classical information. Entanglement as a resource for quantum information. Classic and quantum Turing machines. The quantum computer. Why should theoretical physicists pay attention to quantum computers?<\/p>

2. FUNDAMENTALS OF QUANTUM THEORY. States and sets (\u201cEnsembles\u201d). Density operators. Formalism of the density matrix. Measures and evolution. Orthogonal measures. Generalized measures. Measures of projection operators. Neumark's theorem. Superoperators.<\/p>

3. THE QUANTUM BIT. Characterization of states of a qubit, Hamiltonians and measurements. Spherical representation of Bloch. Physical realizations of qubits.<\/p>

4. QUANTUM ENTANGLEMENT. Composite systems. Product states vs. entangled states. Local operations and classic communication. Entanglement operations. Entanglement measures. Bipartite systems. Decomposition of Schmidt. Reduced density matrix. States of maximum entanglement. Entanglement and mixing. Entropy of entanglement.<\/p>

5. THE TWO QUBITS SYSTEM. Characterization of entangled states of two qubits. Bell States. Physical realization of Bell pairs with pairs of photons or atoms.<\/p>

6. USES OF THE ENTANGLEMENT. Possible machines. Dense coding. Quantum teleportation. Quantum cryptography Impossible machines Communication slower than light. The no cloning theorem.<\/p>

7. BELL INEQUALITIES. Einstein locality and hidden variables. The paradox of Einstein, Podolski and Rosen. No separability of EPR pairs. Hidden quantum information. Bell inequalities. Experimental test of Bell's inequalities. The Aspect\u2019s experiment.<\/p>

8. QUANTUM COMPUTING. Classical computing vs. Quantum computing. Computational complexity. Quantum circuits. Quantum gates. Universal quantum gates. Quantum algorithms The Deutsch algorithm. The quantum database search algorithm of Grover. The Shor factorization algorithm.<\/p>

9. QUANTUAM SIMULATION. The Feynman quantum simulator. The complexity of quantum simulation. Physical realization of a quantum simulator. Example: ultracold atoms in optical networks. The Hubbard tool. Quantum simulation of Bell pairs. Quantum simulation of phases of many strongly correlated bodies.<\/p>

10. TOPOLOGICAL QUANTUM COMPUTING. Quantum error correction. Faulty safe quantum computing. Quantum codes. Topological order. Examples of topological phases in nature. Fractional quantum Hall effect systems. Anions. Abelian and non-Abelian anions. Kitaev\u2019s Toric code. The topological quantum bit.<\/p>

11. ENTANGLEMENT IN MANY BODY SYSTEMS. Entanglement as a useful tool to characterize quantum phases and quantum phase transitions. The area law of entanglement entropy. Renormalization group of the density matrix and tensor networks. Applications to spin lattice systems.
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Introduction to Conformal Field Theory
<\/strong>Germ\u00e1n Sierra (IFT)
January 18 – March 8, 2021

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Conformal Field Theory (CFT) is a topic that relates several branches of Physics such as String Theory, Condensed Matter Physics and Statistical Mechanics, and also in Mathematics, as infinite dimensional Lie algebras and Quantum Groups. In this course we shall introduce the main concepts to CFT, specially in 1 + 1 dimensions, together with some applications to Luttinger liquids, spin chains and the fractional quantum Hall effect.
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VIth\u00a0edition of the INFIERI International Summer School<\/a>
<\/strong>Universidad Aut\u00f3noma de Madrid
August 23 – September 4, 2021

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The programme of the school will cover advanced technologies in semiconductors, deep sub-micron 3D technologies, nanotechnology, interconnects, data transmission, Big Data, artificial intelligence, high-performance and Quantum computing, as well as their scientific motivations. The latter range from the exploration and understanding of the universe (i.e. dark matter\/energy and gravity), particle physics and future accelerators with opening on new energies to the human-body (i.e. neurology and advances in nanomedecine).
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Quantum Entanglement and InformationMaster of Theoretical Physics at the IFT Introduction to Conformal Field TheoryGerm\u00e1n Sierra (IFT)January 18 – March 8, 2021 VIth\u00a0edition of the INFIERI International Summer SchoolUniversidad Aut\u00f3noma de MadridAugust 23 – September 4, 2021<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","footnotes":""},"class_list":["post-451","page","type-page","status-publish","hentry"],"guten_post_layout_featured_media_urls":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"guten_post_layout_landscape_large":false,"guten_post_layout_portrait_large":false,"guten_post_layout_square_large":false,"guten_post_layout_landscape":false,"guten_post_layout_portrait":false,"guten_post_layout_square":false},"_links":{"self":[{"href":"https:\/\/projects.ift.uam-csic.es\/qift\/wp-json\/wp\/v2\/pages\/451","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.ift.uam-csic.es\/qift\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/projects.ift.uam-csic.es\/qift\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/qift\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/qift\/wp-json\/wp\/v2\/comments?post=451"}],"version-history":[{"count":100,"href":"https:\/\/projects.ift.uam-csic.es\/qift\/wp-json\/wp\/v2\/pages\/451\/revisions"}],"predecessor-version":[{"id":961,"href":"https:\/\/projects.ift.uam-csic.es\/qift\/wp-json\/wp\/v2\/pages\/451\/revisions\/961"}],"wp:attachment":[{"href":"https:\/\/projects.ift.uam-csic.es\/qift\/wp-json\/wp\/v2\/media?parent=451"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}