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China Em ail Zhangcb5m ilustceducn Abstract A new not io of con rol il ity e nst te c rol ab ili ty is defined for finitedim ensi onal bil near quantum echani cal system s which are it her rong ly com letely co ntro ll ably nor com le tely co ntr. It is positiv semide57346nite because 0 At dt or all ectors 622 brPage 7br Lemma 0 is positiv de57346nite if and only if there is no ector such that At 0 Proof 0 At dt 0 At 0 722 brPage 8br Theorem The pair A is controllab le reachab le on 0 if and The coupling is described thr ough communication graph wher each system is node and the contr ol action at each node is only function of its state and the states of its neighbors distrib uted contr ol design method is pr esented which equir es the s 241 Dynamic Systems and Contr ol Lecture 6 Dynamical Systems Readings DD V Chapter Emilio razzoli Aeronautics and str onautics Massachusetts Institute of echnology eb rua ry 23 2011 E razzoli MIT Lecture 6 Dyn Modern Physics. 5/10/11 . Spring 2011. Ben Miller, Alexander . DeCarli. , Kevin Shaw. What is it?. How do particles become Entangled?. Parametric Down Conversion. A laser (usually ultraviolet for its high frequency) sends a photon through a nonlinear crystal such as Beta Barium Borate. and . Ultra-Efficient Solar Cells . 2008. “for the Layman”. Disclaimer. The information contained in this document is provided by Phoenix Alliance Corp. through its research sources and is obtained from sources that Phoenix Alliance Corp. believes to be reliable or are otherwise expressions of third party opinion. Whilst Phoenix Alliance Corp. has made reasonable efforts to ensure the accuracy, completeness and appropriateness of such information, any reliance on such information is entirely at the risk of the party using it, and it will not rely on such contents in substitution for making proper and appropriate enquiries from the relevant third parties. . Lecture 8 of “Introduction to Quantum Chaos”. Kicked oscillator: a model of Hamiltonian chaos. 5/8. 1/2. Poincare-. Birkhoff. fixed point theorem. Homoclinic tangle: generic chaos. Tori which survives the onset of chaos. Fang Song. IQC, University of Waterloo. -- “Quantum-Friendly” Reductions. 2. How do . quantum . attacks change classical cryptography?. Crypto-systems based on the hardness of factoring and discrete-log are . Why a Retreat?. Why a Center?. Transforming Caltech Quantum Science. Pre-historic: Feynman, Thorne, …. Pre-millennial: . Preskill. (1983), . Vahala. (1986), Kimble (1989), . Yeh. (1989), Eisenstein (1996). and the monogamy of entanglement. Aram . Harrow. MIT (UCL until Jan 2015). Quantum mechanics. QM has also explained:. the stability of atoms. the photoelectric effect. e. verything else we’ve looked at. Dung Nguyen. Chicago 19. th. January. Content. Motivation . Quantum bit (qubit) vs Classical bit (bit). Quantum Computation . Quantum Communication. Conclusion. Motivation. The end of Moore’s law scaling in silicon (because of quantum effects of particle at scale smaller than 7nm).. Quantum Hamiltonian Complexity. Aram Harrow (MIT). Simons Institute. 16 Jan 2014. Entanglement. Original motivation for quantum computing. [Feynman ‘82]. Nature isn't classical, dammit, and if you want to make a simulation of Nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.. Advanced Scientific Computing Research. Future of Computing:. A BES/ASCR Partnership . Background. Near Term. Exascale. Longer Term. Quantum Information Systems. Neuromorphic . 2. 3. Advanced Scientific Computing Research. Quantum. Communication:. Devices & Systems. Quantum. Sensing &. Metrology. Quantum . Computers:. Hardware & Software. Enabling. Science. Theory,. Algorithms. &. . Protocols. Quantum. Part 1. Outline. Introduction. Problems of classical physics. Black-body Radiation. experimental observations. Wien’s displacement law. Stefan – Boltzmann law. Rayleigh - Jeans. Wien’s radiation law.