PPT-SDP hierarchies and quantum states

Aram Harrow MIT Simons Institute 2014117 a theorem Let M 2 R m n Say that a set S n k is δgood if φm k S such that j 1 j k S fkδ max S Sn. 1HANDMAIDENS, HIERARCHIES, AND CROSSING THE PUBLIC-PRIVATE DIVIDE IN THETEACHING OF INTERNATIONAL LAWDianne OttoI want to address the question of what law students are encouraged to imagine is the rol Efficient Algorithms and their Limits. Prasad . Raghavendra. University of Washington. Seattle. . Max 3 SAT. . Find an assignment that satisfies the maximum number of clauses.. Max 3. SAT. Max 2. Collisions. Collisions. Detection. Broad Phase. Bounding Volumes. Key idea:. Surround the object with a (simpler) bounding object (the bounding volume).. If something does not collide with the bounding volume, it does not collide with the object inside.. Deterministic Discrepancy Minimization. Nikhil Bansal (TU Eindhoven). Joel Spencer (NYU). 2. /17. Combinatorial Discrepancy. Universe:. U= [1,…,n] . Subsets:. S. 1. ,S. 2. ,…,. S. m. . 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 . Raghavendra. University of Washington. Seattle . Optimal Algorithms and . Inapproximability. Results for . Every CSP?. Constraint Satisfaction Problem. A Classic Example : . Max-3-SAT. Given a . 3-SAT. 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. Effectiveness and Limitations. Yuan Zhou. Computer Science Department. Carnegie Mellon University. 1. Combinatorial Optimization. Goal:. optimize an objective function of . n. 0-1 variables. Subject to: . Haggai . Maron, . Nadav. . Dym. , . . Itay. . Kezurer. , . . Shahar. . Kovalsky. , . . Yaron. . Lipman. . Weizmann . Institute of Science. 1. Orthogonal.  .  .  .  . Orthogonal Procrustes Problem. Fernando . G.S.L. . Brand. ão. ETH Zürich. Based on joint work with M. . Christandl. and J. Yard. Journees. . Deferation. de . Reserche. en . Mathematiques. de Paris Centre/GT . Informatique. . Columbia . University. . Graph-Theoretic Algorithm for Arbitrary Polynomial Optimization Problems with Applications to Distributed Control, Power Systems, and Matrix Completion. . Joint work with. :. Senior Program Manager. Master Data Services. Microsoft Corporation. Microsoft . SQL Server 2012. ®. ®. Agenda. Introduction to Hierarchies. Level Based vs. Ragged Hierarchies. Derived Hierarchies. The Quantum Computer. Quantum computers, like all computers, are machines that perform calculations upon data.. Quantum computers use the principles of superposition and entanglement from the field of quantum mechanics to aid in the performance of these calculations. (for Max Cut). Venkatesan. . Guruswami. Fields Institute Summer School. June 2011. (Slides borrowed from Prasad . Raghavendra. ). Dictatorship Test. Given a function . . F : {-1,1}. R. {-1,1}.