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Computer Science Tel-Aviv University 0368.4057 Quantum computation 1 Spring 2012 The class was moved to בניין שאפל125 כיתה Suggestions for a project (for a group of students): 1. The (commutative) Quantum Lovasz Local Lemma. Link. 2. The Adversary method for obtaining Black-box lower bounds: https://www.math.uwaterloo.ca/~amchilds/teaching/w11/l18 .pdf Span programs and quantum query complexity: The general adversary bound is nearly tight for every boolean function. B. Reichardt. Proc. FOCS 2009, Extended abstract, Full version: quantph/0904.2759, 2009. slides 3. Quantum-proof extractors. Konig & Terhal’s paper: http://authors.library.caltech.edu/9660/1/KOEieeetit08.pdf Trevisan's extractor in the presence of quantum side information , Thmas Vidick, Anindya De, Christopher Portmann and Renato Renner. arXiv:0912.5514. [24/10/2013]: An old exercise on tensors, Solution . [Out: 24/10/2013, Due:21/11/2013] Exercise set 1 Figures [Out: 6/11/2013, Due:5/12/2013] Exercise set 2 [Out: 17/12/2013, Due:9/1/2014] Exercise set 3 Figure Some Information Lectures Instructors Open to Textbooks Grading policy Lecture notes on the web Thursday, 10:10-13:00, בניין שאפל125 כיתה Amnon Ta-Shma | Schreiber 127 | 5364 Undergrad and grad students from CS or Physics. Quantum Computation and Quantum Information, M. Nielsen, I. Chuang Classical and Quantum Computation, A. Yu. Kitaev, A. H. Shen, M. N. Vyalyi Homework is mandatory, Exam (mandatory for undergrad) and/or paper presentation/ project Topics in Quantum Information, by Ashwin Nayak. Lecture notes, by John Preskill. More lecture notes on his page. Quantum Computation, by Umesh Vazirani. Quantum Information and Computation, by John Watrous. quant-ph, a repository for all quantum-related research papers Links C Classes so far Date Class Topic 1. Oct 17 Nature as computation. Classical computation. One qubit, X, Y, Z, HAD. Many qubits. Tensor products, two qubits, CNOT. The two-slit experiment. Projection measurements. 2. Oct 24 The quantum world. Superdense coding, Quantum teleporation. Entanglement. No cloning theorem. 3. Oct 31 4. Nov 7 5. Nov 14 General measurements. POVM. Every physical test can be captured by a POVM and vice versa. The density matrix. More on density matrices. Measurements, POVMs and observables. The CHSH game (and Bell inequalities). A quote: Bell expressed his hope that such work would "continue to inspire those who suspect that what is proved by the impossibility proofs is lack of imagination." Analysis of the CHSH game with observables. Tsirelson’s bound. The trace norm. Distinguishing two density matrices. Reduced density matrix. No signaling. Safe storage principle. No signaling vs. local realism. Gonen Krak: QKD and the Lo-Chau protocol and proof. Gonen’s slides. Richard Cleve’s slides. The paper itself. 6. Nov 21 Part II, Quantum algorithms: The quantum circuit model. Uniformity. The class BQP. 7. Nov 28 No class 8. Dec 5 Simulating classical circuit by quantum circuits, effects of garbage. Deutsch's algorithm, Deutsch-Jozsa algorithm, The black-box model, Simon's algorithm. 9. Dec 12 The Fourier transform for Abelian groups. Efficient Fourier transform over (Z_2)^n and Z_(2^n). The Hidden subgroup problem. FFT and HSP. Discrete Log. 10. Dec 19 Phase estimation.Cayley graphs. Efficient Fourier transform over Z_k for any k. Order finding, Shor'sfactoring algorithm. 11. Dec 26 Grover’s algorithm. Estimating the number of solutions using phase estimation. BBBV Lower bound on the OR function. 12. Jan 2 A general lower-bound on quantum black-box computation by polynomials. Black-box computation cannot provide more than a polynomial speedup for total, Boolean functions. Purification. Schmidt decomposition, impossibility of perfect bit commitment. 13. Jan 9 Fidelity. Some facts (without proof) about it. Coin flipping. Ambainis’ ¾protocol. 14. Jan 16 Extractors. Quantum-proof extractors. Konig-terhal generic result for one output-bit extractors. Trevisan’s extractor. Trevisan’s extractor is quantumproof. 15. ??? Student presentations.