Computer
Science
Tel-Aviv
University
0368.4057
Quantum computation 1
Spring
2012
The class was moved to ‫ בניין שאפל‬521 ‫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 שאפל‬521 ‫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.