Cornell

Physics / Computer Science


Physics 481-681 / CS 483: Quantum Computation

Spring 2008
Tue/Thu 1:25-2:40 PM Rockefeller 231
3 credits, S/U Optional


Note: This is the former course website from Spring 2008.
The new website is here: Spring '14


Professor: Paul Ginsparg (325 Clark Hall, 5-7371, ginsparg@cornell.edu)
Office hours: Wednesdays 2-3 PM (or by appointment)
Course website: http://people.ccmr.cornell.edu/~ginsparg/P481-P681-CS483/ (this page)

Hardware that exploits quantum phenomena can dramatically alter the nature of computation. Though constructing a working quantum computer is a formidable technological challenge, the theory of quantum computation is of interest in itself, offering strikingly different perspectives on the nature of computation and information, as well as providing novel insights into the conceptual puzzles posed by the quantum theory.
The course is intended both for physicists, unfamiliar with computational complexity theory or cryptography, and also for computer scientists and mathematicians, unfamiliar with quantum mechanics. The prerequisite is familiarity (and comfort) with finite dimensional vector spaces over the complex numbers.

Topics:

  1. A quick but honest introduction to quantum mechanics for computer scientists and mathematicians, made elementary by focusing only on the specific set of applications at hand.
  2. Some simple, if artificial, quantum algorithms that are surprisingly more efficient than their classical counterparts.
  3. Shor's super-efficient period finding (factoring) algorithm and the threat it poses for the security of cryptography.
  4. Grover's efficient search algorithm.
  5. The miracle of quantum error correction.
  6. Other forms of quantum information processing: restoring security with quantum cryptography; superdense coding; teleportation.
Course Text: N.D. Mermin, Quantum Computer Science: An Introduction, Cambridge Univ Press (2007)

Lecture 1 (Tue 22 Jan 08)

Covered pp 1-10 of course text: intro, Cbits vs Qbits, reversible operations (inversion, swap, Cnot).
(For background on vector spaces and notation, see Appendix A of course text.)

Lecture 2 (Thu 24 Jan 08)

Begin with more historical overview, see, e.g., chapter 1 of Preskill notes.
Others references mentioned: Quantum Computation and Quantum Information (Nielsen and Chuang),
The Feynman Lectures on Computation (Hey and Allen),
Blog review of course text (plus other typical post).

Then continue with pp 11-18 of course text: number op, Hadamard, states of Qbits, entanglement.

Problem Set 1 (due in class Tue 5 Feb 2008)

Lecture 3 (Tue 29 Jan 08)

pp 19-28 of the course text: Exchange operator, reversible operations on Qbits, circuit diagrams, measurement gates, and the Born rule. (See also appendices B,C of course text.)
Two resources mentioned at the end: a) ternary computers, b) more on D-Wave.

Lecture 4 (Thu 31 Jan 08)

pp 28-35 of the course text (finish chapt 1): Generalized Born rule, measurement gates and state preparation, constructing arbitrary 1- and 2-Qbit states.
Some potential realizations of CNOT gates: photonics, Ion traps, Solid-state NMR, Liquid-state NMR, telecom band photonics

Lecture 5 (Tue 5 Feb 08)

Functions, Deutch's problem, pp 36-44 of course text

Lecture 6 (Thu 7 Feb 08)

Finish Deutch's problem, why additional Qbits don't mess things up, pp 44-48 of course text plus Appendix F on other aspects of Deutsch's problem.

Problem Set 2 (due in mailbox Fri 22 Feb 2008)

Lecture 7 (Tue 12 Feb 08)

Appendices B, C and first half of D of course text (p. 16, and pp 168-177): the relation between SU(2) and SO(3), and the "spooky" Hardy State. Finish why additional Qbits don't mess things up, pp. 48-50.

Lecture 8 (Thu 14 Feb 08)

Bernstein-Vazirani problem, Simon's problem, and started quantum Toffoli gates, pp. 50-58 of the course text.

Lecture 9 (Tue 19 Feb 08)

See Putting Weirdness to Work: Quantum Information Science (John Preskill, public lecture, 3 May 2006), for slides and links to audio/video (including podcast).

Lecture 10 (Thu 21 Feb 08)

See either (or both) of Either of these is less than the course time, so also spend 20 min reading the first and last sections ("Complexity 101" and "Anthropic Quantum Computing") of the text of this talk: Computational Complexity and the Anthropic Principle (Scott Aaronson, 15 Dec 2006)

Lecture 11 (Tue 26 Feb 08)

Finish quantum Toffoli gates, review Deutsch/Bernstein-Vazirani/Simons problems, and start chapt 3, period finding and some group theory (pp. 59-64 and appendix I)

Lecture 12 (Thu 28 Feb 08)

RSA (pp. 64-67 of text)

Problem Set 3 (due in class, Thu 13 Mar)

Lecture 13 (Tue 4 Mar 08)

Finish RSA, Euclid's algorithm, plus period finding and factoring (pp. 66-68, appendix J, and pp. 86-87)

Lecture 14 (Thu 6 Mar 08)

Quantum period finding and the quantum Fourier transform (pp 68-73)

Lecture 15 (Tue 11 Mar 08)

Finish quantum Fourier transform, eliminate 2-Qbit gates, and start finding the period (pp 74-81).

Lecture 16 (Thu 13 Mar 08)

Finish finding the period and unimportance of small phase errors (82-86, plus appendix K, and some recreational mathematics)

Problem Set 4 (due in class Thu, 3 Apr)


"Spring" Break

Lecture 17 (Tue 25 Mar 08)

Start chpt 4, pp. 88-94 (search and the Grover iteration), see also pedagogical reviews: Grover's and Lavor et al.'s.
The optimality of Grover's algorithm is shown here.

Lecture 18 (Thu 27 Mar 08)

Finish Chpt 4, pp.94-98: generalization to several special numbers, and construction of W via (n-1)-fold control Z operator.

Lecture 19 (Tue 1 Apr 08)

Start quantum error correction: simplified example of 3 Qbit single bit flip detection, pp. 99-109.

Lecture 20 (Thu 3 Apr 08)

The physics of error generation, and diagnosing error syndromes, pp 109-117.
Two very recent relevant articles mentioned in class: Problem Set 5 (due in class Thu, 17 Apr)

Lecture 21 (Tue 8 Apr 08)

5-qbit codes, pp 117-120.
Also mentioned historical articles (see review ('97)): 9-Qbit: Shor ('95), Shor et al. ('95), 7-Qbit: Steane ('96), 5-Qbit: LANL ('96), IBM ('96)

Lecture 22 (Thu 10 Apr 08)

Almost finish quantum error correction, pp. 121-130, except for parts of section (5.7)

Lecture 23 (Tue 15 Apr 08)

Finish operations on 7-Qbit codewords, pp. 124-127.
Quantum Cryptography, pp. 137-141.
Article mentioned in class: Experimental verification of the feasibility of a quantum channel between Space and Earth (also news items: vnunet, newscientist, arxivblog)

Lecture 24 (Thu 17 Apr 08)

More on photons, polarizers, and half wave plates. Quantum cakes and Bell inequalities. Finish discussion of quantum cryptograhy pp. 141-143. Start bit commitment with discussion of zero knowledge proofs (example of Hamiltonian circuits and graph isomorphism).

Problem Set 6 (due in class Thu, 1 May)

Lecture 25 (Tue 22 Apr 08)

Note: Class cancelled due to (minor) instructor illness, too late to find substitute. Will meet again at regular time on Thurs.

Lecture 26 (Thu 24 Apr 08)

Bit commitment, Bell states, dense coding, started teleportation, pp. 136-137, 143-147
(Stray reference mentioned in class in discussion of hard problems and classical zero knowledge proofs, Twenty-Five Moves Suffice for Rubik's Cube(2008))

Lecture 27 (Tue 29 Apr 08)

More on bit commitment (app. P), dense coding circuit diagrams, realization of controlled unitaries via controlled-SWAP, teleportation, and GHZ, pp 148-155

Lecture 28 (Thu 1 May 08)

Finished teleportation and GHZ, pp 154-158.
Some parting comments on P, NP, et al. and BQP et al., and 3-SAT.

Note: Article Suggestions for Final Project