P4481-P7681-CS4812 Spring 2011

Physics / Computer Science

Physics 4481-7681 / CS 4812: Quantum Information Processing

Spring 2011
Tue/Thu 1:25-2:40 PM, Location: Rockefeller 231
3 credits, S/U Optional

Professor: Paul Ginsparg (452 Phys.Sci.Bldg, ginsparg@cornell.edu)
Office hours: Wed 1-2 PM (or by appointment)
Course website: http://people.ccmr.cornell.edu/~ginsparg/P4481-P7681-CS4812/ (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 prerequisites are familiarity (and comfort) with finite dimensional vector spaces over the complex numbers, some standard group theory, and ability to count in binary. (If this seems too vague, please peruse a copy of the course text in the library to assess its accessibility.)

Topics:

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.
Some simple, if artificial, quantum algorithms that are surprisingly more efficient than their classical counterparts.
Shor's super-efficient period finding (factoring) algorithm and the threat it poses for the security of cryptography.
Grover's efficient search algorithm.
The miracle of quantum error correction.
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)

The most recent previous syllabus is here: Spring 2008

Lecture 1 (Tue 25 Jan 11)

Began with historical overview, see, e.g., chapter 1 of Preskill notes.
Other refs: 20 Jan 2011 news article: "Billions of Entangled Particles Advance Quantum Computing" (arxiv:1010.0107)
Quantum Computation and Quantum Information (Nielsen and Chuang),
The Feynman Lectures on Computation (Hey and Allen)
(see also blog review of course text)
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.)
Some other popular expositions of reversible and quantum computing.

Lecture 2 (Thu 27 Jan 11)

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

Problem Set 1 (due in class Tue 8 Feb 2011)

Lecture 3 (Tue 1 Feb 11)

Covered pp 19-30 of the course text: Reversible operations on Qbits, circuit diagrams, measurement gates, and the Born rule. (See also appendices B,C of course text.)

Lecture 4 (Thu 3 Feb 11)

Covered pp 30-34 of the course text (finish chapt 1): Generalized Born rule, measurement gates and state preparation, constructing arbitrary 1- and 2-Qbit states, including digression on parts of Appendix B on U(2)=SU(2)xU(1) and SO(3)=SU(2)/Z₂.

Lecture 5 (Tue 8 Feb 11)

Functions, Deutch's problem, pp 34-46 of course text

Lecture 6 (Thu 10 Feb 11)

Comments on Alice, permutations, Deutsch -> Deutsch-Jozsa -> Bernstein-Vazirani -> Simon -> Shor, experimental realizations. Finish Deutch's problem, Bernstein-Vazirani problem (pp 50-54 of course text).

Problem Set 2 (due in class Tue 22 Feb 2011)

Lecture 7 (Tue 15 Feb 11)

why additional Qbits don't mess things up (pp 46-50), Simon's problem (pp 54-57)

Lecture 8 (Thu 17 Feb 11)

Finish Simon's problem (p. 57 and appendix G), and quantum Toffoli gates (pp 58-60, and latter part of appendix B)

Lecture 9 (Tue 22 Feb 11)

Finish quantum Toffoli gates (pp 60-62), including more from appendix B (pp 170-172) on relation between SU(2) and SO(3), and appendix D on the "spooky" Hardy State (pp 175-178). See also "Shut up and calculate"

Lecture 10 (Thu 24 Feb 11)

start chapt 3, period finding, some group theory, and RSA (pp. 63-67 and appendix I)

Problem Set 3 (due in class Thu 10 Mar)

Lecture 11 (Tue 1 Mar 11)

Finish RSA, Euclid's algorithm, start Quantum period finding (pp. 67-70, appendix J)

Lecture 12 (Thu 3 Mar 11)

Some comments on RSA numbers, Period finding and factoring (p.87), noted classical polynomial algorithm for primality test, Quantum period finding and the quantum Fourier transform (pp 70-72), finding the period (pp 79-81).

Lecture 13 (Tue 8 Mar 11)

More on discrete Fourier transforms, and continue finding the period (pp 80-83). (plus appendix K, 197-198, and some recreational mathematics)

Lecture 14 (Thu 10 Mar 11)

How to factor N=15, Fermat primes, more recreation, using continued fractions to finish finding the period (82-83, 198-200), start implementation of quantum Fourier transform (72-74).

Problem Set 4 (due in class Thu 31 Mar — Tue 5 Apr)

Lecture 15 (Tue 15 Mar 11)

Finish implementation of quantum Fourier transform, eliminate 2-Qbit gates (74-79), start unimportance of small phase errors (84-86).

Lecture 16 (Thu 17 Mar 11)

Finish calculating period function and unimportance of small phase errors (83-86).
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.

"Spring" Break

Lecture 17 (Tue 29 Mar 11)

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

Sample search for project ideas. (More explicit ideas in list linked at bottom of this page.)

Lecture 18 (Thu 31 Mar 11)

Finish discussion of (n-1)-fold control Z operator (figs 4.5-4.7).
Discussion of universality of reversible, irreversible, and quantum computing (See Preskill notes: pp 1-3 for Nand universality for classical functions "disjunctive normal form", and pp 12-15 for Tofolli gate universality for reversible computing, see also Toffoli+cNOT+... for quantum universality)
Plus some gratuitious comments on black hole info.

Lecture 19 (Tue 5 Apr 11)

Mentioned controlled SWAP (Fredkin) gate, controlled Grover, proof that Grover is optimal, Quantum cakes and Bell inequalities, generalized/structured search, Grover integration.
(see Preskill notes pp 54-57 for optimality of Grover, pp 57-59 for generalized/structured search, and 59-63 for discussion of problems that admit no quantum speedup)

Lecture 20 (Thu 7 Apr 11)

Start quantum error correction, chpt 5: simplified example of 3 Qbit single bit flip detection (pp 99-109), the physics of error generation (pp 109-113).

Problem Set 5 (due in class Thu, 21 Apr)

Lecture 21 (Tue 12 Apr 11)

Diagnosing error syndromes (pp 114-117), 5-qbit codes (pp 117-119).
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 14 Apr 11)

7 Qbit code and operations on 7-Qbit codewords (pp. 119-127).

Lecture 23 (Tue 19 Apr 11)

Almost finished quantum error correction: 7- and 5-Qbit encoding circuits (pp 127-129), Bell states (p. 136-137), physical realization of cNOT gate (Appendix H, pp.189), started discussion of quantum teleportation

Lecture 24 (Thu 21 Apr 11)

Finished preparing 7 Qbit codewords (p. 123-124).
More on photons, polarizers, and half wave plates.
quantum dense coding (pp 146-149), teleportation protocol (149-151)

Comments on why EPR was Einstein's last Phys Rev article: Einstein Versus the Physical Review (see also focus story for more refs, and gr-qc/9704002 by same author from before referee identity was known).

Some articles mentioned in class:

Last week's (15 Apr 2011) Teleportation (plus news articles: forbes, UNSW: "Quantum teleporter breakthrough")
2008 Quantum channel between Earth and Space (2 x 1485km, and comtemporary news items: newscientist, arxivblog, "boffins bounce photons")
Entanglement based quantum communication over 144 km optical free-space link: quant-ph/0607182 (2006), 0902.2015 (2009), quantum key distribution over 144km (2007) and 300km 1007.4645 (2010)
2011 quantum key distribution in Tokyo metropolitan area: 1103.3566
Entangled photon pairs over noisy ground atmosphere of 13km (2004)
Entangled photons in 100km fibre optic (2007)
2008 quantum repeater (and news article "Quantum cryptography can go the distance")

Problem Set 6 (due in class Thu, 5 May)

Lecture 25 (Tue 26 Apr 11)

Some comments on prob set 6 (how to detect the exploding measurement gate, how to represent error correcting codes in Matlab).
finish teleportation (151-154), more comments on photons and wave vectors, started Quantum Cryptography, pp. 137-140.

Lecture 26 (Thu 28 Apr 11)

Loose ends: mentioned compendium of quantum algorithms, 2.376, more on Ising (App H with isotropic interaction), completed teleportation of entangled states (p.154).
Finish discussioned of quantum cryptography (pp. 140-143), started bit commitment, with discussion of classical zero knowledge proofs (examples of graph coloring and Hamiltonian circuits / graph isomorphism). (See also ZKP of identity for use of difficulty of factoring in this context, same Shamir as RSA.)

Lecture 27 (Tue 3 May 11)

forgotten comments about Eve's other options in QKD (pp. 141-142), Bit commitment (pp. 143-146, and appendix P), GHZ (pp 154-158), and review circuit diagrams of Deutsch/Bernstein-Vazirani/Simons/Shor/Grover.

Lecture 28 (Thu 5 May 11)

Complexity Zoo: Some parting comments on P, NP, et al. and BQP et al., and 3-SAT (see also Preskill notes chpt 6, pp. 5-10, 22-24, 26-28),
plus a recent relevant rant (3 May '11) about popular complexophobia.

Note: Article Suggestions for Final Project