Physics / Computer Science |

Tue/Thu 1:25-2:40 PM, Location: PSB 120

3 credits, S/U Optional

The new website is here: Spring '14

Hardware that exploits quantum phenomena can dramatically alter
the nature of computation. Though constructing a working quantum
computer is a formidable technological challenge, there has been much recent
experimental progress.
In addition, 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. Notes on which the text was based are still available here.)

**Topics:**

- A quick but honest introduction to quantum mechanics for computer scientists and mathematicians, simplified by focus on the specific set of relevant applications (measurement, not dynamics)
- Some simple, if artificial, quantum algorithms that are surprisingly more efficient than their classical counterparts
- Shor's super-efficient period finding (factoring) algorithm and its threat to cryptographic security
- Grover's efficient search algorithm
- The miracle of quantum error correction
- Quantum "weirdness": applications of Bell's theorem
- Other forms of quantum information processing and conundra: quantum cryptography; superdense coding; teleportation

**Course Text:**
N.D. Mermin,
*Quantum Computer Science: An Introduction*, Cambridge Univ Press (2007)

Supplemented by
Quantum Computation and Quantum Information (Nielsen and Chuang), and other on-line resources

The most recent previous syllabus is here: Spring 2011

Covered roughly pp 1-7 (1.1-1.2) of course text: intro, Cbits vs Qbits

(For background on vector spaces and notation, see Appendix A of course text.)

Some other popular expositions of reversible and quantum computing.

A couple other popular refs mentioned (access from within Cornell network): The Fundamental Physical Limits of Computation (Bennett and Landauer, SciAm Jul 1985); Demons, Engines and the Second Law (Bennett, SciAm Nov 1987)

Problem Set 1 (due in class Thu 6 Sep 2012)

Start functions, pp 36-39 (2.1) of course text

Overall progression to come: Deutsch -> Deutsch-Jozsa -> Bernstein-Vazirani -> Simon -> Shor, experimental realizations.

Problem Set 2 (due in class Thu 20 Sep 2012)

Started chpt. 3 (3.1-3.2), period finding and "Fermat's Little theorem"

Problem Set 3 (due in class Thu 4 Oct, or via alternate means by 11 Oct)

9 Oct 2012: coincidental news on Nobel Prize for Quantum info to Wineland and Haroche (plus Monroe/Wineland (2008) SciAm article on quantum computing)

Problem Set 4 (due in class Thu 25 Oct)

Current quantum factoring record is 143.

Started chpt 4, pp. 88-91 (4.1-4.2, search and the Grover iteration)

The optimality of Grover's algorithm is shown here.

Now finished the basic basic quantum algorithms.

comment on Grover integration.

Comments on Quantum cakes and Bell inequalities.

Start quantum error correction, simplified example of 3 Qbit single bit flip detection (5.1-5.2, pp 99-109)

Surface code review mentioned in class

Problem Set 5 (due in class Thu 8 Nov)

Mentioned historical articles (see review ('97)):

5.6-5.7: 7 Qbit code and operations on 7-Qbit codewords (pp. 119-127)

Start discussion of superconducting qubits (note also .1 ms coherence time and 98% fidelity cNOT) and surface codes

6.1: Bell states (pp 136-137), surface codes.

For next time, briefly discussed entanglement based quantum communication over 144 km optical free-space link: quant-ph/0607182 (2006), 0902.2015 (2009), and even bigger: 2008 Quantum channel between Earth and Space (2 x 1485km, and contemporary news items: newscientist, arxivblog, "boffins bounce photons")

Prob Set 5 due (with auto extension til Tues)

Re quantum key distribution, mentioned

- 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")

Re teleportation news Apr 2011 (plus news articles: forbes, UNSW: "Quantum teleporter breakthrough")

plus a relevant rant (3 May '11) about popular complexophobia.

Note: Article Suggestions for Final Project

Recall diagrammatic review of first part of course

See also "Quantum Algorithm Zoo": compendium of quantum algorithms