Physics / Computer Science |

Tue/Thu 1:25-2:40 PM Rockefeller 231

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, 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:**

- 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.

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

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)

Two resources mentioned at the end: a) ternary computers, b) more on D-Wave.

Some potential realizations of CNOT gates: photonics, Ion traps, Solid-state NMR, Liquid-state NMR, telecom band photonics

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

- "Spooky Actions at a Distance?" (N. David Mermin, public lecture, 12 Apr 2007), search the page Princeton University Hamilton Lecture Series for "mermin", or use this 350K RealMedia link.
- Quantum Mechanics in your face (Sidney Coleman, general lecture for APS sectional meeting, Apr 9 1994)

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

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

"Spring" Break

The optimality of Grover's algorithm is shown here.

Two very recent relevant articles mentioned in class:

- Realization of the quantum Toffoli gate with trapped ions (T. Monz, et al., 2008)

- Quantum computing using shortcuts through higher dimensions (B. P. Lanyon, et al., 2008)

Also mentioned historical articles (see review ('97)):

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)

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

(Stray reference mentioned in class in discussion of hard problems and classical zero knowledge proofs, Twenty-Five Moves Suffice for Rubik's Cube(2008))

Some parting comments on P, NP, et al. and BQP et al., and 3-SAT.

Note: Article Suggestions for Final Project