**Audience:** The course is intended for graduate and senior undergraduate students of Physics, Computer Science and Mathematics. A background in Quantum Mechanics is expected.

**Credits:** 3.

**Grading:** 1/3 homework assignments, 1/3 in-class written exam, 1/3 essay/ oral presentation.

Every processing of data such as transmission or a computation is realized as a physical process. This relation is not merely a question of physical implementation. Rather, the underlying laws of physics govern which ways of information processing are possible. Since the fundamental laws of physics are quantum mechanical so should be a theory of information processing. To work out this theory is the goal of quantum information science, being at the junction of quantum physics, computer science and mathematics. At present, we only know parts of this theory. In addition, we possess a collection of puzzling examples which demonstrate the advantage of quantum over classical information processing. Among them, most notably, is Shor's factoring algorithm. It allowed, once a large-scale quantum computer could be built, breaking the widely used RSA crypto system.

In this course we address the questions of which physical systems, from the current perspective, are suitable for building a quantum computer; how to counteract the effects of decoherence; and -- once we have a large-scale quantum computer -- what can be done with it. In more detail, the course outline is as follows:

Introduction

Essentials: pure and mixed quantum states; unitary evolution vs. measurement. Local vs. non-local properties of quantum states.

Alternative models of quantum computation (1): Adiabatic quantum computation. See "Announcements" for schedule of two guest lectures.

Entanglement

- First applications: teleportation, entanglement purification and the quantum repeater
- Separability critera and entanglement measures

Quantum cryptography

Quantum computation: the circuit model; Quantum algorithms:

- Grover's algorithm for data base search
- Shor's algorithm for factoring

Physical systems for quantum computation: Ion traps, Josephson junction arrays, optical lattices with cold atoms.

Quantum error-correction: quantum error-correcting codes, techniques for fault-tolerant quantum computation, the threshold theorem.

Topological quantum computation. Covered by visitor Dr. Parsa Bonderson from Microsoft Research Station Q. Theory Seminar, Mon Nov 17 + Quantum Information Seminar, Tue Nov 18.

Foundational issues of Quantum Mechanics: Quantum Mechanics vs. local hidden variable models, Bell inequalities, the Kochen-Specker Theorem.

Alternative models of quantum computation (2): Measurement-based quantum computation.

Student Presentations:

- The Knill-Laflamme-Milburn (KLM) scheme of linear optics quantum computation.
- Quantum walks: NAND-tree evaluation
- Adiabatic quantum computation and quantum phase transitions - first vs. second order.
- Quantum information processing in ion traps.

M.A. Nielsen and I.L. Chuang,

*Quantum computation and Quantum Information*, Cambridge University Press (2000).J. Preskill's lecture notes, Caltech Phy/CS 219.

J.J. Sakurai,

*Modern Quantum Mechanics*, Addison-Wesley Publishing Company (1994).S. Loepp and W.K. Wootters,

*Protecting Information - From Classical Error Correction to Quantum Cryptography*, Cambridge University Press (2006).C. Isham,

*Lectures on Quantum Theory: Mathematical and Structural Foundations,*Imperial College Press (1995).

None of these texts is strictly required but I suggest you get hold of a copy of Nielsen and Chuang. John Preskill's lecture notes are an excellent resource available online. The Sakurai will be our Quantum Mechanics reference for this course. I will use Loepp and Wootters' book for Quantum Cryptography. Isham's text is supplementary reading for foundational issues of Quantum Mechanics such as the Bell inequalities and the Kochen-Specker theorem.