**Introduction to
Quantum Information Processing
**QIC 710, CS 667,
C&O 681, PHYS 767, AM 871

Fall 2011 (http://www.cs.uwaterloo.ca/~cleve/courses/F11CS667/index.html)

Classical lower bound for Simon's problem

**Objectives
**Quantum Information Processing (also known as "quantum computing") seeks to
harness the strange power of quantum mechanics to provide a qualitatively
different and more powerful way of processing information than "classical"
physics seems to allow. The objective of this course is to introduce this
multidisciplinary subject at the graduate level.

**Topics to be covered **

●
Detailed syllabus: [PDF]

●
Overview
(timing information is approximate):

○
Introduction to the quantum
information framework (3 lectures).

○
Quantum algorithms and
complexity theory (8 lectures).

○
Density matrices and quantum
operations on them (3 lectures).

○
Distance measures between
quantum states (1 lecture).

○
Entropy and noiseless coding
(1 lecture).

○
Error-correcting codes and
fault-tolerance (3 lectures).

○
Nonlocality (2 lectures).

○
Cryptography (3 lectures).

**Intended audience**

This course is mainly intended for graduate students in CS, C&O or Physics.
Other students may take this course with the permission of the instructor.

Prerequisites are MATH 235 or equivalent (e.g. PHYS 364 & 365); STAT 230 or
equivalent. Note: this course cannot be taken for credit by students who have
taken CO 481 / CS 467 / PHYS 467.

**Evaluation**

5 assignments 12% each

1 project 40%

**Lecture notes from Fall 2011
**
Lecture 11 [PPT,
PDF]

Lecture 14 [PPT, PDF] Bloch sphere, general quantum operations in Krauss form, POVMs

Lecture 15 [PPT, PDF] Stinespring vs. Krauss, separable states, trace distance

Lectures 16 [PPT, PDF] Holevo-Helstrom Theorem, entropy, compression

Lectures 17-19 [PPT, PDF] NP (briefly), Grover's algorithm & lower bound for searching

Lectures 20-21 [PPT, PDF] Quantum error-correcting codes

**Lecture notes from Fall 2008
**
Lectures 1-3 [PPT,
PDF]

Lectures 4-6 [PPT, PDF]

Lectures 7-9 [PPT, PDF]

Lectures 10-14 [PPT, PDF]

Lectures 15-20 [PPT, PDF]

**Lecture notes from Fall 2009
**
Lecture 14 [PPT,
PDF]
Bloch sphere, general quantum operations in Krauss form, POVMs

Lecture 15 [PPT, PDF] Stinespring vs. Krauss, separable states, trace distance

Lectures 16-17 [PPT, PDF] Holevo-Helstrom Theorem, entropy, compression

Lecture 18 [PPT, PDF] Grover's algorithm & lower bound for searching

Lecture 19 [PPT, PDF] Nonlocality (GHZ and CHSH)

Lectures 20-21 [PPT, PDF] Quantum error-correcting codes

Lectures 22-23 [PPT, PDF] Fault-tolerance (brief); BB84 quantum key distribution; Schmidt decomposition

Lecture 24 [PPT, PDF] Lo-Chau quantum key distribution protocol and its security

**Projects** (worth 40% of the final grade)

Each project consists of a written component and an oral presentation to the
class.
It should explain and analyze
some topic in quantum information processing, selected with the approval of the
instructor. Your presentation should be about 30 minutes in length and your
written component is not required to be of any particular length, but around 10
pages would be typical (PDF, PS, and Word are acceptable formats). You should
explain the topic in your own words, at a level accessible to your classmates.

**Partial list of possible project topics
**[ PDF format,
Word format ]

Note that you are welcome to pursue a project topic that is not on the list. In any event, you should seek approval from the instructor for your project topic.

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