An illustration of the Bloch sphere, which provides a geometrical representation of the pure state space of a 1 qubit quantum register. (Image courtesy of Wikipedia.)
This course features a complete set of lecture notes and assignments.
This is an advanced graduate course on quantum computation and quantum information, for which prior knowledge of quantum mechanics is required. Topics include quantum computation, advanced quantum error correction codes, fault tolerance, quantum algorithms beyond factoring, properties of quantum entanglement, and quantum protocols and communication complexity.
Syllabus
Course Description
This advanced graduate course on quantum computation and quantum information assumes a prior knowledge of quantum mechanics. We will cover models of quantum computation, advanced quantum error correction codes, fault tolerance, quantum algorithms beyond factoring, properties of quantum entanglement, and quantum protocols and communication complexity.
Prerequisites
Quantum Computation, Fall 2003 (2.111/18.435J)
Assignments
Students will complete one problem set every two weeks during the first half of the course. In the remaining half of the course, each student will pursue an active area of research in the field of theoretical quantum computing. Students will use their results to prepare an American Physical Society style paper and formal presentation.
Textbook
Nielsen, Michael A., and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge, UK: Cambridge University Press, 2000. ISBN: 9780521635035.
Grading Policy
Grading criteria.
| ACTIVITIES |
PERCENTAGES |
| Homework (4 Problem Sets) |
40% |
| Project Presentation |
20% |
| Project Paper |
40% |
Calendar
Instructors
C = Isaac Chuan
S = Peter Shor
H = Sean Hallgren, Guest Lecturer
Course calendar.
| SES # |
INSTRUCTORS |
TOPICS |
KEY DATES |
| 1 |
C |
Quantum Operations; Operator Sum Representation; System-Environment Model |
Problem set 1 out |
| 2 |
C |
Quantum Error Correction - Criteria and Examples |
|
| 3 |
S |
Calderbank Shor Steane Codes |
|
| 4 |
S |
Stabilizers; Stabilizer Quantum Codes |
Problem set 2 out
Problem set 1 due |
| 5 |
S |
Topological Quantum Codes; Kitaev's Anyon Model |
|
| 6 |
C |
Stabilizers II; Computing on Quantum Codes |
|
| 7 |
C |
Concatenated Codes; The Threshold Theorem |
Problem set 3 out
Problem set 2 due |
| 8 |
C |
Cluster State Quantum Computation |
|
| 9 |
C |
Measurement and Teleportation Based Quantum Computation |
|
| 10 |
C |
Adiabatic Quantum Computation |
|
| 11 |
S |
Quantum Algorithms on Graphs; Quantum Random Walks |
Problem set 4 out
Problem set 3 due |
| 12 |
H |
Quantum Algorithms: The Abelian Hidden Subgroup Problem; QFT Over Sn |
|
| 13 |
H |
The Nonabelian HSP; Hidden Dihedral Group; Positive and Negative Results |
|
| 14 |
S |
Channels I: Quantum Data Compression; Entanglement Concentration; Typical Subspaces |
|
| 15 |
S |
Channels II: Holevo's Theorem; HSW Theorem; Entanglement Assisted Channel Capacity |
Project forms out
Problem set 4 due |
| 16 |
S |
Channels III: Quantum-Quantum Channels, Mother/Father Protocol; Distillable Entanglement |
|
| 17 |
C |
Entanglement as a Physical Resource |
|
| 18 |
C |
Quantum Protocols - Quantum Communication Complexity; Distributed Algorithms |
Project forms due |
| 19 |
C |
Quantum Games |
|
| 20 |
C |
Quantum Cryptography |
|
| 21-22 |
|
Project Meetings |
|
| 23-26 |
|
Project Presentations |