Chem/CS/Phys191: Qubits, Quantum Mechanics, and Computers
Lecture Tue & Thu 9:30 - 11:00am (306 Soda Hall)
Section 101 W 11-12pm 405 Soda
Section 102 F 1-2pm (325 LeConte)
Prof. Umesh Vazirani
Office hours: Monday 2-3 in 671 Soda
Office hours: Thursday 2-3 in 751 Soda
Office hours: Monday 1-2 in 651 Soda
Seung Woo Shin
- Guoming Wang's office hours have been posted (M 1-2 pm in 651 Soda). Prof. Vazirani's office hours have been moved to M 2-3 in 671 Soda.
- 01/18/12 The Wed discussion section (11-12pm) has been scheduled in 405 Soda Hall. Still working on getting a room for Friday discussion sections.
- 01/17/12 Homework 1 has been posted. It is due at 5 pm next Monday.
- Here is a (tentative) lecture-by-lecture outline + dates of midterms and project presentations [outline].
Homework is due Monday at 5 pm in the drop box labeled cs191, in 283 Soda Hall.
- Homework 1 [pdf] due Monday 1/23. Solution [pdf]
- Homework 2 [pdf] due Monday 1/30. Solution [pdf]
- Homework 3 [pdf] due Monday 2/06. Solution [pdf]
- Homework 4 [pdf] due Monday 2/13. Solution [pdf]
- Homework 5 [pdf] due Tuesday 2/21. Solution [pdf]
- Homework 6 [pdf] due Monday 2/27. Solution [pdf]
- Homework 7 [pdf] due Monday 3/5. Solution [pdf]
- Homework 8 [pdf] due Monday 3/12. Solution [pdf]
- Homework 9 [pdf] due Monday 3/19. Solution [pdf]
- Homework 10 [pdf] due Monday 4/16. Solution [pdf]
Chapters 1 and 2: "Qubits and Quantum Measurement" and "Entanglement".
Chapters 3 and 4: "Observables" and "Continuous Quantum States".
Notes on "Reversible Computation"
Notes on "Fourier Sampling"
Notes on "Simon's Algorithm"
Notes on "Quantum Fourier Transform & Factoring"
Notes on "Quantum Search"
Notes on "Spin"
Notes on "Spin Precession"
Project List and Guidelines
The project is worth 30% of the grade. You should work in teams of 2-3. At the end of the semester each team will submit a project report (ideally 5-10 pages), as well as give a 20 minute oral presentation.
Here are a few suggestions of broad topics for projects, together with a pointer to a good starting point for your exploration. Please feel free to google or search on the quant-ph archive for more information on these or other topics. We will add to the list, and you should feel free to suggest any topic that you are interested in. Please email me (vazirani@cs) by April 11, the composition of your team, the topic, and a one to two sentence description.
quant-ph refers to the Los Alamos archives: link
1. Adiabatic Quantum Computation (AQC)
AQC, though formally equivalent to circuit model QC, is quite
different in its formulation. What are the advantages, and
disadvantages of AQC compared to the circuit model? What are some
promissing physical systems in which to implement AQC?
The original paper by Farhi, Goldstone, Gutmann
and Sipser provides a good starting point, and a web search will
reveal a lot of follow up work.
2. Computation by teleportation
3. Designing quantum algorithms by phase estimation:
4. Algorithmic cooling
5. Quantum error correction
6. Quantum random walks
7. Quantum money
8. Interpretations of quantum mechanics and the measurement problem
A good starting point is the following paper:
Interpretations of quantum mechanics and the measurement problem.
Adv. Sci. Lett. 3, 249 - 258 (2010).
9. Quantum random number generators
10. Simulating quantum systems
One of the lessons of quantum computation is that quantum systems are exponentially powerful, so classical computers cannot efficiently simulate general quantum systems. Nevertheless, there are beautiful results sho
wing how to simulate certain "natural" quantum systems efficiently on a classical computer. Here is a survey paper that provides a good starting point:
11. 7. Quantum algorithm for solving linear equations
Kitaev's phase estimation algorithm is a beautiful building block
in quantum algorithms. A recent paper uses it to speed up solutions of
systems of linear equations:
12. Physical Implementations of QC
In class we discussed a number of physical implementations. What are
the advantages of each? What are the dominant decoherence processes?
Pick one and do a detailed analysis - or maybe do a general survey.
You can start with David DiVincenzo's famous paper and references
13. Decoherence Mitigation
There are many ways to protect a quantum computer from decoherence:
dynamical decoupling, decoherence free subspaces, quantum feedback
control, quantum Zeno effect, and quantum error correction. Talk
about one in detail or do an overview. You can start by looking at
the first couple of chapters of Dave Bacon's thesis,
- Los Alamos archive of papers and preprints on Quantum Mechanics and
Quantum Computation: link
- John Preskill's Quantum Computation course at Caltech: link
- Umesh Vazirani's Quantum Computation course at UC Berkeley: link
- Daniel Lidar's page of teaching links for Quantum Mechanics and
For all topics, the first recommended reading is
the lecture notes. For a second point of view, or if the notes are
confusing, try the other sources listed below.
On quantum computation
- Benenti, Casati and Strini, Principles of Quantum
Computation, v. 1: Basic Concepts
Introductory. See v. 2 for more advanced topics.
- Kaye, LaFlamme and Mosca, An Introduction to Quantum
- McMahon, Quantum Computing Explained
New undergraduate-oriented text.
- Stolze and Suter,Quantum Computing: a short course from theory to experiment
Physics-oriented introduction with discussion of experimental implementation.
- Mermin, Quantum Computer Science
- Nielsen and Chuang, Quantum Computation and Quantum
An encyclopedic reference.
- Pittenger, An introduction to Quantum Computing
Introduction to algorithms.
- Lo, Popescu and Spiller, Introduction to Quantum Computation and
Introductory review chapters to basic concepts and
- Kitaev, Shen and Vyalyi, Classical and Quantum Computation
- Strang, Gilbert. Linear Algebra and Its Applications
Good review of matrix theory and applications.
- Jordan, Thomas F. Linear operators for Quantum Mechanics
Thorough presentation of operators and mathematical
On quantum mechanics in general
- Feynman, Richard P. The Feynman Lectures on Physics, volume 3
A famous introduction to undergraduate physics. Good
section on 2-state systems.
- Griffiths, David J. Quantum Mechanics
Very clear explanations, doesn't cover
- Liboff, Richard L. Introductory Quantum Mechanics
Good coverage, explanations medium. See Ch. 16 in the
new (4th) edition for intro. to Quantum Computing.
- Baym, Gordon. Lectures on Quantum Mechanics
Graduate level textbook. Very clear exposition of the
- Feynman, Richard. QED
Nice leisure reading.