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

Teaching Assistants

Dylan Gorman
Office hours: Thursday 2-3 in 751 Soda

Guoming Wang
Office hours: Monday 1-2 in 651 Soda

Seung Woo Shin
Office hours:


Course Outline


Homework is due Monday at 5 pm in the drop box labeled cs191, in 283 Soda Hall.

Lecture notes

Topic Notes
Chapters 1 and 2: "Qubits and Quantum Measurement" and "Entanglement". [pdf]
Chapters 3 and 4: "Observables" and "Continuous Quantum States". [pdf]
Notes on "Reversible Computation" [pdf]
Notes on "Fourier Sampling" [pdf]
Notes on "Simon's Algorithm" [pdf]
Notes on "Quantum Fourier Transform & Factoring" [pdf]
Notes on "Quantum Search" [pdf]
Notes on "Spin" [pdf]
Notes on "Spin Precession" [pdf]

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:
M. Genovese. 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 therein.

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,

Useful Links:

Recommended reading

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

Mathematical background

On quantum mechanics in general