Webpage with schedule and lecture notes for Spring semester 2005 can be found here

The course now has a newsgroup, at `ucb.class.cs191`

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The schedule for the project presentations and links to all other project related pages can be found here

Lectures: Tuesday/Thursday 12:30-2 in 180 Tan

Office hours: Thursday 3-5 in 219 Gilman

whaley@berkeley

Office Hours: Monday 11:30-12:30 / Tuesday 9-10 / Wednesday 12-2 in 418 Hearst Mining Bld.

janiko@berkeley

- Homework 1 [pdf, ps] due Thursday 9/15

*Note*: Some of you may find this problem set easy, but some may find it quite challenging.*Do not hesitate*to contact Jan if you need help. You are encouraged to come to office hours and section, or send an e-mail if you would like to set up a meeting time outside of office hours.

- Homework 2 [pdf,
ps] due Thursday 9/22

Feedback [pdf, ps] for homework 2

- Homework 3 [pdf,
ps] due Thursday 9/29

- Homework 4 [pdf,
ps] due Thursday 10/6

Feedback [pdf, ps]

- Homework 5 [pdf,
ps] due Thursday 10/13

Feedback [pdf, ps]

- Homework 6 [pdf,
ps] due Thursday 10/20

Feedback [pdf, ps]

- Homework 7 [pdf,
ps] due
*Tuesday*11/1

- November will be spent working on the term project. Information about the project is here.

Date | Topic |
Notes | Date updated | |

1 | 8/30 | Quantum States, Superposition | [pdf,ps] | 09/06 |

2 | 9/01 | Qubits, Measurements, Notation | [pdf,ps] | 09/13 3:47pm |

3 | 9/06 | Unitaries/Gates, Multiqubit and Bell States | [pdf,ps] | 09/08 |

4 | 9/08 | 2 Qubit gates, EPR, Bell inequalities | [pdf,ps] | 09/14 |

5 | 9/13 | Entanglement can facilitate information processing | [pdf,ps] | 09/14 |

6 | 9/15 | No-Cloning, Teleportation | [pdf,ps] | 09/17 |

7 | 9/20 | Superdense Coding, Quantum Cryptography | [pdf,ps] | 09/27 |

8 | 9/22 | Quantum Gates and Universality | [pdf,ps] | 09/25 |

9 | 9/27 | Solovay-Kitaev, Complexity, Reversible Computing | [pdf] | 10/10 |

10 | 9/29 | Circuits, Randomized computation, Deferred measurements | [pdf] | 10/03 |

11 | 10/04 | Quantum Mechanics in a Nutshell I | [pdf,ps] | 10/04 |

12 | 10/06 | Quantum Mechanics in a Nutshell II | [pdf,ps] | 10/08 |

13 | 10/11 | Uncertainty principle, Spin algebra | [pdf,ps] | 10/12 |

14 | 10/13 | Spin operators, spin measurement, spin initialization | [pdf,ps] | 10/18 |

15 | 10/18 | The Hamiltonian with spin, spin manipulation I (precession) | [pdf,ps] | 10/20 |

16 | 10/20 | Spin manipulation II (resonance), quantum gates for spins |
[pdf] | 10/25 |

17 | 10/25 | Deutsch and Deutsch-Jozsa algorithms | [pdf,ps] | 10/25 |

18 | 10/27 | Quantum Fourier Transform |
[pdf,ps] see also: [pdf] | 10/28 |

19 | 11/01 | Shor's order (period) finding algorithm and factoring | [pdf, ps] | 11/11 |

00 | 11/03 |
Midterm Quiz
| ||

20 | 11/08 | Quantum phase estimation, eigenvalue calculations | [pdf,ps] | 11/25 |

21 | 11/10 | Grover's quantum search algorithm | [pdf,ps] | 11/16 |

22 | 11/15 | Amplitude amplification, quantum bomb detection | [pdf,ps] | 11/19 |

23 | 11/17 | Quantum random walks, Error correction |
[pdf] see also: [pdf] | 11/17 |

24 | 11/22 | Guest lecture: Si quantum computation | [pdf] | 12/01 |

00 | 11/24 |
Thanksgiving - no lecture
| ||

25 | 11/29 | Guest lecture: Ion trap quantum computation | [pdf] | 12/02 |

00 | 12/01 |
Student presentations
| [webpage] | 12/07 |

26 | 12/06 | Guest lecture: Neutral atom quantum computation | [pdf] | 01/09/2006 |

27 | 12/06 | Lecture: The measurement problem, when has a quantum system been measured | [pdf] | 01/09/2006 |

**9/13:**The figure of the Bloch sphere in the lecture notes from 9/1 has now been updated with a corrected version which does not interchange the x- and y-axes.**9/14:**Added notes about Bell's inequalities from Hideo Mabuchi's course at Caltech to lecture notes for 9/8**9.25:**Pdf version of lecture 8 updated to add more figures and correct some typos (ps not updated).**9/27:**1 qubit operations for messsages 01 and 10 were exchanged in Superdense coding section of lecture 7. A couple of other typos fixed. Changes to pages 1, 2, 4.**10/6:**The section on reversible computing in lecture 9 has been substantially modified to try to clear up some confusing points. Please let us know if some things in that section still require more careful explanation.**10/8:**Lecture 11 introduction has uncertainty principle removed from list, appears in Lecture 12, p. 1 of lecture 11 otherwise unchanged. Lecture 9 will be revised once more - check the web page in a couple of days...**10/9:**A typo has been corrected in the expression for the energy valies on the middle of p. 7 of lecture 12 (a factor of l^2 was missing in the denominator of the final expression).**10/10:**Updated version of lecture 9 posted, various significant changes to section on reversible computing.**10/25:**Typo in equation with rotating wave approximation on page 3 of lecture 16 corrected. Exponent on right-hand side of first equal sign had i*omega_0*t, corrected to 2*i*omega_0*t.**10/28:**Some small rewording and punctuation changes on pp. 1, 3, 4. Added note about unitary nature of QFT, on new p. 5.

Below are some handouts given out in the Wednesday sections, most of them worksheets with questions designed to (hopefully) increase your understanding of some key concepts of the course and of quantum mechanics in general. Most of them were designed specifically to be used for plenary discussion in section, so if you read them on your own for the first time, you may find them somewhat vague or difficult but hopefully still helpful. Don't hesitate to contact Jan with questions if you want to make sure you are getting the full picture.

**9/7:**Handout from first section. Contains some practical information about the sections, and then some discussion questions to get you started thinking about some basic questions in quantum mechanics and quantum information.**9/21:**State vectors and measurement bases. Discussion questions about the connection between state space bases and measurements, basis changes and change of measurement setup, and what the difference between the quantum and the classical situation really is.**9/28:**Why unitary operators? Discussion questions about the role that unitary operators play in quantum mechanics, and why it is important that they be unitary.**10/5:**Measurements and entanglement. Some problems that illuminate the connection between measurement and entanglement, why entanglement with an ancilla or other "external" system can destroy intereference, and perhaps some hints about what measurements really are.**10/19:**Spin and generators of rotations. Questions that explore what happens to the state of a quantum system when you rotate it, how the operators that effect the rotation are tied to angular momentum, with the goal of trying to understand what intrinsic spin is.

**EPR paper:**Phys. Rev. 47 (1935), 777**Mernin's article on EPR paradox:**Physics Today vol. 38, pp. 38-47 (interesting reply letters on pp. 9-15 and 136-142)- Benenti/Casati/Strini, chapter 2.5
- Styer, chapter 6 + references at end of chapter

- 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 Quantum Computation: link
- Basic intro to topics in physics at the University of Colorado. Click on the link "Science Trek" on the main page: link

**Recommended text for the class:**

- Benenti, Casati, and Strini,
__Principles of Quantum Computation and Information__

An excellent concise introduction to the subject.

**Recommended alternative text:**

- Stolze and Suter,
__Quantum Computing: A short course from theory to experiment__

Also good introduction, more experimental details than Benenti et al.

**Other texts for quantum computation**

- Nielsen and Chuang,
__Quantum Computation and Quantum Information__

An encyclopedic reference.

- Pittenger, Arthur O.
__An introduction to Quantum Computing Algorithms__

Elementary introduction to algorithms. - Lo, Popescu and Spiller,
__Introduction to Quantum Computation and Information__

Introductory review chapters to basic concepts and tools. - Kitaev, Shen and Vyalyi,
__Classical and Quantum Computation__

Thorough treatment.

**Mathematical background**

- 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 structure.

**On quantum mechanics in general**

- Styer, Daniel F.
__The Strange World of Quantum Mechanics__

Very basic introductory book to quantum mechanics - 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 everything. - 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 physics. - Feynman, Richard.
__QED__

Nice leisure reading.