C/CS/Phys191: Qubits, Quantum Mechanics and Computers - Fall 2005

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

The course now has a newsgroup, at ucb.class.cs191. If you have a newsreader linked to your web browser, you may be able to access it by clicking this link. If not, or if you are trying to access the newsgroup from outside the UCB network, go to this page and click on the link "How Do I Access Newsgroups?" for instructions.

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


  • CS191 made the national news last spring! The Wall Street Journal had this to say about quantum computing.
  • Lecture notes, problem sets and solutions will be posted on this webpage weekly.
  • 9/1: We have added a link under the "Useful links" section to a nice page at the University of Colorado with some very basic introductory information about various topics in Physics, e.g. quantum physics and polarization.
  • 9/1: Added reference to Styer's introductory quantum mechanics book under "Recommended reading"
  • 9/6: First homework has been posted. Remember, office hours are there to be used, as is Jan's e-mail address...
  • 9/7: Jan's Thursday office hour has been moved to Monday 11:30-12:30 to avoid overlap with prof. Whaley's office hours.
  • 9/8: References to material about EPR paradox and Bell's inequalities have been added under the "References" section, below the lecture notes.
  • 9/13: We have corrected some typos in the lecture notes from the first week, there may still be many more left. If you see anything suspicious in the notes, or if you cannot get what the notes are saying to rhyme with your own calculations, then e-mail us and ask. There is a very much non-zero probability that the problem is not your calculations...
  • 9/13: NB! On the illustration of the Bloch sphere in versions of the 9/1 lecture notes from before 9/13 at 3:45pm, the x- and y-axes have been mixed up. This can cause strange results on the homework, so be careful. The phi-coordinate should be the coordinate relative to the x-axis, not the y-axis. We have now updated the lecture notes with a corrected figure taken from Nielsen/Chuang p. 15, but the axis labels may be a little hard to read. You can also find illustrations of the Bloch sphere on p. 103 of Benenti/Casati/Strini.
  • 9/21: The first homework set will be given back in class on Thursday 9/22, or can be picked up from a box outside Jan's office in 418 Hearst Mining from Friday 9/23. Some important information about homework submissions and grading procedures has also been posted, please read!
  • 9/25: Professor Whaley's office hours changed to start at 3 pm on Thursdays.
  • 9/27: Homework 2 has been graded and will be handed back in class today. Afterwards it can be picked up from the box outside 418 Hearst Mining Bldg. There is also important feedback for everyone, please read! (may be important for some of the problems on this week's problem set!). Solutions for homework 1 have also been posted.
  • 9/28: Some typos in homework 4 have been corrected (a subscript in problem 4 and a normalization constant in problem 3b), and some explanatory words have been added to explain the notation in problem 4. Please download the new version of homework 4 if you have a version from before 2pm on Wed 9/28.
  • 10/18: The wording on question 1b of problem set 6 has been altered slightly to reduce ambiguity. When the problem says "copy the output" into the ancilla qubit, what it means is only to copy the output of the second qubit (and note that you will need a slightly lax definition of copying here, since you clearly cannot copy the complete state of the second qubit in this case, so be content with something that is just capable of copying basis states, as in 1a).
  • 10/20: The handouts with discussion questions that have been given out some weeks in the discussion sections have now been posted online. You can find them on this page just below the lecture notes. Contact Jan if you have any questions about them, since they have been designed for use in section and may seem a little vague at first if you see them for the first time and try to work through them alone.
  • 10/20: The midterm (or 2/3-term if you like) is scheduled for Thursday 11/3, in class 12:40-2:00pm. The section on Wed 11/2 and possibly also 10/26 will be dedicated to reviewing anything you want to have reviewed before the midterm, so talk to or e-mail Jan with any questions or topics that you want me to go over.
  • 10/21: Feedback for homework set 5 has been posted. There were some subtleties with question 3 on this homework that you may want to read about.
  • 10/25: The last homework set (#7) has been posted. Note that this set is due already on Tuesday November 1, not Thursday 11/3.
  • 10/30: Important: typo in homework 7 question 4! There was a typo in the last part of question 4 on homework 7. The definition of omega was missing a factor of 1/n in the exponent. The homework has now been updated, please download it again if you have a version that was downloaded before 2pm on Sunday 10/30.
  • 10/31: Yet another typo in homework 7, this time on question 3. In the second paragraph, the explanatory statement about the "cryptic subscript" on the summation sign is misplaced, it is supposed to refer to the summation in the first paragraph. The homework has been updated once again, please download one more time if you have a version from before 10:15am on Monday 10/31.
  • 10/31: ...and another one!. Yet another typo in question 4 on homework 7. The offset +l in the last part of the problem is actually supposed to be -l. Update posted at 3:45pm on Monday 10/31, download the homework yet again if you have a version older than this.
  • 11/1: Guidelines for the term project have been posted.
  • 11/9: The newsgroup for the class is ucb.class.cs191. Instructions on how to access it can be found on the top of this webpage. As well as general discussion, the newsgroup can be used to set up groups for the term project, so if you still need partners for a project group, put a posting on the newsgroup indicating what topics you might be interested in working on and how many people you still need.
  • 11/9: The midterm has been graded and will be handed back in class on Thursday 11/10. After that it will be put in the homework return box outside Jan's office in Hearst Mining Building. The grade is a numerical score (like for the homeworks), no letter grade. The total number of points on the test was 38, the average score was 33.1 and the median score was 34, with a standard deviation of 5.0 points.
  • 11/17: A list of term project groups and topics has been posted. Please check and e-mail us ASAP if there are any errors.
  • 11/17: Sections for the last three weeks (11/23, 11/30 and 12/7) have been converted to office hours on Wednesdays from 12-2. E-mail Jan if you want to meet sometime outside this or the original Monday or Tuesday office hours.
  • 11/27: The schedule for the project presentations has now been posted. Please review it and let us know immediately if any changes are necessary. The schedule page also contains important practical information, so do read the whole page!
  • 12/7: The project presentation slides that we have received so far have now been posted on this page. We have so far received slides from 6 of the 10 groups. Please submit the rest as soon as you can, and let us know if there are any issues.
  • 1/9/2006: The notes for the last two lectures and all the project reports have now been posted. Barring any errors, this should be the final update of this page for Fall 2005. Thank you for a great semester!


    Birgitta Whaley
    Lectures: Tuesday/Thursday 12:30-2 in 180 Tan
    Office hours: Thursday 3-5 in 219 Gilman

    Teaching Assistant

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


    Please read: Important information about homework and grading

    Lecture notes

    Below are lecture notes covering material for the whole semester. They will be modified as the semester progresses to reflect the material taught in the lectures and to make improvements, and topics and content may be moved around and reordered, so keep checking for updates! The dates in the left column lists the date at which a lecture was given, and the date in the rightmost column gives the date during Fall 2005 at which a set of notes was last updated. If no date is given on the lefthand side, it means that that lecture has not yet been given this semester. If no update date is listed on the righthand side, it means that the notes have not been updated yet this semester, and are unmodified notes from earlier semesters.

    Date Topic NotesDate updated
    18/30 Quantum States, Superposition [pdf,ps] 09/06
    29/01 Qubits, Measurements, Notation [pdf,ps] 09/13 3:47pm
    39/06 Unitaries/Gates, Multiqubit and Bell States [pdf,ps] 09/08
    49/08 2 Qubit gates, EPR, Bell inequalities [pdf,ps] 09/14
    59/13 Entanglement can facilitate information processing [pdf,ps] 09/14
    69/15 No-Cloning, Teleportation [pdf,ps] 09/17
    79/20 Superdense Coding, Quantum Cryptography [pdf,ps] 09/27
    89/22 Quantum Gates and Universality [pdf,ps] 09/25
    99/27 Solovay-Kitaev, Complexity, Reversible Computing [pdf] 10/10
    109/29 Circuits, Randomized computation, Deferred measurements [pdf] 10/03
    1110/04 Quantum Mechanics in a Nutshell I [pdf,ps] 10/04
    1210/06 Quantum Mechanics in a Nutshell II [pdf,ps] 10/08
    1310/11 Uncertainty principle, Spin algebra [pdf,ps] 10/12
    1410/13 Spin operators, spin measurement, spin initialization [pdf,ps] 10/18
    1510/18 The Hamiltonian with spin, spin manipulation I (precession) [pdf,ps] 10/20
    1610/20 Spin manipulation II (resonance), quantum gates for spins [pdf]
    1710/25 Deutsch and Deutsch-Jozsa algorithms [pdf,ps] 10/25
    1810/27 Quantum Fourier Transform [pdf,ps]
    see also: [pdf]
    1911/01 Shor's order (period) finding algorithm and factoring [pdf, ps] 11/11
    0011/03 Midterm Quiz  
    2011/08 Quantum phase estimation, eigenvalue calculations [pdf,ps] 11/25
    2111/10 Grover's quantum search algorithm [pdf,ps] 11/16
    2211/15 Amplitude amplification, quantum bomb detection [pdf,ps] 11/19
    2311/17 Quantum random walks, Error correction [pdf]
    see also: [pdf]
    2411/22 Guest lecture: Si quantum computation [pdf] 12/01
    0011/24 Thanksgiving - no lecture
    2511/29 Guest lecture: Ion trap quantum computation [pdf] 12/02
    0012/01 Student presentations [webpage]12/07
    2612/06 Guest lecture: Neutral atom quantum computation [pdf] 01/09/2006
    2712/06 Lecture: The measurement problem, when has a quantum system been measured [pdf] 01/09/2006


    Below are changes made to the lecture notes on or after the afternoon of September 13:

    Handouts from section

    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.


    References listing only authors and chapters or page numbers refer to books listed in the "Recommended reading" section.

    EPR paradox and Bell's inequalities (9/8, under construction)

    Below are references about entanglement, the EPR paradox and Bell's inequalities mentioned in class on Sept. 8. Only some are available electronically, and those may require you to use a computer on the UCB network (or the library proxy service) to work. We may post scans and downloaded pdf's if we manage to sort out the copyright issues.

    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 texts listed below.

    Recommended text for the class:

    Recommended alternative text:

    Other texts for quantum computation

    Mathematical background

    On quantum mechanics in general