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
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
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
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
9/1: Added reference to Styer's introductory quantum mechanics book under
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
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
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
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
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
10/25: The last homework set (#7) has been posted. Note that this
set is due already on Tuesday November 1, not
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: ...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
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!
Lectures: Tuesday/Thursday 12:30-2 in 180 Tan
Office hours: Thursday 3-5 in 219 Gilman
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
- 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
- Homework 7 [pdf,
ps] due Tuesday 11/1
- November will be spent working on the term project. Information
about the project is here.
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.
Quantum States, Superposition
Qubits, Measurements, Notation
Unitaries/Gates, Multiqubit and Bell States
2 Qubit gates, EPR, Bell inequalities
Entanglement can facilitate information processing
Superdense Coding, Quantum Cryptography
Quantum Gates and Universality||
Solovay-Kitaev, Complexity, Reversible Computing
Circuits, Randomized computation, Deferred measurements
Quantum Mechanics in a Nutshell I
Quantum Mechanics in a Nutshell II
Uncertainty principle, Spin algebra
Spin operators, spin measurement, spin initialization
The Hamiltonian with spin, spin manipulation I (precession)
Spin manipulation II (resonance), quantum gates for spins
Deutsch and Deutsch-Jozsa algorithms
Quantum Fourier Transform
see also: [pdf]
Shor's order (period) finding algorithm and factoring
Quantum phase estimation, eigenvalue calculations
Grover's quantum search algorithm
Amplitude amplification, quantum bomb detection
Quantum random walks, Error correction
see also: [pdf]
Guest lecture: Si quantum computation
Thanksgiving - no lecture
Guest lecture: Ion trap quantum computation
Guest lecture: Neutral atom quantum computation
Lecture: The measurement problem, when has a quantum system been measured
Below are changes made to the lecture notes on or after the afternoon
of September 13:
- 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
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.
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.
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
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.
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.
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.
- 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
- Basic intro to topics in physics at the University of Colorado. Click on
the link "Science Trek" on the main page:
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:
- Benenti, Casati, and Strini, Principles of Quantum Computation and
An excellent concise introduction to the subject.
Recommended alternative text:
- Stolze and Suter, Quantum Computing: A short course from theory to
Also good introduction, more experimental details than
Benenti et al.
Other texts for quantum computation
- Nielsen and Chuang, Quantum Computation and Quantum
An encyclopedic reference.
- Pittenger, Arthur O. An introduction to Quantum Computing
Elementary 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
- 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
- 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.