UNM Physics 452/581: Introduction to Quantum Information 
Announcements and updates 
Mon Dec 17  Congratulations to the entire class for a job well done. We covered a wide range of challenging material in a short time, and everyone did well on the problem sets and Wikipedia projects. I encourage each of you to copy your Wikipedia articles from our local server to the global Wikipediait would be a great service to the community. Once there, be aware that it may be ruthlessly edited. That said, Wikipedia is in desparate need of your content, and it would be valued greatly. Have a great holiday! 
Sat Nov 24  Minor corrections to Problem set 6: corrected spelling of tintinnabulation, changed problems to start with "6," not "5," normalized Kraus operators in Extra Credit problem 6.7(a), and dropped superfluous "p" subscripts in Kraus operators of problem 6.5(e). 
M Nov 12  Problem set 6 is now available. It has five problems and two extra credit problems, but I'm giving you all over two weeks to finish itit's due the Tuesday after Thanksgiving. Also, here is a link to the directions for the Wikipedia project that I emailed to the class. Please submit your proposals for a wiki article to me by this Thursday. 
Tu Oct 9  Problem set 5 is due Thursday, Oct. 18; I had originally listed the nonexistent date of Thursday, Oct. 16; even though the set only has two problems, there is Fall break in between so that you should still have a full week of nonholiday time to work on it. Remember: No class next Thursday or Tuesday. 
W Oct 3  Extension: Problem set 4 will be due Tuesday, Oct. 9 instead of Thursday, Oct. 4. That should also get us back on track; had I given a weeklong problem set this Thursday, it could not be due the following Thursday because that is a UNM Holiday. 
W Oct 3  Students seem to having particular difficulty with problem 4.2(b). I've added a further hint to the problem that reminds that it is the worstcase input that is relevant when calculating the complexity of the algorithm. 
M Oct 1  Another minor update to Problem set 4: the hint for problem 4.3(e) should state that the trace of a matrix times a Pauli operator yields 2^n times the corresponding Pauli coefficent of the matrix. 
M Oct 1  Minor update to Problem set 4: the base of the logarithm in problem 4.2(c) should be k, not 2. 
W Sep 26  I've posted Problem set 4 and I've extended its deadline to next Thursday instead of next Tuesday. 
M Sep 17 
The material we've been discussing lately hasn't really lended itself to a
good problem set, so I'm going to skip handing out a problem set for this
week. As I said on the first day of classes, I plan on handing out problem
sets roughly weekly, but I'm not a slave to that.
That of course gives at least two options for how to handle the assignment due on Tuesday (tomorrow). The first is to make it still be due tomorrow so that the remainder of the week nobody has to think about an IQI problem set. The other is to have the problem set be due the following Tuesday (9/25), giving students more time to work on the problems and polish their answers. Given that a number of students have expressed some difficulty with this problem set, I've decided to take the latter course. I'd much rather have the class understand a few problems well than many problems hardly at all. So please, if you have questions about this problem set in the upcoming week, I encourage you to stop by my office hours or send an email requesting a meeting at another time. 
M Sep 17  For problem 3.1(d), the angle should be 2*pi/3, not pi/3. You'll get full credit if you work out either angle, but the 2*pi/3 angle is much easier to work with and has a simpler geometric interpretation. I also added hints to problems 3.1(a) and 3.2(b), for those of you needing a jumpstart. 
W Sep 12  I've added the third problem to Problem set 3; there will be no extra credit problem this week. 
W Sep 12  Problem set 3 has now been posted; the third problem and extra credit problem still need to be added, but the current problems should keep you busy until then. 
Sat Sep 8  Typedup lecture notes for lecture 6 are now available. 
F Sep 7  Extra credit problem 2.4: Bob doesn't have to reverse his "reveal" strategy relative to Alice's as originally indicated; PS 2 amended to indicate this. 
Th Sep 6  Problem 2.3(c) should evaluate to 80.18%; I added an extra credit problem describing an even better strategy that achieves the optimal 85.35% success rate for the game. 
W Sep 5  Minor typeos have been fixed in problems 2.2(e) and 2.2(g), notation has been clarified for 2.2(g) and 2.2(i). I have also made clearer what is being asked for problems 2.2(d) and 2.3(a). 
W Sep 5  I have posted scannedin versions of my notes from lectures 3 to 5. They are really rough (esp. lecture 4); I hope to get them typed up soon. 
W Sep 5  Problem set 2 has now been posted. I generally won't use this announcement section to indicate that a problem set has been posted; please just check the course calendar section at the bottom of the web page shortly after a previous problem set has been handed in and a new problem set should appear. 
F Aug 31  Problem set 1 has been reposted again, with yet further clarifications, corrected problem numbers, and a new set of probability values to use for problem 1.2. These are the numbers I meant to use, but constant cuttingandpasting caused me to flipflop some of them. Sorry for the bugs in this first problem set! Future assignments should be more stable. 
Th Aug 30  I've simplified and clarified the first problem set. I removed problem 1.1(c)(iii)I had meant to put k(i + j) not k+(ij). I also added a hint for problem 1.1(b) and clarified what I am asking for in 1.2(ce). 
M Aug 27  I added links to my notes for lectures 1 and 2 in the calendar section at the bottom of the course website. The lecture 1 notes are 10 typedup pages. I haven't had time to type up the second lecture's notes, so I just scanned in my handwritten notes from the lecture. I wanted to put these here because some of what I covered in lecture, notably how to represent the measurement process classically using pbits and Bayes' rule, is not discussed in any of the reference material for this course. 
Th Aug 23  I added Brad's office hours and removed the defunct links to the first problem set to remove any confusion. The link will appear once the set is available. In addition to recommending Chapter 1 of Nielsen & Chuang as a supplement to the first couple of lectures, I added a link to the first in a series of lecture notes by Dave Bacon that covers some of the same material I covered in class. In lecture, I went into much greater detail about Bayes' Rule and pbit measurements, and I plan to post lecture notes on that soon. 
W Aug 1  Course credit info (3) and TA info (Brad Chase) has now been added below. 
M Apr 30  The course website is under development. If you have questions about the course, please send me email and I'll do my best to answer. In the meanwhile, here is an advertisement for the course. 
Course descriptionThis course surveys four major areas of quantum information: algorithms, error correction, communication, and cryptography. Students taking this course will learn how quantum computers can solve problems and crack cryptosystems beyond the reach of classical computers, how noise and decoherence afflicting quantum systems can be reversed with better quantum "software" rather than better quantum hardware, how quantum data can be supercompressed and teleported from one place to another, and how secrets can be protected by the laws of quantum physics rather than the assumed computational difficulty of certain mathematical problems. Linear algebra preparation at the level of Math 314 or Math 321 is required. Prior knowledge of quantum theory is not necessary. Emphasis will be on developing understanding through examples and problem solving. Students taking this course for graduate credit will be expected to solve additional problems and create a Wikipedia article on a quantum information subdiscipline to be presented in class. 
General course information 
Course Credits: 3 
Instructor
Dr. Andrew
Landahl (alandahl@unm.edu) 
Teaching Assistant
Brad Chase 
Class schedule 
Physics 452/581: T,Th 1112:15, P&A 184 
TA Office Hrs.: W, 23 
Prerequisites and corequisitesPrerequisite: Linear algebra at the level of Math 314 or Math 321. 
Grading
Undergraduates: Problem sets (100%), Wikipedia article (10%),
Inclass presentation (10%). (Hence, article & presentation are extra
credit.) 
Problem setsHanded out Tuesdays, due the following Tuesday by 5 p.m. If not turned in during class, use handin box labeled "Landahl 452" in Physics and Astronomy main office. Graduate students must do additional indepth problems on some assignments. Lowest problem set grade dropped; late problem sets not accepted. Each student will be issued a unique "Introduction to Quantum Information (IQI)" number. Keep your IQI number private! You may sign all work by IQI number if you so desire. Homework will be returned in class. Collaboration is fine, indeed encouraged, but you must put significant effort into problems before collaboration and you must write up solutions in your own words. Address all grading issues first with the TA and then with me if they are unresolved. 
Wikipedia article and presentationGraduate students enrolling in the course for credit must create or substantially contribute to a Wikipedia article on a subdiscipline of quantum information. Additionally, a multimedia inclass presentation on the article must be given. Undergraduate students may also undertake this assignment for extra credit. 
Lecture notesI will be posting regular lecture notes to this website. They will be organized somewhat differently than the textbook we are using and may not go into as much depth as the textbook as this is an undergraduate survey course. When possible, I will list on this website which sections in Nielsen & Chuang (NC) a given week's lecture material corresponds to. The optional books and online resources listed above delve more deeply into some of the subjects covered in the required textbook. 
AccessibilityStudents with special needs should coordinate through Accessibility Services in Mesa Vista Hall (2773506). 
Exam scheduleThere are no exams for this course. (Woo hoo!) 
Syllabus (tentative) 
Mathematics of quantum information
Vectors: Dirac notation, outer product, inner product (NC 2.1)

Quantum algorithms
Quantum gates, circuits, universality (NC 4.2, 4.4, 4.5)

Quantum error correction
Density matrix, quantum operation, POVM, fidelity (NC 2.4, 8.2, 8.3,
2.2.6, 9)

Quantum communication
Teleportation, superdense coding, nocloning (NC 1.3.7, 2.3, 1.3.5,
box 12.1)

Quantum cryptography
Key distribution (NC 12.6)

Lectures and Problem sets 
Tu Aug 21  Course overview; bits and gates; pbits and pgates  (Landahl 1;
NC 1.1; Bacon
1.II; Preskill
Ch. 1) 
Th Aug 23  Pbit measurement: Bayes rule; sqrt(NOT) by beamsplitters; complex numbers; qubits and (qu)gates  (Landahl 2;NC 1.2, 1.3; Bacon
1.III) 
Tu Aug 28  Gate unitarity, Born rule, Dirac notation  (Landahl 3;
NC 2.1, 2.2; Bacon
1.III, Bacon
2) Problem Set 1 Solution Set 1 
Th Aug 30  Dirac notation examples, linear algebra, spin as a physical qubit  (Landahl 4; NC 2.1, 2.2; Bacon 2, 3.I; Preskill 2.2) 
Tu Sep 4  Bloch sphere, Deutsch's Algorithm  (Landahl 5; NC 1.2, 1.3, 4.2, 1.4.3;
Bacon 2,
3.II.A;
Preskill 6.3) Problem Set 2 Solution Set 2 
Th Sep 6  Examples of query complexity problems  (Landahl 6; NC 1.4.3, 1.4.4, 6.1, 5.4.3; Bacon 3.II.A, 6.II, 7, 8) 
Tu Sep 11  Simon's problem; BigO notation; query models & kinds of query algorithms  (Landahl 7)
Problem Set 3
Solution Set 3 
Th Sep 13  Query complexity results; Deutsch's algorithm walkthrough  (Landahl 8) 
Tu Sep 18  Analog vs. Digital computation; linear scaling of gate errors; universal gate bases  (Landahl 9) 
W Sep 19  Repetition code; reversible encoding; nocloning theorem; observables  (Landahl 10) 
Th Sep 20  Quantum compiling: the SolovayKitaev Theorem and the SolovayKitaev algorithm  (Landahl 11; DawsonNielsen) 
M Sep 24  Observables for error correction; circuits for quantum bit flip code and phase flip code  (Landahl 12) 
Tu Sep 25  GottesmanKnill Theorem; Magic states; Grover's algorithm: algebraic analysis  (Landahl 13)
Problem Set 4 Solution Set 4 
Th Sep 27  Grover's algorithm: geometric analysis; reduction of factoring to orderfinding  (Landahl 14) 
Tu Oct 2  Orderfinding as a query problem; reduction of orderfinding to the quantum Fourier transform (QFT), modular exponentiation, and the continuedfraction algorithm; discrete and quantum Fourier transform; product representation and quantum circuit for QFT  (Landahl 15) 
Th Oct 4  Continuous fraction algorithm; modular exponentiation; factoring overview; quantum algorithms not (obviously) based on Grover/QFT: ordered search, element distinctness, NAND trees, welded binary trees  (Landahl 16) 
Tu Oct 9  Shor code; Schmidt decomposition  (Landahl 17)
Problem Set 5 Solution Set 5 
Th Oct 11  UNM Holiday  Fall Break 
Tu Oct 16  Class cancelled: made up in Lecture 10 
Th Oct 18  Class cancelled: made up in Lecture 12 
Tu Oct 23  Class cancelled 
Th Oct 25  Schmidt decomposition; density matrices  (Landahl 18) 
Tu Oct 30  Quantum operations  (Landahl 19) 
Th Nov 1  Examples of quantum channels  (Landahl 20) 
Tu Nov 6  POVMs; distance measures for quantum states  (Landahl 21) 
Th Nov 8  Unambiguous state discrimination; distance measures for quantum states; quantum error correcting criteria  (Landahl 22) 
Tu Nov 13  Quantum State Discrimination; QEC Criteria; degenerate vs. nondegenerate codes  (Landahl 23)
Problem Set 6 Solution Set 6 
Th Nov 15  Located errors; error detection; QEC critera proof; linearity of QEC; bounds on QEC parameters  (Landahl 24) 
Tu Nov 20  Pauli group; stabilizer coding theory  (Landahl 25) 
Th Nov 22  UNM Holiday  Thanksgiving 
Tu Nov 27  Stabilizer codes: syndrome & recovery; examples of stabilizer codes  (Landahl 26) 
Th Nov 29  Quantum Key Distribution  (Landahl 27) 
Tu Dec 4  Quantum Communication  (Landahl 28) 
Th Dec 6  WIKIPEDIA PROJECT PRESENTATIONS 
Tu Dec 11  WIKIPEDIA PROJECT PRESENTATIONS 12:302:30 p.m. 
Th Dec 13  No class  Final exam week 
Material on this site is subject to revision. Last updated: Nov. 12, 2007.