C/CS/Phys191: Qubits, Quantum Mechanics and Computers - Fall 2009

The webpage from Fall semester 2008 can be found here

Instructor

Birgitta Whaley
Lectures: Tuesday/Thursday 12:30-2 in 70 Evans Hall
Office hours: M, F 1.30-2.30 in 219 Gilman
whaley@berkeley

Teaching Assistant (part time)


Dylan Gorman
Office hour: Thursday 11-12 in 410 Hearst Mining Building
dgorman@berkeley.edu

Announcements

  • Lecture notes, problem sets and solutions will be posted on this webpage weekly.
  • 8/29 Next week my Friday office hour will be replaced by an hour on Wednesday afternoon, time to be scheduled in class on Tuesday.
  • 9/02 Discussion this week will be on Thursday 5-6 pm in 410 HMB, thereafter on Tuesdays 5-6 pm in 410 HMB unless otherwise updated.
  • 9/03 ROOM CHANGE! Starting next Tuesday, Sep 8, class will meet in 70 Evans Hall
  • NEW DISCUSSION ROOM! Effective 9/15, discussion will be held in B56 Hildebrand. The time is, as always, 5-6pm.
  • Homework box: Homework should now be dropped off in the "Physics 191" homework box in 251 LeConte, the Physics Department reading room. The previous solution was unsustainable.
  • Homework 2 due date has been extended to Monday Sep 21.
  • Reminder: the midterm will be held on Tuesday Oct 20, in class.
  • 10/08 Homework 5 was posted on Monday Oct 5 but apparently did not show up on the web page, apologies. I have extended the due date to Thursday Oct 15 (a week from today).
  • 10/13 Lecture 13 will be completed later today (first half is posted). Dylan will give a review for the midterm in Discussion today.
  • 10/13 Homework 5 due date has been moved to Friday, Oct 16.
  • 10/13 Problem Set 6 will be due Mon Oct 26 (the Monday after the midterm), and will be posted on Friday, Oct 16.
  • 10/13 Lecture 13 now updated.
  • 10/14 A second midterm review session will be held Friday, 4:30-6:30 in 410 Hearst Mining Building.
  • 10/25 Project Guidelines have been posted below the lecture list.
  • 10/28 new results addition to project guidelines!
  • 11/04 Project presentations will be held in class on Tues Dec 1 and Thurs Dec 3. Pizza will be provided.
  • 11/04 Term papers should be typed and of length not less than 10 pages single spaced and not more than 20 pages single spaced.
  • 11/10 Midterm solutions posted.
  • 11/23 Term paper groups, topics and presentation schedule posted. Please let me know if you have a problem with the schedule. All students will be required to attend all presentations.

    Homework

    Homework is due on the date specified for each set below, at 5 pm in the drop box labeled Physics 191, in 251 LeConte Hall.

    Lecture notes

    Date Topic Notes
    18/27 Introduction, Quantum States [pdf]
    29/01 Basic Principles of QM, Qubits [pdf]
    39/03 Measurements, Multiple Qubits [pdf]
    49/8 Physical Qubits, EPR [pdf]
    59/10 Teleportation [pdf]
    69/15 Superdense Coding, No Cloning [pdf]
    79/17 Quantum Cryptography [pdf]
    89/22 Unitaries and Quantum Gates [pdf]
    99/24 Universality, Solovay-Kitaev, Complexity [pdf]
    109/29 Reversible Computing, Randomized Computation, Deferred Measurements [pdf]
    1110/01 Deutsch and Deutsch-Josza algorithms [pdf]
    1210/06 Quantum Mechanics in a Nutshell [pdf]
    1310/08 Mixed States and Density Matrix, Entanglement measures [pdf]
    14,1510/13,10/15 Quantum Computing With Physical Spins [pdf]
    1610/20 Midterm
    1710/22 Wiring Up Trapped Ions [pdf]
    1810/27 Quantum Fourier Transform [pdf]
    see also: [pdf]
    1910/29 Quantum phase estimation, finding eigenvalues [pdf]
    2011/03 Shor's order (period) finding algorithm and factoring [pdf]
    2111/05 Grover's Quantum Search Algorithm [pdf]
    2211/10 Amplitude Amplification, Quantum Zeno, Vaidman's bomb [pdf]
    2311/12 Introduction to Quantum Error Correction [pdf]
    2411/17 Quantum Computer Architectures in Silicon and Diamond [pdf]

    Project Guidelines


  • Term Project list will be posted here as you choose projects. [pdf] You should work in teams of 2-3. We encourage cross-disciplinary teams, since ideally a project should address both CS and Physics aspects of the question being studied. At the end of the semester each team will submit a project report, as well as give a 15-20 minute oral presentation.

    Here are a few suggestions of broad topics for projects. You should feel free to suggest any additional topic that you are interested in. All topics will require approval of the instructor and you are encouraged to discuss your choice with Prof. Whaley and/or Dylan. When you are ready, please email us the composition of your team, the topic, and a brief description.

    quant-ph refers to the Los Alamos archives: link

  • Cluster state computation - an alternative paradigm to the circuit model.
  • Topological quantum computation - the promise of natural fault tolerance.
  • Adiabatic quantum algorithms - this provides an alternate paradigm for the design of quantum algorithms. A number of papers explore this subject: paper1.pdf paper2.pdf paper3.pdf
  • Kitaev's phase estimation algorithm has a number of applications. It gives an example of a quantum speedup without entanglement. And a recent paper claims that it leads to a significant speedup in solving classical differential equations: paper.pdf paper.pdf
  • Quantum Error-correcting codes (see quant-ph/0304016, Preskill chapter 7 and Vazirani lecture notes 11 and 12)
  • Teleportation
  • Quantum communication (see quant-ph/9904093, quant-ph/9804043,
  • Limits on quantum computation
  • What is a quantum measurement?
  • Many worlds interpretation (see quant-ph/0003084)
  • Algorithmic cooling and quantum architectures (see quant-ph/9804060 and http://www.cs.berkeley.edu/~kubitron/papers/ "Building quantum wires: the long and short of it")
  • Simulating quantum systems is a fundamental problem. Some ideas from quantum computation have lead to efficient classical algorithms for simulating special types of systems: paper1.pdf paper2.pdf You might find this paper easier to read: paper3
  • Quantum Cryptography: paper.pdf paper.pdf
  • Physical Realization - there are many options here....
    NUCLEAR SPIN QUBITS:
    1. A Silicon-based Nuclear Spin Quantum Computer , B. E. Kane, Nature 393, 133 (1998).
    2. Single Spin Measurement using Single Electron Transistors to Probe Two Electron Systems, B. E. Kane, N. S. McAlpine, A. S. Dzurak, R. G. Clark, G. J. Milburn, He Bi Sun, Howard Wiseman, Phys. Rev. B 61, 2961 (2000).
    QUANTUM TELEPORTATION:
    1. Quantum teleportation of light beams," T. C. Zhang, K. W. Goh, C. W. Chou, P. Lodahl, and H. J. Kimble, Phys. Rev. A. 67, 033802 (2003)
    2. Anton Zeilinger
    JOSEPHSON JUNCTION QUBITS:
    Gerd Schoen, John Clarke H. Mooij Superconducting Qubits: A Short Review, M. H. Devoret, A. Wallraff, and J. M. Martinis cond-mat/0411174 (2004)
    NMR-BASED QUANTUM COMPUTING:
    Isaac Chuang N. Gershenfeld and I. Chuang, Science, 275, pp. 350-356, 1997). More recent experimental and theoretical papers are available at the Physics and Media Group's publications page,
    QUANTUM DOT QUBITS:
    [1] D. Loss, D.P. DiVincenzo, Phys. Rev. A 57 (1998) 120; cond-mat/9701055.
    [2] See review by, G. Burkard and D. Loss, in "Semiconductor Spintronics and Quantum Computation", eds. D. Awschalom, D. Loss, N. Samarth, Springer, Berlin, 2002.
    [3] J. M. Elzerman et al., cond-mat/0212489.
    [4] R. Hanson et al., cond-mat/0303139.
    5. Recipes for spin-based quantum computing, Veronica Cerletti, W. A. Coish, Oliver Gywat, Daniel Loss, Nanotechnology 16, R27 (2005).
    6. Controlling Spin Qubits in Quantum Dots, Hans-Andreas Engel, L.P. Kouwenhoven (Delft), Daniel Loss, C.M. Marcus (Harvard) Quantum Information Processing 3, 115 (2004) http://journals.kluweronline.com/article.asp?PIPS=493103.
    QUANTUM COMPUTING W/ MOLECULAR MAGNETS:
    Quantum computing with spin cluster qubits Florian Meier, Jeremy Levy (Pittsburgh), Daniel Loss Phys. Rev. Lett. 90, 047901 (2003).
    Quantum Spin Dynamics in Molecular Magnets Michael N. Leuenberger, Florian Meier, Daniel Loss Monatshefte für Chem. 134, 217(2003); cond-mat/0205457
    Electron Spins in Artificial Atoms and Molecules for Quantum Computing Vitaly N. Golovach, Daniel Loss Semicond. Sci. Technol. 17, 355- 366 (2002); cond-mat/0201437
    CAVITY QUANTUM ELECTRODYNAMICS:
    http://www.cco.caltech.edu/~qoptics/cqed.html
    BOSE EINSTEIN CONDENSATES AND QUANTUM CONTROL:
    [1] M. Greiner, et al., Nature 415, 39 (2002).
    QUANTUM COMPUTING AND OPTICAL LATTICES: [1] D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 82, 1975 (1999).
    [2] D. Jaksch, J.I. Cirac, P. Zoller, S.L. Rolston, R. Cote, and M.D. Lukin, Phys. Rev. Lett. 85, 2208 (2000).
    ELECTRONS ON LIQUID HELIUM AS QUBITS:
    1. M.J.Lea, P.G.Frayne and Y.Mukharsky,Fortshritte der Physik, 48 (2000), 1109 - 1124. Could we compute with electrons on helium?
    2. Quantum Physics, abstract quant-ph/0111029 Using Electrons on Liquid Helium for Quantum Computing Authors: A.J. Dahm, J.M. Goodkind, I. Karakurt, S. Pilla
    3. Qubits with electrons on liquid helium, M. I. Dykman,1,* P. M. Platzman,2 and P. Seddighrad, PHYSICAL REVIEW B 67, 155402 ~2003!
  • recent advances (2009)
    [1] Shor's algorithm on a photonic chip, A. Politi, J. C. F. Matthews, J. L. O'Brien, Science 325, 1221 (2009).
    [2] Complete Methods Set for Scalable Ion Trap Quantum Information Processing, J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried, D. J. Wineland, Sence Express, August 6, 2009.
    [3] Quantum Algorithm for Linear Systems of Equations, A. W. Harrow, A. Hassidim, S. Lloyd, Phys. Rev. Lett. 103, 150502 (2009).

    Useful Links:


  • 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 reading

    For all topics, the first recommended reading is the lecture notes. For complementary reading, see the texts below. All texts are available in the Berkeley libraries, click on the links below (Engineering has the biggest selection).

    Recommended texts for the class: