Chem/CS/Phys191: Qubits, Quantum Mechanics and Computers

Meets Tue & Thu 12:30-2 in 180 Tan, section Tue 4-5 in 6 Evans Hall


Prof. Umesh Vazirani
Office hours: Monday 1-2 in 671 Soda

Prof. Birgitta Whaley
Office hours: Wednesday 1.30-2.30 & Thursday 2.30-3.30 in 219 Gilman

Teaching Assistants

Daniel Preda
Office hours: Monday 3-4 in 411 Soda & Friday 11-12 in 411 Soda

Kevin Young
Office hours: Thursday 4-5 in 410 Hearst Mining Building


  • 12/10/08 First four project slides published online
  • 12/02/08 Term paper due date revised to Monday Dec 15.
  • 12/02/08 Updated Schedule of Project Presentations - please check. Note that the last class, Tuesday Dec 9 will be held in 410 Hearst Mining Building and we will provide pizza. We will start at 12.30 in order to get through the presentations but may go a little beyond 2 pm since we have 95 minutes of presentation scheduled for that day. The order of presentations will be as listed in the schedule. Course evaluations will be made this Thursday, Dec 4.
  • 12/01/08 Schedule of Project Presentations is now online - please check when you present!
  • Project presentations will take place in class on Thursday Dec 4 and Tuesday Dec 9. The term paper is due on Friday Dec 12.
  • The term project list has been updated 11/26.
  • Guest lectures on experimental implementations: Tues Nov 25 - Ion trap Quantum Computation, Tues Dec 2 - Silicon based Quantum Computation
  • typo corrected on HW 7 (problem 4)
  • Midterm II will be on Thursday November 13.
  • Midterm solutions now posted.
  • Midterm I will be on Thursday October 9. Those unable to take the exam because of the religious holiday should contact Professor Whaley to set up an alternative time.
  • Please skip question 3 on Problem Set 2. It will be on the next assignment.


    Homework is due Monday at 5 pm in the drop box labeled cs191, in 283 Soda Hall.


    Error Correction
    Adiabatic QC
    Quantum Dots I
    Josephson Junction Qubits
    Quantum Cryptography
    Quantum Simulation
    Reversing Quantum Measurements
    Quantum Control
    Quantum Dots II
    Cavity QED

    Lecture notes

    Topic Notes
    18/28 Qubits, Measurements [pdf,ps]
    2,39/2, 9/4 Bell States, Bell Inequalities [pdf,ps]
    49/9 Physical Qubits [pdf]
    59/11 No Cloning Theorem & Teleportation [pdf,ps]
    6,79/16, 9/18 Teleportation & Bell Inequalities notes from lectures 2 & 5.
    89/23 Observables, Hamiltonian, Schrodinger's Eqn [pdf,ps]
    99/25 Continuous quantum states, particle on a line, uncertainty relations [pdf,ps]
    109/30 Representations and Wavefunctions [pdf]
    1110/02 Particle-in-a-box, Spin [pdf]
    1210/07 Spin measurements, initialization, manipulation by precession [pdf]
    0010/09 Midterm Quiz #1
    1310/14 Spin manipulation by resonance [pdf]
    1410/16 Spin rotation subtleties, Spin entanglement [pdf]
    1510/21 Tensor products, 2 qubit gates with coupled spins [pdf]
    1610/23 5 criteria for qu comp, Universal gate sets [pdf]
    1710/28 Extended Church Turing Thesis [pdf]
    18&1910/30&11/4 Chapter 2 Fast Fourier Transform, and
    Chapter 10 Quantum Factoring Algorithm
    [book ]
    2011/6 NP-complete problems and quantum search [pdf]
    0011/13 Midterm Quiz #2
    2111/18 Mixed states, density matrix, decoherence [pdf]
    2211/20 Quantum Error Correction [pdf]
    2311/25 Guest Lecture - QC with Ion Traps [pdf]
    2412/02 Guest Lecture - Silicon-based QC [pdf]

    Project Guidelines

  • Term Project list [pdf] The project is worth 35% of the grade. 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. We will add to this list, and you should feel free to suggest any topic that you are interested in. When you are ready, please email the course instructors the composition of your team, the topic, and a brief description. You are also encouraged to discuss your topic in person with any of the faculty.

    quant-ph refers to the Los Alamos archives: link

  • Physical Realization
    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).
    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
    Gerd Schoen, John Clarke H. Mooij Superconducting Qubits: A Short Review, M. H. Devoret, A. Wallraff, and J. M. Martinis cond-mat/0411174 (2004)
    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,
    [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)
    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
    [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).
    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 From: Ismail Karakurt [view email] Date: Mon, 5 Nov 2001 21:02:00 GMT (170kb) 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. Seddighrad1PHYSICAL REVIEW B 67, 155402 ~2003!
  • 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 "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

    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 other sources listed below.

    On quantum computation

    Mathematical background

    On quantum mechanics in general