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

Instructors


Michael Crommie
Wednesday 11-12 in 361 Birge
crommie@physics

Umesh Vazirani
Tuesday 3-4 in 671 Soda
vazirani@cs

Teaching Assistants

Kevin Moore
Office Hours: Thursday 3-4 in 307 Birge
Section: Monday 12-1 in 310 Soda
klmoore@socrates

Daniel Preda
Office Hours: Thursday 4-5 in 711 Soda alcove
Section: Monday 11-12 in 310 Soda
dpreda@eecs

Lecture notes

Topic Notes (modified)
11/18 Qubits, Measurements [pdf,ps] (8/30)
21/20 Bell States, Bell Inequalities [pdf,ps] (8/30)
31/25 Hilbert Spaces, Tensor Products [pdf,ps] (9/4)
41/27 Unitary Evolution, No Cloning Theorem, Superdense Coding [pdf,ps] (9/6)
52/1 Universal Gate Sets, Schrödinger's Equation, Quantum Teleportation [pdf,ps] (9/15)
62/3 operators, Physical Postulates, Hamiltonians [pdf,ps] (9/20)
72/8 Planck-Einstein,Schrödinger eq., position/momentum reps., deBroglie [pdf,ps] (9/22)
82/10 Schrodinger equation, time dependence, commutators [pdf,ps] (2/10)
92/15 Introduction to Spin - Magnetic Moment [pdf,ps] (2/15)
102/17 Spin Properties, Angular Momentum [pdf,ps] (10/2)
112/22 Manipulating Spins, B-fields [pdf,ps] (10/6)
scan: [pdf,ps]
122/24 Spin Precession [pdf,ps] (10/7)
scan: [pdf,ps]
133/1 Spin resonance, 2-slit expt. [pdf,ps] (3/2)
scan: [pdf,ps]
143/3 Entanglement and spins, Atoms as 2-level Systems [pdf,ps] (3/3)
scan: [pdf,ps]
153/8 Atoms and Photons - atomic qubits [pdf,ps] (3/10)
scan: [pdf,ps]
163/15 Photon Polarization - photon qubits [pdf,ps] (3/10)
scan: [pdf,ps]
173/17 Reversibility, Quantum Circuits [pdf,ps] (10/29)
183/29 Quantum Fourier Transform [pdf,ps] (12/3)
See also: [ps]
scan: [pdf,ps]
193/31 Quantum Factoring Algorithm scan: [pdf,ps] see also: [ps]
204/5 Quantum Search and the Quantum Zeno Paradox see: [ps]
214/7 Midterm Quiz  
214/12 Quantum search contd. + Density matrices see: [ps]
224/14 Quantum Teleportation Experiments scan: [pdf,ps]
Nature
234/19 Silicon-based Quantum Computation: guest lecturer Thomas Schenkel, LBNL
244/21 Cavity QED: guest lecturer Kevin Moore, UCB slides: [pdf] (4/21)
254/26 Josephson Junction Qubits: guest lecturers Travis Hime and Paul Reichardt, UCB
264/28 Single photon sources: guest lecturer Charles Santori, Stanford Univ.
275/3 The Dirac equation and the origin of spin
305/10&5/12 Project Presentations

Homework

Homework is due Friday at noon in the drop box labeled cs191, in 283 Soda Hall.

Project Guidelines


  • Term Project list [pdf] The project is worth 40% 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
    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 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
  • 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
  • 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")

    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