CS294-2: Quantum Computation Spring 2007



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CS294-2: Quantum Computation

Spring 2007

Instructor Umesh Vazirani


Office: 671 Soda, 642-0572
Lectures: MW 2:30-4 (410 HMMB)
Office Hours: M 1-2 (671 Soda)

Announcements




Homework


 Homework 1 [pdf,ps] (1/31)

 Homework 2 [pdf,ps] (2/12)



 Homework 3 [pdf,ps] (3/22)

Lecture notes








Topic

Notes (modified)

1

1/17

Intro, Axioms, Bell Inequalities.                                           

[pdf,ps] (1/19)

2

1/22

Hilbert Space, Tensor product, Quantum gates, Bell states. Inequalities.                                           

[pdf,ps] (1/22)

3

1/24

Hilbert Space, Superdense Coding, Teleportation. Inequalities.                                           

[pdf,ps] (1/24)

4

1/29

Reversibility, Quantum Computers are Digital .                                           

[pdf,ps] (1/29)

5

1/31

Quantum Complexity Theory .                                           

[pdf,ps,tif]

6

2/5

Quantum Computation and Extended Church-Turing Thesis .                                           

[pdf,ps]

7

2/7

Simon's Agorithm + QFT .                                           

[pdf,ps]

8

2/12

Quantum Factoring .                                           

[pdf,ps]

9

2/14

Abelian HSP + Discrete Log .                                           

[pdf,ps]

10

2/21

Lower Bounds for Unstructured Search, Quantum Zeno Effect. .                                           

[pdf,ps]

11

2/28

Quadratic speedup for Unstructured Search - Grover's Algorithm. .                                           

[pdf,ps]

12

3/5

Phase Estimation .                                           

[pdf,ps]

13

3/7

Quantum Information .                                           

[pdf,ps]

14

3/12

Bipartite States, Schmidt Decomposition, Bit Commitment .                                           

[pdf,ps]

15

3/14

Quantum Lower Bounds - Guest Lecture by Robert Spalek .                                           

[pdf,ps]

16

3/19

Search by Quantum Walk - Guest Lecture by Ashwin Nayak .                                           

[pdf,ps]

17

3/21

Holevo's Theorem, Random Access Codes. .                                           

[pdf,ps]

18

4/2

Applications of Random Access Codes. .                                           

[pdf,ps]

19

4/4

Adiabatic Quantum Computation .                                           

[pdf,ps]

20

4/9

QMA Completeness .                                           

[pdf,ps]

21

4/11

Quantum Error Correction .                                           

[pdf,ps]

22

4/16

Stabilizer Formalism .                                           

[pdf,ps]

23

4/18

Quantum Non-locality - guest lecture Jeremy Roland .                                           

[pdf,ps]

24

4/25

Non-abelian HSP .                                           

[pdf,ps]

25

4/30

Fault tolerance I - guest lecture Ben Reichardt .                                           

[scanned, pdf,ps]

26

5/2

Fault tolerance II - guest lecture Ben Reichardt .                                           

[scanned,pdf,ps]

27

5/7

Universality of Adiabatic QC + Low entanglement .                                           

[pdf,ps]

Some suggestions for projects [pdf]


Scribe Schedule [pdf]
Style file [cs294.sty]
[ Latex macro package for typesetting quantum circuits ]


Useful Links:





  • Los Alamos archive of papers and preprints on Quantum Mechanics and Quantum Computation: link



Recommended reading

On quantum computation



  • John Preskill's Quantum Computation course at Caltech: link

  • Nielsen and Chuang, Quantum Computation and Quantum Information
    An encyclopedic reference for quantum information theory. weaker coverage on computational issues.

  • Kitaev, Shen and Vyalyi, Classical and Quantum Computation
    Interesting but idiosyncratic.

Mathematical background

  • 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 structure.

On quantum mechanics in general

  • 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 everything.

  • 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 physics.

  • Feynman, Richard. QED
    Highly recommended popular science book.


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