Quantum Computational Complexity
John Watrous
arXiv:0804.3401v1 [quant-ph] 21 Apr 2008
Institute for Quantum Computing and School of Computer Science
University of Waterloo, Waterloo, Ontario, Canada.
Article outline
I.
II.
Denition of the subject and its
COT 6200 Quantum Computing Fall 2010
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Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 23 Monday, November 8, 2010
n
Last time:
The expression of the logarithm of an operator
v
COT 6200 Quantum Computing Fall 2010
Click to edit Master subtitle style
Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 22 November 5, 2010
n
Last time:
n
von Neumann entropy
Today:
The expression of the logari
COT 6200 Quantum Computing Fall 2010
Click to edit Master subtitle style
Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 21 Monday, November 3, 2010
n
Last time:
n
Today:
n
von Neumann entropy
Simon oracle
Next
COT 6200 Quantum Computing Fall 2010
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Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 20 Monday, November 1, 2010
n
Last time:
Density operator
von Neumann entropy
n
Today:
Pr
COT 6200 Quantum Computing Fall 2010
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Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 19 Wednesday, October 27, 2010
n
Last time:
Solutions to HW2 problems
Density operator
n
COT 6200 Quantum Computing Fall 2010
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Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 18 Monday, October 25, 2010
n
Last time:
Quantum algorithms
Deutsch oracle
n
Today:
Solut
COT 6200 Quantum Computing Fall 2010
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Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 16 Monday, October 18, 2010
n
Last time:
Operator norm, Group Commutator, Ring Commutator
COT 6200 Quantum Computing Fall 2010
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Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 15 Wednesday, October 13, 2010
n
Last time:
n
Presentation of a paper on the SK Theorem.
T
COT 6200 Quantum Computing Fall 2010
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Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 24
Lecture 24 Wednesday, November 10, 2010
n
Last time:
Presentation of the paper: A.K.Ekert and R.J
COT 6200 Quantum Computing Fall 2010
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Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 24
Lecture 25 Monday, November 15, 2010
n
Last time:
Quantum phase estimation and its application to
COT 6200 Quantum Computing Fall 2010
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Dan C. Marinescu
Office: HEC 304
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 24
Lecture 26 Wednesday, November 17, 2010
n
Last time:
Example of phase estimation
Inversion about t
Quantum Information and Computation, Vol. 0, No. 0 (2005) 000000
c Rinton Press
arXiv:quant-ph/0505030 v2 23 Aug 2005
THE SOLOVAY-KITAEV ALGORITHM
CHRISTOPHER M. DAWSON
School of Physical Sciences, The University of Queensland,
Brisbane, Queensland 4072,
COT6600 Quantum Computing Fall 2010
Schedule of Class Presentations
Wednesday September 8 Ramya Pradham
R. P. Feynman, Simulating Physics with Computers, International Journal of
Theoretical Physics, 21: 467 - 488, 1982.
Monday October 11 Seghey Leontiev
1
Simulation of Quantum Circuits
The set of unitary operations performed by quantum gates is continuous; thus, the problem
of dening a nite, and hopefully small, set of universal quantum gates is slightly more
convoluted than the universality of classical
Department of Computer Science
University of Central Florida
COT 6600 Quantum Computing
Fall 2008 (dcm)
Name:
Midterm Exam Thursday, October 23, 2008.
Read carefully and follow the rules below.
1. This is an open book, and open notes exam.
2. This exam co
COT 6200 Quantum Computing Fall 2010
Click to edit Master subtitle style
Dan C. Marinescu
Office: HEC 304
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 24
Lecture 29 Monday, November 29, 2010
n
Last time:
n
Walsh-Hadamard and QFT
Today
Tensor product fac
COT 6200 Quantum Computing Fall 2010
Click to edit Master subtitle style
Dan C. Marinescu
Office: HEC 304
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 24
Lecture 28 Wednesday, November 24, 2010
n
Last time:
Presentation of the paper on Quantum Complexit
COT 6200 Quantum Computing Fall 2010
Click to edit Master subtitle style
Dan C. Marinescu
Office: HEC 304
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 24
Lecture 27 Monday, November 22, 2010
n
Last time:
Presentation of Jozsas paper on quantum factoring
COT 6200 Quantum Computing Fall 2010
Click to edit Master subtitle style
Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 14 Monday, October 11, 2010
n
Last time:
Universal quantum gates.
Simulation of a Toffoli
COT 6200 Quantum Computing Fall 2010
Click to edit Master subtitle style
Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 13 Monday, October 4, 2010
n
Last time:
A circuit reversing the role of the control and ta
COT 6200 Quantum Computing Fall 2010
Click to edit Master subtitle style
Dan C. Marinescu
Office: HEC 439 B
Office hours: M-Wd 2:45-3:45 PM
8/8/11
Lecture 6
Lecture 12 Wednesday, September 30, 2010
n
Last time:
A circuit reversing the role of the control
Department of Electrical Engineering and Computer Science
University of Central Florida
COT 6600 Quantum Computing
Fall 2010 (dcm)
Homework Assignment 5. Due Monday November 21, 2010.
Problem 1 (60 points) Search and then read several papers discussing th
Department of Electrical Engineering and Computer Science
University of Central Florida
COT 6600 Quantum Computing
Fall 2010 (dcm)
Homework Assignment 4. Due Monday November 8, 2010
Problem 1 (30 points) Show that the following relations exist among the i
Department of Electrical Engineering and Computer Science
University of Central Florida
COT 6600 Quantum Computing
Fall 2010 (dcm)
Homework Assignment 3. Due Monday, October 26, 2010.
Problem 1 (20 points) A linear operator A is said to be normal if it co
Department of Electrical Engineering and Computer Science
University of Central Florida
COT 6600 Quantum Computing
Fall 2010 (dcm)
Homework Assignment 2. Due Wednesday November 5, 2008.
Problem 1 (30 points)
Prove the following properties of a tensor prod
Electrical Engineering and Computer Science Department
University of Central Florida
COT 6600 Quantum Computing
Fall 2010 (dcm)
Homework Assignment 1. Due Wednesday, September 22, 2008.
Problem 1 (20 points)
Show that:
ei = cos + i sin
and
ei
n
= cos(n)
Fortschr. Phys. 48 (2000) 9 11, 771 783
The Physical Implementation of Quantum Computation
David P. DiVincenzo
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598 USA
Abstract
After a brief introduction to the principles and promise of quantum in
COT6600 Quantum Computing Fall 2010
Lecture: M Wd 1:30 -2:45 Eng 0383
Instructor: Dan C. Marinescu
Office HEC 439 B
Office hours: M-Wd 2:45 3:45 PM
Class outline
Quantum Computing and Quantum Information Theory The Big Picture
Mathematical Foundation
Alg