This preview shows pages 1–5. Sign up to view the full content.
Quantum Computing  Lecture Notes
Mark Oskin
Department of Computer Science and Engineering
University of Washington
Abstract
The following lecture notes are based on the book
Quantum Computation and Quantum In
formation
by Michael A. Nielsen and Isaac L. Chuang. They are for a mathbased quantum
computing course that I teach here at the University of Washington to computer science grad
uate students (with advanced undergraduates admitted upon request). These notes start with a
brief linear algebra review and proceed quickly to cover everything from quantum algorithms
to error correction techniques. The material takes approximately 16 hours of lecture time to
present. As a service to educators, the L
A
T
E
Xand
Xfig
source to these notes is available online
from my home page:
http://www.cs.washington.edu/homes/oskin
. In addition, under
the section “course material” from my web page, in the spring quarter/2002 590mo class you
will find a sequence of homework assignments geared to computer scientists. Please feel free to
adapt these notes and assignments to whatever classes your may be teaching. Corrections and
expanded material are welcome; please send them by email to
[email protected]
.
The following work is supported in part by NSF CAREER Award ACR0133188.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Contents
1
Linear Algebra (short review)
4
2
Postulates of Quantum Mechanics
5
2.1
Postulate 1: A quantum bit .
. ............................
5
2.2
Postulate 2: Evolution of quantum systems .
.....................
6
2.3
Postulate 3: Measurement .
. . ............................
7
2.4
Postulate 4: Multiqubit systems.
..........................
8
3
Entanglement
9
4
Teleportation
11
5
Superdense Coding
15
6
Deutsch’s Algorithm
16
6.1
DeutschJozsa Algorithm .
2
0
7
Bloch Sphere
22
7.1
Phase traveling backwards through control operations.
...............
2
7
7.2
Phaseflips versus bitflips .
2
8
8
Universal Quantum Gates
29
8.1
More than two qubit controlled operations .
3
1
8.2
Other interesting gates .
. . . ............................
3
1
8
.
3 Sw
a
p .........................................
3
2
2
9
Shor’s Algorithm
33
9.1
Factoring and orderfinding .
. ............................
3
3
9.2
Quantum Fourier Transform (QFT) .
. . . . .....................
3
4
9.3
Shor’s Algorithm – the easy way.
..........................
3
8
9.4
Phase estimation
...................................
3
9
9.5
Shor’s Algorithm – Phase estimation method .
...................
4
0
9.6
Continuous fraction expansion .
...........................
4
2
9.7
Modular Exponentiation .
. . ............................
4
2
10 Grover’s Algorithm
43
11 Error Correction
46
11.1 Shor’s 3 qubit bitflip code .
4
7
11.2 Protecting phase .
5
0
11.3 7 Qubit Steane code.
.................................
5
1
11.4 Recursive error correction and the threshold theorem .
...............
5
3
3
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 1
Linear Algebra (short review)
The following linear algebra terms will be used throughout these notes.
Z
 complex conjugate
if
Z
a
b
i
then
Z
a
b
i
ψ
 vector, “ket” i.e.
c
1
c
2
c
n
ψ
 vector, “bra” i.e.
c
1
c
2
c
n
ϕ
ψ
 inner product between vectors
ϕ
and
ψ
.
Note for QC this is on
n
space not
n
!
Note
ϕ
ψ
ψ
ϕ
Example:
ϕ
2
6
i
,
ψ
3
4
ϕ
ψ
2
6
i
3
4
6
24
i
ϕ
ψ
 tensor product of
ϕ
and
ψ
.
Also written as
ϕ
ψ
Example:
ϕ
ψ
2
6
i
3
4
2
3
2
4
6
i
3
6
i
4
6
8
18
i
24
i
A
 complex conjugate of matrix
A
.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/27/2011 for the course CMPSC 290h taught by Professor Chong during the Fall '09 term at UCSB.
 Fall '09
 Chong

Click to edit the document details