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Quantum computing
Jan 14, 2016
Quantum computing. Motivation. Two approaches to increase efficiency: Nanotechnologies Quantum computers Take advantage of quantum effects and design quantum algorithms. Reversibility. Content. Qubits Multiple qubits Computational basis Quantum gates Bell states circuit - PowerPoint PPT Presentation
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Two approaches to increase efficiency:◦ Nanotechnologies◦ Quantum computers
Take advantage of quantum effects and design quantum algorithms.
Reversibility
2
1. Qubits2. Multiple qubits3. Computational basis4. Quantum gates5. Bell states circuit6. Teleportation circuit
3
The equivalent to a classical bit Can be in the states or as classical bits But also in a superposition state
Possibility of representing different numbers at the same time with only one qubit
But measurement put it back in the state or with probabilities and
0 1
10
0
1 2 2
122
4
4 computational basis states for a 2 qubit system
Superposition state
00 01 10 11
11100100 11100100
5
2
10
2
10
10
2222
6
X 10 10
01
10X
IXX
10
01
01
10
01
10†
7
After measurement becomes or
H 10
2
10
2
10
11
11
2
1H
2
1100 00'
11'
8
A
B
A
AB
11
10
01
00
0100
1000
0010
000111100100
CNOTU
IUU CNOTCNOT
1000
0100
0010
0001
0100
1000
0010
0001
0100
1000
0010
0001
†
9
A
B
C
A
B
BAC
01000000
10000000
00100000
00010000
00001000
00000100
00000010
00000001
ToffU
10
H x
y
xy
00
2
1100
2
10000
2
1000
CNOTH
01
2
1001
2
11011
2
1001
CNOTH
10
2
1100
2
10000
2
1010
CNOTH
11
2
1001
2
11011
2
1011
CNOTH
2
110 yy x
xy
11
H
2MX 1MZ
1M
2M
00
0 1 2 3 4
10
11001110002
1
2
110010000
01101110002
11
0110101100102
12
01111010010110002
12
12
H
2MX 1MZ
1M
2M
00
0 1 2 3 4
01111010010110002
12
100000 3
01)01(01 3
10)10(10 3
01)11(11 3 13
H
2MX 1MZ
1M
2M
00
0 1 2 3 4
1010)00(3
1001)01(3X
1010)10(3Z
101001)11(3ZX
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M.A. Nielsen & I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000.
P. Kaye, R. Laflamme & M. Mosca, An Introduction to Quantum Computing, Oxford University Press, 2007.
M. Nakahara & T. Ohmi, Quantum Computing: from Linear Algebra to Physical Realizations, CRC Press, 2008.
T. Hey, Quantum Computing: an introduction, Computing & Control Engineering Journal, vol. 10, n°3, 105-112, 1999.
A. Barenco & al., Elementary gates for quantum computation, Phys. Rev., A52, 3457-3467, 1995.
D. Deutsch, R. Jozsa, Rapid Solution of Problems by Quantum Computation, Proceedings: Mathematical and Physical sciences, vol. 439, n°1907, 553-558, 1992.
P. Shor, Algorithms for Quantum Computation: Discrete Logarithms and Factoring, Proceedings: 35th Annual Symposium on Fundamentals of Comp. Science (FOCS), 124-134, 1994.
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