A pedestrian introduction to quantum computing

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55 pages

English

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A pedestrian introduction to quantum computing jerome.milan (at) lix.polytechnique.fr June 2010 Or quantum computing poorly explained by a dummy

computing poorly explained

quantum computing

components onto integrated

quantum communication

grover's algorithm

factorization records

integer factorization

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A pedestrian introduction to quantum computing
Or quantum computing poorly explained by a dummy
jerome.milan (at) lix.polytechnique.fr
June 2010Outline
Quantum computation
Shor’s algorithm
Grover’s algorithm
Quantum communication
2Introduction – Factorization records
# decimal digits
year
From “Thirty Years of Integer Factorization”, F. Morain, 2001
3Introduction – Factorization records
313
1039 2 - 1
RSA-768
(232 digits)
2007 2010
4
?

Introduction – Moore’s law

From “Cramming more components onto integrated circuits”, Gordon E. Moore.
Electronics, Volume 38, Number 8, April 19, 1965
5
???????,??????i??}??????iL?? ??i?????v???x???????
????V??
`?i>?????
}?????V???>?????>?????i???*??????{??x?xi{???????i?>
??iv?

Introduction – Moore’s law

From “Cramming more components onto integrated circuits”, Gordon E. Moore.
Electronics, Volume 38, Number 8, April 19, 1965
6
??????????x
???{???????????????????????x????>ii??9??x??????V??L?v???`?{i?????>n??}{i???}*?v??ii???? ???{????xi?????????n??????????????????????????x?Introduction – Moore’s law
Process size in nanometers
10000
11
µm
1000
130
nm
350
nm 32100
nm
4
10 nm22
nm
1970 1980 1990 2000 2010 2020
7Introduction – Moore’s law
Process size in nanometers
10000
11
µm
The end of Moore’s law
1000
130
nm
2020?
350
nm 32100
nm2030?
4What alternative?10 nm22
nm
1970 1980 1990 2000 2010 2020
8The quantum bit
Classical bit is either•
• 0 or 1
Quantum bit (qubit) can be•
• the eigenstates or |0 |1
• or a superposition |ψ=α|0+β|1
• are probability amplitudesα,β∈C
2 2• | α| + |β| =1
9The quantum bit
Geometrical interpretation – the Bloch sphere•
iφ|ψ = cos(θ/2)|0+ e sin(θ/2)|1
10