### Quantum Computing

```Quantum Computing
By
Guru Chandrasekhara
(Jan 9th 2015)
1
Agenda
• Introduction
• History
• Motivation
• Basic concepts of quantum computer
• Applications
• Summary
2
Introduction
• What is a quantum computer?
 A quantum computer is a machine that performs
calculations based on the laws of quantum mechanics, which
is the behavior of particles at the sub-atomic level.
3
History
 “I think I can safely say that nobody understands
quantum mechanics” - Feynman
 1982 - Feynman proposed the idea of creating
machines based on the laws of quantum mechanics
instead of the laws of classical physics.
 1985 - David Deutsch developed the quantum turing
machine, showing that quantum circuits are universal.
 1994 - Peter Shor came up with a quantum algorithm
to factor very large numbers in polynomial time.
 1997 - Lov Grover develops a quantum search
algorithm with O(√N) complexity
Source: http://www.telegraph.co.uk/
4
Why do we need quantum computer?
Gordon Moore, Co-founder Intel
Source:
http://www3.pcmag.com/media/images/246128gordon-moore.jpg
Source:
http://tedxsydney.com/site/item.cfm?ite
m=2B8FBE09C290F6C9771E4D98A24DC6
81
5
Motivation: Travelling Salesman Problem
Older than
universe
1600 years
100 sec
1 Ghz Computer:
14 Cities: 1011 routes  100 sec
22 Cities: 1019 routes  1600 years
28 Cities: ???
6
Basic concepts : Qbits(1)
• A classical computer performs operation using classical bits (0 & 1).
• A Quantum computer performs operations using Quantum bits (Qbit).
• Qbit is a unit of quantum information
which can be 0 and 1 at the same time.
• Many different objects can be used as quantum state
(Photons, nucleus, electrons).
7
Basic concepts : Qbits(2)
• An electron has dual nature: particle or wave.
• Wave exhibits a phenomenon known as superposition of waves.
Super position, 1 spin: |> = 1 |0> + 2 |1
No of Qbits
Classical possibilities
power
1
0 or 1
2
2
00, 01, 10, 11
4
3
000,…,111
8
2N
N
30 Qbit  More powerful than super computer
300 Qbit  ?
8
Representation of Data - Qubits
• A physical implementation of a qubit could use the two energy levels
of an atom - excited state ( |1> ), ground state (|0>)
Light pulse of
frequency  for
time interval t
Excited
State
Nucleus
Electron
State |0>
State |1>
9
Applications
• Factorization
• True randomness
• Quantum teleportation
• Quantum networking
• Encryption problem & quantum chemistry
• Molecular simulations
• Searching
• Artificial intelligence
10
• Could process massive amount of complex data
• Ability to solve scientific and commercial problems
• Process data in much faster speed
• Security and Privacy Issues
• Ability to crack down passwords
• Capability to break down every level of encryption
• Not suitable for word processing and email.
• Complex hardware
11
Summary
• Quantum computer – A computer which works on the principles of
quantum mechanics
• End of Moore’s law
• Wide range of applications
12
References
• http://en.wikipedia.org/wiki/Quantum_computing
• http://arxiv.org/pdf/quant-ph/9602014.pdf
13
14
BACK-UP
15
Deutsch’s Algorithm
•
•
David Deutsch: famous British physicist
Deutsch’s algorithm allows us to compute, in only one
step, the value of
f (0)  f (1)
•
To do this classically, you would have to:
1. compute f(0)
2. compute f(1)
–
Remember:
f : 0,1  0,1
16
Circuit for Deutsch’s Algorithm
0
H
1
H
x
H
x
Uf
 0  01
y
1 
yf(x)
0 1
2

0 1
2
17
Circuit for Deutsch’s Algorithm (2)
0
H
1
H

2
x
x
H
Uf
y
yf(x)

0  1 0  1

 if f ( 0 )  f (1), 

2
2

0  1 0  1
 if f ( 0 )  f (1), 


2
2
18
Circuit for Deutsch’s Algorithm (3)
0
H
1
H
x
x
H
Uf
y
yf(x)

0 1
if f (0)  f (1),  0 
2
3  
 if f (0)  f (1),  1  0  1

2
...and so we have computed
this simplifies to
 3   f (0)  f (1) 
0 1
2
f (0)  f (1)
19
```