This is a ppt about Quantum computing...

2. ENGINEERING PHYSICS II

3. QUANTUM COMPUTER
EVOLUTION LIES A HEAD
PRESENTED BY :
P.SAI VARUN
T.MURALI KRISHNA
(1St Year) C.S.E Branch

4. CONTENTS
Quantum Theory
Influence of Quantum Theory
Quantum Mechanics
Two Slit Experiment with Electrons
Applications

5. In 1900, physicist Max Planck presented
his Quantum Theory to the German
Physical Society.
Max Planck
1858-1947
Quantum theory:
Quantum theory is the theoretical basis of modern physics that
explains the nature and behavior of matter and energy on the
atomic and subatomic level.

6. INFLUENCE OF QUANTUM THEORY
Evolution of the Materials
Bombs Power
Universe Medical &
Uses Technolog
SUB ATOMIC y
ATOMS &
NUCLEAR PHYSICS
PARTICLES MOLECULES
QUANTUM THEORY
QUANTUM OPTICS
QUANTUM Quantum
COMPUTIN Laser Communications Cryptography
G s

7. QUANTUM MECHANICS
Quantum mechanics is used to explain microscopic phenomena
such as photon-atom scattering and flow of the electrons in a
semiconductor.

8. QUANTUM MECHANICS is a collection of postulates based on a
huge number of experimental observations.

9. TWO SLIT EXPERIMENT
Electrons
9

10. TWO SLIT EXPERIMENT
Observing Electrons
10

11. APPLICATIONS OF QUANTUM MECHANICS
TRANSISTORS
The Transistors work on the unique properties of semiconductors --
materials that can act as either a conductor or an insulator -- to
operate.

12. LASERS
Lasers work is by exciting the electrons orbiting atoms, which then
emit photons as they return to lower energy levels.
The photons are released of the same energy level and direction,
creating a steady stream of photons we see as a laser beam.

13. 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.
Quantum Computer has the potential to perform calculations
billions of times faster than silicon-based computer

14. CONTENTS
History of Quantum Computer
Quantum Computer Principle
Basic Quantum Computation
Bits Vs Qubits
Bloch Sphere
Quantum Gates

15. HISTORY OF QUANTUM COMPUTERS
Paul Benioff is credited with first applying Quantum theory to
computers in 1981.
Quantum Computer was first discovered by Richard Feynman
in 1982.
David Albert made the second discovery in 1984 when he described a
'self measuring quantum automaton'.
David Deutsch was made the most important quantum computing in
1989.
The finite machine obeying the laws of quantum computation are
contained in a single machine called as a „universal quantum computer‟.

16. QUANTUM COMPUTER PRINCIPLE
Church-Turing Principle
Alonzo Church Alan Turing
(1903-1995) (1912-1954)
“If There exists or can be built a universal quantum computer that
can be programmed to perform any computational task that can be
performed by any physical object”.
Every „function which would naturally be regarded as computable‟ can be
computed by the Universal Turing machine.

17. BASIC QUANTUM COMPUTATION
The Qubit - can be 1, 0 or both 1 and 0
representation for a quantum number is the “Ket”-‟I>‟
|x> - number in Quantum Computer
Superposition states:
2 N
1 2N 1
2
ai si Where:
ai 1
i 0 i 0

18. EXAMPLES:
1 1
0 1
2 2
1 1 1 1
00 01 10 11
2 2 2 2

19. REPRESENTATION
n Qubits: 2nx1 matrix represents the state:
1
|0> would be represented by
0
0
|1> would be represented by
1
1
2
Equal superposition would be 1
2

20. BITS VS QUBITS
Classical bits are either 0 or 1
Quantum bits “qubits” are in linear superposition of | 0> and | 1>
16 Qubits

21. Qubits and Quantum Registers

22. BLOCH SPHERE
The Bloch sphere is a geometric representation of qubit states as
points on the surface of a unit sphere.

23. QUANTUM GATES
Quantum Gates are similar to classical gates, but do not have a
degenerate output. i.e. their original input state can be derived from
their output state, uniquely. They must be reversible.
This means that a computation can be performed on a quantum
computer only if it is reversible.
In 1973,Charles Bennet shown that any computation can be
reversible.

24. QUANTUM GATES ARE REVERSIBLE
In designing gates for a quantum computer, certain
constraints must be satisfied.
A consequence of this requirement is that any quantum computing
operation must be reversible.
Reversible gates must have the same number of inputs and outputs.

25.  The most simple reversible classical gate is the infamous
XOR (Exclusive or gate).
 In quantum computing it is usually called controlled-NOT
or CNOT -gate.
 Observe that reversible (quantum) gates have equal number
of inputs and outputs.

26. LOGIC GATES FOR QUANTUM BITS:
0 1 0 1
=
1 0 1 0
0 1 1 0
=
1 0 0 1

27. Quantum Logic Gates

28. QUANTUM GATES
Hadamard Gate
Controlled Not Gate (CN)
Controlled Controlled Not Gate(CCN)
Universal Quantum Gates
Quantum Entanglement
Quantum Teleportation

29. QUANTUM GATES - HADAMARD
Simplest gate involves one qubit and is called a Hadamard Gate
(also known as a square-root of NOT gate.) Used to put qubits
into superposition.
H H
State |0> State |0> + |1> State |1>
Note: Two Hadamard gates used in
succession can be used as a NOT gate

30. QUANTUM GATES - CONTROLLED NOT
A gate which operates on two qubits is called a Controlled-
NOT (CN) Gate. If the bit on the control line is 1, invert
the bit on the target line.
Input Output
A - Target A’ A B A’ B’
0 0 0 0
B - Control B’ 0 1 1 1
1 0 1 0
1 1 0 1
Note: The CN gate has a similar behavior to the XOR gate
with some extra information to make it reversible.

31. EXAMPLE OPERATION - MULTIPLICATION
BY 2
 We can build a reversible logic circuit to calculate multiplication
by 2 using CN gates arranged in the following manner:
Input Output
Carry Ones Carry Ones
Bit Bit Bit Bit
0 0 0 0
0 1 1 0
0
Carry Bit
Ones Bit
H

32. QUANTUM GATES - CONTROLLED CONTROLLED
NOT (CCN)
A gate which operates on three qubits is called a
Controlled Controlled NOT (CCN) Gate. If the bits on
both of the control lines is 1,then the target bit is inverted.
Input Output
A B C A’ B’ C’
A - Target A’ 0 0 0 0 0 0
0 0 1 0 0 1
B - Control 1 B’ 0 1 0 0 1 0
0 1 1 1 1 1
C - Control 2 1 0 0 1 0 0
C’
1 0 1 1 0 1
1 1 0 1 1 0
1 1 1 0 1 1

33. A UNIVERSAL QUANTUM GATES
 The CCN gate has been shown to be a universal reversible
logic gate as it can be used as a NAND gate.
A - Target Input Output
A’
A B C A’ B’ C’
0 0 0 0 0 0
B - Control 1 B’
0 0 1 0 0 1
0 1 0 0 1 0
C - Control 2
C’ 0 1 1 1 1 1
1 0 0 1 0 0
1 0 1 1 0 1
When our target input is 1, our target 1 1 0 1 1 0
output is a result of a NAND of B and C.
1 1 1 0 1 1

34. OTHER 1*1 UNITARY GATES (QUANTUM)
1 1 1
Hadamard H 2 1 1
Pauli-X X 0 1
1 0
Classical inverter
0 i
Pauli-Y Y i 0
1 0
Pauli-Z Z 0 1

35. OTHER 1*1 UNITARY GATES (QUANTUM)
1 0
Phase S 0 i
1 0
/8 T i /4
0 e

36. 2*2 UNITARY GATES
1 0 0 0
Controlled-Not
0 1 0 0
(Feynman) 0 0 0 1
0 0 1 0
1 0 0 0
0 0 1 0
swap 0 1 0 0
These are counterparts of standard logic 0 0 0 1
because all entries in arrays are 0,1

37. 2*2 UNITARY GATES
These are truly quantum
logic gates because not Controlled-Z
all entries in arrays are
0,1 1 0 0 0
Z
0 1 0 0
0 0 1 0
Another
0 0 0 1
symbol
1 0 0 0
0 1 0 0
Controlled-phase 0 0 1 0
S
0 0 0 i

38. 3*3 UNITARY GATES
This is a counterpart of standard logic
because all entries in arrays are 0,1
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
Toffoli 0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1
0 0 0 0 0 0 1 0

39. 3*3 UNITARY GATES
abc
This is a counterpart of standard
logic because all entries in arrays are
0,1
1 0 0 0 0 0 0 0
abc 0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0
Fredkin 0 0 0 0 0 1 0 0
This is one more notation for Fredkin
that some papers use
0 0 0 0 0 0 0 1

40. QUANTUM ENTANGLEMENT
 The fact that a quantum bit, qubit, can be in several states is called
entanglement. An electron can have both spin up and down.
 When we try to measure the state of electron, it is found either as spin
up or down, not both.
 The entanglement can be seen only when repeating the measurement.
(with other electrons being in the same entangled state).

41. QUANTUM TELEPORTATION
 Teleportation means transmission of quantum states. That is quite
difficult even if not impossible.
 That is used in telecommunication to protect telecommunication
from eavesdropping (salakuuntelu) because the listening is not
possible without destroying information...

42. QUANTUM MAN
“I learned very early the difference between knowing the
name of something and knowing something.”
-Richard P. Feynman

43. “A person who never made a mistake never tried
anything new.”
-ALBERT EINSTEIN

44. Be a Hero .
Always Say,
“I Have No Fear.”
-Swami Vivekananda

45. Thank s
to
the
Humanities and Basic Sciences
Physics Department
T.BHIMA RAJU SIR & K.DHANUNJAYA SIR

46. THANK YOU!