quantum computing
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This is a ppt about Quantum computing...TRANSCRIPT
ENGINEERING PHYSICS II
PRESENTED BY :
P.SAI VARUN
(1St Year) C.S.E Branch
EVOLUTION LIES A HEAD
QUANTUM COMPUTER
T.MURALI KRISHNA
CONTENTS
Quantum Theory
Influence of Quantum Theory
Quantum Mechanics
Two Slit Experiment with Electrons
Applications
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.
In 1900, physicist Max Planck presented his Quantum Theory to the German Physical Society.
1858-1947
Max Planck
INFLUENCE OF QUANTUM THEORY
QUANTUM THEORY
QUANTUM OPTICS
QUANTUM COMPUTING
Lasers
Communications Quantum Cryptography
SUB ATOMIC PARTICLES
NUCLEAR PHYSICS ATOMS & MOLECULES
Evolution of the Universe
BombsMedical Uses
Power Materials & Technology
QUANTUM MECHANICS
Quantum mechanics is used to explain microscopic phenomena such as photon-atom scattering and flow of the electrons in a semiconductor.
QUANTUM MECHANICS is a collection of postulates based on a huge number of experimental observations.
TWO SLIT EXPERIMENT
Electrons
TWO SLIT EXPERIMENTObserving Electrons
APPLICATIONS OF QUANTUM MECHANICS
The Transistors work on the unique properties of semiconductors -- materials that can act as either a conductor or an insulator -- to operate.
TRANSISTORS
LASERS
The photons are released of the same energy level and direction, creating a steady stream of photons we see as a laser beam.
Lasers work is by exciting the electrons orbiting atoms, which then emit photons as they return to lower energy levels.
QUANTUM COMPUTER
Quantum Computer has the potential to perform calculations billions of times faster than silicon-based 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.
CONTENTS
History of Quantum Computer
Quantum Computer Principle
Bits Vs Qubits
Basic Quantum Computation
Bloch Sphere
Quantum Gates
HISTORY OF QUANTUM COMPUTERS
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’.
Paul Benioff is credited with first applying Quantum theory to computers in 1981.
QUANTUM COMPUTER PRINCIPLE
“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 becomputed by the Universal Turing machine.
Alonzo Church(1903-1995) (1912-1954)
Alan Turing
Church-Turing Principle
BASIC QUANTUM COMPUTATION
|x> - number in Quantum Computer
Superposition states:
Where:
12
0
N
iii sa 1
12
0
2
N
iia
The Qubit - can be 1, 0 or both 1 and 0 representation for a quantum number is the “Ket”-’I>’
EXAMPLES:
112
110
2
101
2
100
2
1
12
10
2
1
REPRESENTATION
n Qubits: 2nx1 matrix represents the state:
|0> would be represented by
|1> would be represented by
Equal superposition would be
1
0
0
1
2
12
1
BITS VS QUBITS
Classical bits are either 0 or 1
Quantum bits “qubits” are in linear superposition of | 0> and | 1>
16 Qubits
Qubits and Quantum Registers
BLOCH SPHERE
The Bloch sphere is a geometric representation of qubit states as
points on the surface of a unit sphere.
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.
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.
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.
LOGIC GATES FOR QUANTUM BITS:
01
10
0
1
1
0=
01
10
1
0=
0
1
Quantum Logic Gates
QUANTUM GATES
Hadamard Gate
Controlled Not Gate (CN)
Controlled Controlled Not Gate(CCN)
Universal Quantum Gates
Quantum Entanglement
Quantum Teleportation
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
State |0> State |0> + |1>
H
State |1>
Note: Two Hadamard gates used in succession can be used as a NOT gate
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.
A - Target
B - Control
A B A’ B’
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 1
Input Output
Note: The CN gate has a similar behavior to the XOR gate with some extra information to make it
reversible.
A’
B’
EXAMPLE OPERATION - MULTIPLICATION BY 2
Carry Bit
Carry Bit
Ones Bit
Carry Bit
Ones Bit
0 0 0 0
0 1 1 0
Input Output
Ones Bit
We can build a reversible logic circuit to calculate multiplication by 2 using CN gates arranged in the following manner:
0
H
QUANTUM GATES - CONTROLLED CONTROLLED NOT (CCN)
A - Target
B - Control 1
C - Control 2
A B C A’ B’ C’
0 0 0 0 0 0
0 0 1 0 0 1
0 1 0 0 1 0
0 1 1 1 1 1
1 0 0 1 0 0
1 0 1 1 0 1
1 1 0 1 1 0
1 1 1 0 1 1
Input Output
A’
B’
C’
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.
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
B - Control 1
C - Control 2
A B C A’ B’ C’
0 0 0 0 0 0
0 0 1 0 0 1
0 1 0 0 1 0
0 1 1 1 1 1
1 0 0 1 0 0
1 0 1 1 0 1
1 1 0 1 1 0
1 1 1 0 1 1
Input OutputA’
B’
C’
When our target input is 1, our target output is a result of a NAND of B and C.
OTHER 1*1 UNITARY GATES (QUANTUM)
HHadamard
11
11
2
1
Pauli-X X
01
10
Pauli-Y Y
0
0
i
i
ZPauli-Z
10
01
Classical inverter
OTHER 1*1 UNITARY GATES (QUANTUM)
SPhase
/8 T
ei 4/
0
01
i0
01
2*2 UNITARY GATES
Controlled-Not (Feynman)
swap
0100
1000
0010
0001
1000
0010
0100
0001
These are counterparts of standard logic because all entries in arrays are 0,1
2*2 UNITARY GATES
Controlled-Z
1000
0100
0010
0001Z
Another symbol
S
i000
0100
0010
0001
Controlled-phase
These are truly quantum logic gates because not all entries in arrays are 0,1
3*3 UNITARY GATES
Toffoli
01
10
00
00
00
00
00
0000
00
10
01
00
00
00
0000
00
00
00
10
01
00
0000
00
00
00
00
00
10
01
This is a counterpart of standard logic because all entries in arrays are 0,1
3*3 UNITARY GATES
Fredkin
10
00
00
10
00
00
00
0001
00
00
01
00
00
00
0000
00
00
00
10
01
00
0000
00
00
00
00
00
10
01
This is a counterpart of standard logic because all entries in arrays are 0,1
This is one more notation for Fredkin that some papers use
a b c
a b c
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).
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...
-Richard P. Feynman
“I learned very early the difference between knowing the name of something and knowing something.”
QUANTUM MAN
“A person who never made a mistake never tried anything new.”
-ALBERT EINSTEIN
Be a Hero .Always Say,“I Have No Fear.”
-Swami Vivekananda
Thank sto the
Humanities and Basic Sciences
Physics DepartmentT.BHIMA RAJU SIR & K.DHANUNJAYA SIR
THANK YOU!