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Page 1: Quantum Computing
Page 2: Quantum Computing

ENGINEERING PHYSICS II

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PRESENTED BY :

P.SAI VARUN

(1St Year) C.S.E Branch

EVOLUTION LIES A HEAD

QUANTUM COMPUTER

T.MURALI KRISHNA

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CONTENTS

Quantum Theory

Influence of Quantum Theory

Quantum Mechanics

Two Slit Experiment with Electrons

Applications

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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

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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

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QUANTUM MECHANICS

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

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

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TWO SLIT EXPERIMENT

Electrons

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TWO SLIT EXPERIMENTObserving Electrons

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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

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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.

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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.

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CONTENTS

History of Quantum Computer

Quantum Computer Principle

Bits Vs Qubits

Basic Quantum Computation

Bloch Sphere

Quantum Gates

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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.

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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

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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>’

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EXAMPLES:

112

110

2

101

2

100

2

1

12

10

2

1

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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

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BITS VS QUBITS

Classical bits are either 0 or 1

Quantum bits “qubits” are in linear superposition of | 0> and | 1>

16 Qubits

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Qubits and Quantum Registers

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BLOCH SPHERE

The Bloch sphere is a geometric representation of qubit states as

points on the surface of a unit sphere.

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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.

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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.

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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.

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LOGIC GATES FOR QUANTUM BITS:

01

10

0

1

1

0=

01

10

1

0=

0

1

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Quantum Logic Gates

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QUANTUM GATES

Hadamard Gate

Controlled Not Gate (CN)

Controlled Controlled Not Gate(CCN)

Universal Quantum Gates

Quantum Entanglement

Quantum Teleportation

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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

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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’

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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

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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.

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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.

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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

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OTHER 1*1 UNITARY GATES (QUANTUM)

SPhase

/8 T

ei 4/

0

01

i0

01

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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

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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

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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

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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

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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).

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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...

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-Richard P. Feynman

“I learned very early the difference between knowing the name of something and knowing something.” 

QUANTUM MAN

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“A person who never made a mistake never tried anything new.”

-ALBERT EINSTEIN

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Be a Hero .Always Say,“I Have No Fear.”

-Swami Vivekananda

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Thank sto the

Humanities and Basic Sciences

Physics DepartmentT.BHIMA RAJU SIR & K.DHANUNJAYA SIR

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THANK YOU!


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