Quantum computation

Based on nanotechnology

Speed of

computation:

Vaccum tubes

Transistors

Devices that perform

quantum computing

Quantum

mechanics

Physical phenomena at

microscopic scales

Completely different from

classical mechanics

Quantum computing

Theoretical study of

quantum systems

Those systems are

applied to make a

quantum computer

Uses “QUBITS”

Bits (classical computing)

A bit can exist only in one

state

Either 0 or 1

Information behaviour : one

single direction

Logic gates are irreversible

Qubit

s Can exist as 0 or 1 or

coherent superposition of

both

Operation on a qubit

effectively acts on both

values at a same time

An exist in both values

simultaneously

Bloch’s sphere:|1>

|0>

Ket notation:

q= a l0> + b l1>

Qubit system

(n)

No. of

operations

2 4

3 8

4 16

Representation of Data -

Qubits

|0>

Light pulse of

frequency for time

interval t

|1>

Physical interpretation

Light pulse of frequency for

time interval t/2

State |0> State |0> + |1>

Representation of Data -

Superposition

A single qubit can be forced into a superposition

of the two states denoted by the addition of the

state vectors:

|> = |0> + |1>

Where and are complex numbers and | |

+ | | = 1

Processors

Classical processors

Each processor perform

one computation,while

other processors do

other computations

Quantum processors

Single processor can

perform multiple

computations on its own

simultaneously

As increase in no.of Qubits

Increase in quantum parallelism

Quantum parallelism

+

Algorithm

Solve

problems in

fraction of

time

A B C

0 0 0

0 1 0

1 0 0

1 1 1

Ex.

The AND Gate

GATES:

Can achieve reversible operations by using quantum

gates

Reversible operations

For a computer to run fast

Inputs can be correctly deduced from

outputs

Irreversible computation involve loss of

information

Taffoli gate:

It’s a reversible gate

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 computer

Use direct use of quantum mechanical

phenomena

Utilizes quantum properties to represent data

Could solve certain problems much faster

Shor’s algorithm

Allows extremely quick factoring

To factor a 1000 digit number

For a classical computer it take 10

million billion years

For a quantum computer its just 20 min

Building a quantum

computer

It can’t be from transistor and diodes

A new type of technology is needed

A technology that enables qubits to exist

as coherent superposition of 0 and 1

Why Nanotechnology is

applied?

References

Text books: 1. Palanisamy

2. A quantum revolution for computing. Julian

Brown, New Scientist 24/9/94

Wikipedia.org

Videos on quantum computation by

“centre for quantum computation and

communication technology”

Queries ?

Thank you