Quantum Theory in Modern Computer_quantum Computer

8/13/2019 Quantum Theory in Modern Computer_quantum Computer

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SEMINAR REPORT

ON QUANTUM THEORY IN MODERN

COMPUTER__QUANTUM COMPUTER

Presented by__

ABHISHEK GUPTA

ELECTRONICS ENGINEERING

KNIT SULTANPUR


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WHAT IS QUANTUM THEORY

Computer technology is making

devices smaller and smaller…

…reaching a point where classical

physics is no longer a suitable

model for the laws of physics.


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Quantum Theory is the description of

Microscopic motion.

In nature , action values smaller than

ħ=1.06*10-34Js are not observed.

**The existence of smallest action value apply on light , time

, measurement , motion of matter , motion of space time ,and on every physical phenomenon in Microscopic World.

**There are two popular equation in quantum development

is_ΔE*Δt⩾ ħ/2,

Δx*Δp⩾ ħ/2,

These are the indeterminacy relation.


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**Because of the finite accuracy with which microscopic

motion can be observed, faster than-light motion is possible

in the microscopic domain! Quantum theory thus predicts

tachyons, at least over short time intervals. Motion backwards in time is possible over

microscopic times and distances.


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**What happens if we try to measure a change smaller than

the quantum of action?

Answer: We Get Random Results.

Ex. :-If a particle is sent through a screen with two

sufficiently close slits less than ħ . it is impossible to say

which slit the particle passed through.


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“In the micro-world , subatomic particles really can existsimultaneously in combination many different states.”

__QUANTUM SUPERPOSITION

A particle contain both wave behaviour and

particle behaviour . Thus accurate position and accurate

frequency can not determine simultaneously .


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“Here in this image the window is exhibiting 3 images

simultaneously , the image of the girl , the image of the

outside view and both images simultaneously.”


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CONCEPT OF QUANTUM COMPUTER

A quantum computer (also known as a quantumsupercomputer) is a computation device that makes direct use

of quantum-mechanical phenomena, such

as superposition and entanglement , to perform operations

on data.

.


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BIT V/S QUBIT__

A bit of data is represented by a single atom that is inone of two states denoted by |0> and |1>. A single bitof this form is known as a qubit .


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REPRESENTATION OF DATA - QUBITS

A physical implementation of a qubit could use the

two energy levels of an atom. An excited state representing

|1> and a ground state representing |0>.

State |0> State |1>

Excited

State

Nucleus Ground

State

Light pulse of frequency for

time interval t

Electron


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A QUBIT IN SUPERPOSITION IS IN BOTH OF THE

STATES |1> AND |0 > AT THE SAME TIME ….

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 | |2 + | |2 = 1


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State |0>

Consider a 3 bit qubit register. An equally weighted

superposition of all possible states would be denoted by:

|> = |000> + |001> + . . . + |111>

Electron

Excited

State

Ground

State

State |0> + |1>

Nucleus


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RELATIONSHIPS AMONG DATA -

ENTANGLEMENT

Entanglement is the ability of quantum systems to exhibitcorrelations between states within a superposition.

Imagine two qubits, each in the state |0> + |1> (a

superposition of the 0 and 1.) We can entangle the two

qubits such that the measurement of one qubit is alwayscorrelated to the measurement of the other qubit.


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In a 8-bit device data can be stored in

any “one” value from 0 to 255.But in a quantum computer an8-qubit device can be stored “every” value from 0 to 255.

Thus a 32 qubit device could store 4 billion

values at “same time”. Calculation could be done with allthese values “simultaneously”.

In a classical computer a latch can be stored ‘0’ or

‘1’ , but in quantum computer a qu-latch can stored ‘0’ or

‘1’ or all possible ‘superposition of 0 and 1’ .


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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 deterministic computation can be

performed on a quantum computer only if it is reversible.

Luckily, it has been shown that any deterministiccomputation can be made reversible.(Charles Bennet, 1973)


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QUANTUM GATES - CONTROLLED

NOTA 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.


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QUANTUM COMPUTER LANGUAGES

Even though no quantum computer has been builtthat hasn’t stopped the proliferation of papers on variousaspects of the subject. Many such papers have been writtendefining language specifications.

QCL - (Bernhard ¨ Omer ) C like syntax and very complete.http://tph.tuwien.ac.at/»oemer/qcl.html .

qGCL - (Paolo Zuliani and others)

http://web.comlab.ox.ac.uk/oucl/work/paolo.zuliani/

Quantum C - (Stephen Blaha) Currently just aspecification,


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APPLICATIONS

Efficient simulations of quantum systems Phase estimation; improved time-frequency and other

measurement standards (e.g. GPS)

Factoring and Discrete Logarithms

Hidden subgroup problems

Amplitude amplification

and much more…


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CONCLUSION

Qubits have probabilistic nature

N-qubit register have 2^N basis functions

Gates that are direct product of other gates do notproduce entanglement.

cNOT and one-qubit gates form a universal set of gates.

In principle there is an infinite number unitary operators U.


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REFERENCES

“A survey of quantum computing and automata” . E. deDoncker and L. Cucos, In Fourth World Multiconference onSystemics, Cybernetics, and Informatics (SCI'00), (2000).

“The Temple of Quantum Computing”, Riley T. Perry.2004

“ Quantum Computation:A Computer Science Perspective”,

Anders K.H. Bengtsson. 2005

http://www.nec.co.jp/rd/Eng/innovative/E3/top.html

http://www.sciencedaily.com/

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Quantum Theory in Modern Computer_quantum Computer