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/