quantum computing basic

7/31/2019 quantum computing basic

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KALYANI GOVT. ENGG. COLLEGE ECE DEPT.

PRESENTED BY * PARTHA PAUL

* SUBHAJIT MONDAL* SUDIPAN SINGHA


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OUTLINE

HistoryMotivationQuantum vs. ClassicalQuantum GatesQuantum Circuits

Physical Implementation


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HISTORY

Abacus

Gear Driven

Integrated Circuits

Over 200 million transistors


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computational LIMITS

Some important computational problemsseem to be permanently intractable

> Their complexity grows exponentially with

problem size, e.g. factoring largenumbers the basis for unbreakableInternet codes

Performance improvements in classical computer circuits may be approaching alimit > This is described by Moores Law


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Moores Law In 1965 Gordon Moore predicted that

number of transistors per square inchon integrated circuits had doubled

every year since the integrated circuitwas invented. Moore predicted thatthis trend would continue for theforeseeable future.

This has held true .. So far
http://www.webopedia.com/TERM/M/transistor.htmlhttp://www.webopedia.com/TERM/M/integrated_circuit_IC.htmlhttp://www.webopedia.com/TERM/M/integrated_circuit_IC.htmlhttp://www.webopedia.com/TERM/M/integrated_circuit_IC.htmlhttp://www.webopedia.com/TERM/M/integrated_circuit_IC.htmlhttp://www.webopedia.com/TERM/M/transistor.html


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* In 1965 - Gordon Moore announced that his predictionwould not remain true for much longer because of modern

technology.The ability to put transistors on chips was approaching theatomic level.

* In 1982 - Feynman proposed the idea of creating machinesbased on the laws of quantum mechanics instead of the lawsof classical physics.

*In 1994 - Peter Shor came up with a quantum algorithm tofactor very large numbers in polynomial time.

* In 1997 - Lov Grover develops a quantum search algorithmwith O(N) complexity


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Quantum Computer

A quantum computer is a machine thatperforms calculations based on the laws ofquantum mechanics, which is the behaviorof particles at the sub-atomic level.


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Two States Are Better Than One !!

Digital Computers rely on Os and 1 s

Voltage produces high and lows

Can only have one state at a time

Quantum computers can have multiple states

Two places at once


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A single qubit can be forced intoa superposition of the twostates denoted by the additionof the state vectors:

1

Where 1 and are complex

numbers and | 1|^2 +| |^2 = 1


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Representation of Data -Superposition

Light pulse offrequency fortime interval t/2

State |0> + |1>


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Quantum Information


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Quantum Gates :


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Quantum Gates

X

X X

N0T MATRIX


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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 H

StateI0>

StateI0>+I1>

StateI1>

Note: Two Hadamard gates used in succession can be used as a NOTgate


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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 A B

0 0

0 1

1 0

1 1

1 1

0 0

1 0

0 1Note: The CN gate has a similarbehavior to the XOR gate with someextra information to make it reversible.


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Quantum Logic Circuits A beam splitter

Half of the photons leaving the light source arrive at detector A;

the other half arrive at detector B.


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A beam-splitter0

1

0

1

%50

%50

Equal path lengths, rigid mirrors. Only one photon in the apparatus at a time. All photons leaving the source arrive at B. WHY?


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Quantum Circuits

A quantum (combinational) circuit is a sequence ofquantum gates, linked by wiresThe circuit has fixed width corresponding to thenumber of qubits being processedLogic design (classical and quantum) attempts tofind circuit structures for needed operations thatare

Functionally correctIndependent of physical technologyLow-cost, e.g., use the minimum number of qubits orgates

Quantum logic design is not well developed!


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Ad hoc designs known for many specific functions andgatesExample 1 illustrating a theorem by [Barenco et al.

1995]: Any C2

(U ) gate can be built from CNOTs, C( V ),and C( V ) gates, where V 2 = U

V V V

=

U

(1+i) (1-i)

(1-i) (1+i)(1-i) (1+i)

(1+i) (1-i)1/2

1/2


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Example 1 : Simulation

|0

|1

|x

|0

|1

|x

|0

|1

|x V V V

=

U

|0

|1

V |x

|0

|1

|0

|1

|x

|0

|1

|0

|1

|x

?


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Implementing a Half Adder

Problem: Implement the classical functions sum = x 1 x 0 and carry = x 1x 0

Generic design:

|x 1

U add |x 0 |y 1

|y 0

|x 1 |x 0 |y 1 carry

|y 0 sum

0001000000000000

0000100000000000

1000000000000000

0100000000000000

0000010000000000

0000100000000000

0000000100000000

0000001000000000

0000000001000000

0000000010000000

0000000000010000

0000000000100000

0000000000001000

0000000000000100

0000000000000010

0000000000000001

ADDU

Half Adder : Generic

design (contd.)


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Physical ImplementationMain Contenders

Nuclear magnetic resonance (NMR) Ion traps Semiconductor quantum dots Optical lattices etc.

Main Deficiency

Poor scalability

Chris Monroe,University ofMichigan

Ion traps


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Summary: State of the Art

Quantum circuits can solve some important problems withexponentially fewer operations than classical algorithms

Small quantum circuits have been demonstrated in thelab using various physical technologies

Quantum cryptography has been demonstrated over longdistances

Current technologies are fragile, and appear to be limitedto tens of qubits and hundreds of gates

Big gaps remain in our understanding of quantum circuitand algorithm design, as well as the necessaryimplementation techniques


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