Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf

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08-11-2013

1

MNT-301Introduction to Quantum Computer

UNIT-3

The integrated circuit (IC) manufactured by optical

lithography

bull Silicon-based technology allows for the fabrication of electronic devices with high

reliability and of circuits with near-perfect precision

bull In fact the main challenges facing conventional IC technology are not so much in

making the devices but in interconnecting them and in managing power dissipation

bull IC miniaturization has provided the tools for imaging manipulating and modeling onthe nanometer scale These new capabilities have led to the discovery of new

physical phenomena which have been the basis for new device proposals

bull Advantages of nanodevices include low power high-packing densities and speed

bull While there has been significant attention paid to the physics and chemistry of

nanometer-scale device structures there has been less appreciation of the need for

new interconnection strategies for these new kinds of devices

bull In fact the key problem is not so much how to make individual devices but how to

interconnect them in appropriate circuit architectures



08-11-2013

2

Introduction to Nanocomputer architecture

bull Nanotechnology holds the promise of putting a trillion molecular-scale devices in a square

centimeter How does one assemble a trillion devices per square centimeter Moreover

this needs to be done quickly inexpensively and sufficiently reliably What does one do

with a trillion devices

bull If we assume that one can make them (and they actually work) how can this massive

amount of devices be harnessed for useful computation These questions highlight the

need for innovative nanoelectronic circuit architectures

bull Recent accomplishments include the fabrication of molecular circuits that are capable of

performing logic operations

bull So the Nanocomputer architecture is based on the QCA single electron circuit

molecular circuit ets

Quantum Dot Cellular Automata

bull For the purpose of quantum computing a molecular structural model has been proposed

that utilizes quantum dots is termed as quantum cel lular automata(QCA) in which four

quantum dots in square array are placed in a cell such that electrons are able to tunnel

between the dots but are unable to leave the cell

bull When two excess electrons are placed in the cell coulomb repulsion will force the electron

to occupy dots on opposite corners

bull Two ground states are energetically equivalent and can be labeled logic lsquo1rsquoand lsquo0rsquo

respectivelyFIGURE 1 The two possible ground-state

polarizations denoted ldquo0rdquo and ldquo1rdquo of a four-dot

QCA cell

Flipping the logic state of one cell for instance by applying a negative potential to a lead

near the quantum dot occupied by an electron will result in the next door cell flipping

ground state in order to reduce coulomb repulsion

In this way a line of QCA cells can be used to do computation



08-11-2013

3

bull The QCA cellular architecture is similar to other cellular arrays such as cellular

neuralnonlinear networks (CNN) in that they repeatedly employ the same basic cell with its

associated near-neighbor interconnection pattern

bull In short QCA is a proposed scheme for computing with cells of coupled quantum dots where

coupling between the cells is given by their direct physical interactions(and not by wires)

bull The physical mechanism available for interactions in such field coupled architectures are

electric (coulomb ) or magnetic interactions in conjunction with quantum mechanical tunneling

bull 11 A quantum-dot cell

bull The quantum-dot cellular automata (QCA) scheme is based on a cell which contains four quantum dots as

schematically shown in figure (a)

bull The quantum dots are represented by the open circles which indicate the confining electronic potential In

the ideal case each cell is occupied by two electrons (shown as solid dots)

bull P ri n c ip l e o f q u a n t u m d o t c el l T u n n el i n g B e t w e en d o t s amp C o u lo m b i n t er a ct i o n

between electrons

bull The two electrons experience their mutual Coulombic repulsion yet they are constrained to

occupy the quantum dots inside the cell

bull So they placed by hopping between the dots that configuration which corresponds to the

physical ground state of the cell

bull Two electrons will tend to occupy different dots on opposing corners of the cell because of

the Coulomb energy associated with having them on the same dot or bringing them together

closer

bull Figure (a) Schematic diagram of a QCA cell consisting of five

quantum dots and occupied by two electrons



08-11-2013

4

bull Polarization (P=+1 or P=-1)

bull These two configurations may be interpreted as binary information thus encoding bit

values in the electronic arrangement inside a single cell

bull The ground state of an isolated cell is a superposition with equal weight of the two basic

configurations and therefore has a net polarization of zero

Figure (b) The two basic electronic arrangements in the cell

which can be used to represent binary information P = +1 and

P = minus1

bull 12 Cell-cell coupling

bull The two polarization states of the cell will not be energetically equivalent if other cells are nearby

bull The electrons are allowed to tunnel between the dots in the same cell but not between different

cells

1 2

bull Figure shows two cells where the polarization of

cell 1 (P 1) is determined by the polarization of its

neighbor (P 2 )

bull The polarization of cell 2 is presumed to be fixed at

a given value

bull corresponding to a certain arrangement of charges

in cell 2 and this charge distribution exerts its

influence on cell 1 thus determining its polarization

P 1

bull As shown in the figure cell-1 is almost completely polarized even though cell-2 might only be

partially polarized

bull For example a polarization of P 2=01 induces almost perfect polarization in cell 1 ie P 1=099

bull In other words even a small asymmetry of charge in cell-2 is sufficient to break the degeneracy of

the two basic states in cell-1 by energetically favoring one configuration over the other



08-11-2013

5

bull 13 QCA Logic

bull Simple QCA cell logic line where a logic input of 1 gives an logic output of 1

bull This structure could be called a binary wire where a lsquo1rsquo input gives a lsquo1rsquo output

bull All of the electrons occupy positions as far away from their neighbors as possible and they

are all in ground state polarization

bull Flipping the ground state of the cell on the left end will result in a domino effect where each

neighboring cell flips ground states until the end of the wire is reached

bull Inverter Built From QCA Cells The output isrdquo0rdquo when the input is ldquo1rdquo

bull CORNER

bull Information can also flow around corners as shown in figure

bull Fan-Out



08-11-2013

6

bull Majority Gate

bull The QCA topology that can produce AND amp OR gates is called a majority gate Where three input cells ldquo

vote on the polarization of central cell ldquoThe polarization of central cell is then propagated as the output

bull One of the input can be designated a programming input and determines whether the majority gate

produces an AND or an OR If the programming gate is a logic 1 then the result is OR while

programming gate equal to logic 0 would produce a result of AND

A B C Output

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1

bull In other words majority gates may be viewed as programmable AND amp OR gates and

hence the functionality of the gates may be determined by the state of computation itself

bull Computing With QCA

bull For the purpose of quantum computation QCA array can be used

bull In a QCA array cells interact with their neighbors via repulsion (ie coulomb interaction) and

no circuitry or wires are used to connect the interior cells with each other

bull This can over come the drawback of heat dissipation appears in conventional circuits

bull The information in a QCA array is contained in the physical ground state of the system

bull The two key features that characterize this new computing model are

minus Computing with the ground state

minus Edge driven computation



08-11-2013

7

bull Computing With The Ground State

bull Consider a QCA array before the start of a computation

bull The array left to itself will have assumed its physical ground state Presenting the input

data ie setting the polarization of the input cells will deliver energy to the system thus

promoting the array to an excited state

bull In the computation the array reaches the new ground-state configuration according to the

boundary conditions given by the fixed input cells

bull The information is contained in the ground state itself only and not in how the ground state

is reached ie the dynamics of computation

bull But the dynamics of the computation is important for the actual implementation purpose

bull There may be two approaches that can explain computationdynamics

ndash The system is completely left to itself

ndash The system is externally controlled

bull The system is completely left to itself

bull The natural tendency of the system to achieve the ground state may be used to drive the

computation process

bull The interaction of cells (with each other and also with the system) present in the surrounding of the

system try to relax the system from the excited state to the new ground state

bull The actual dynamics will be too complicated because the interactions are uncontrollable

bull There is also a drawback that the system may get stuck in meta stable states it implies that no fixed

time in which a computation is completed

bull The system is externally controlled

bull Adiabatic computing

bull This is accomplished by rising or lowering the potential barrier within the cells in concert with clock

signals

bull This change of potential barriers inhibits or allows the changes of the cell polarization On this basis

pipeline architectureshave been proposed


signals





08-11-2013

8

bull EDGE DRIVEN COMPUTATION

bull Edge-driven computation means that only the periphery of a QCA array can be contacted

which is used to write the input data and to read the output of the computation No internal

cells may be contacted directly

bull This implies that no signals or power can be delivered from the outside to the interior of an

array All interior cells only interact within their local neighborhood The absence of signal and

power lines to each and every interior cell has obvious benefits for the interconnect problem

and the heat dissipation

bull The lack of direct contact to the interior cells also has profound consequences for the way

such arrays can be used for computation Because no power can flow from the outside

interior cells cannot be maintained in a far-from-equilibrium state Because no external signals

are brought to the inside internal cells cannot be influenced directly

bull These are the reasons why the ground state of the whole array is used to represent the

information as opposed to the states of each individual cell In fact edge-driven computation

necessitates computing with the ground state



08-11-2013

9

Single Electron Circuit

bull A single electron circuit (SEC) consists of electronic devices (like transistor

diodes etc) whose working is based on the State change of device due to

presence or absence of a single electron

bull Single electron transistors (SETs) can be used (in principle) in circuit to the

conventional silicon FETs MOSFETs

bull But there are practical problem in using SETs as logic devices in conventional

circuit architectures

bull One of the main problem related to the presence of charges in the surrounding

circuitry which change the SET characteristics in an uncontrollable way because

the SET is sensitive to the charge of one electron So Solution of above

problem is the whole surrounding circuitry must be of same nature ie it must

use all single electron devices

bull Design As schematically shown in Figure the basic building block for SEC logic family consists

of three conducting islands where the middle island is slightly shifted off the line passing through

the centres of the edge island

bull Electrons are allowed to tunnel through small gaps between the middle and edge islands but not

directly between the edge islands (due to their larger spatial separation)

bull Let us assume that each cell can be occupied by one additional

electron and that a clock electric field is applied that initially

pushes this electron onto the middle island (the direction of this

clock field is perpendicular to the line connecting the edge

islands)

bull Now that the electron is located on the central island the clock field is reduced and the electron

eventually changes direction At some point in time during this cycle it will be energetically

favourable for the electron to tunnel- off of the middle island and onto one of the edge islands

bull If both islands are identical the choice of island will be random However this symmetry can be

broken by a small switching field that is applied perpendicular to the clock field and along the line

of the edge cells This control over the leftndashright final position of the electron can be interpreted as

one bit of binary information the electron on the right island might mean logical ldquo1rdquo and the left

island logical ldquo0rdquo



08-11-2013

10

Molecular Circuit

bull Chemical self-assembly processes look promising since they (in principle) allow vast

amounts of devices to be fabricated very cheaply

bull But there are key problems

(1) the need to create complex circuits for computers appears to be ill suited for chemical

self-assembly which yields mostly regular (periodic) structures and

(2) the need to deal with very large numbers of components and to arrange them into useful

structures is a hard problem (NP-hard problem)

bull Molecular circuit is a architectures for Nanoprocessor systems which integrated on the

molecular scale

bull There are some approach to built molecular circuit

bull First

bull One approach to molecular electronics is to build circuits in analogy to conventional

silicon-based electronics The idea is to find molecular analogs of electronic devices

(such as wires diodes transistors etc) and then to assemble these into molecular

circuits

bull Second

bull Another idea of a switch (and related circuitry) at the molecular level is the (mechanical)

concept of an atom relay which was proposed by Wada and coworkers

bull The atom relay is a switching device based upon the controlled motion of a single atom

bull The basic configuration of an atom relay consists of a (conducting) atom wire a switching

atom and a switching gate

bull The operation principle of the atom relay is that the switching atom is displaced from the atom

wire due to an applied electric field on the switching gate (ldquooffrdquo state of the atom relay)

bull Memory cell and logic gates (such as NAND and NOR functions) based on the atom relay

configuration have been proposed and their operation was examined through simulation



08-11-2013

11

bull Transistor

bull A popular group of molecules that can work as the semiconducting channel material in a

molecular transistor is the oligopolyphenylenevinylenes (OPVs) that works by the Coulomb

blockade mechanism when placed between the source and drain electrode in an appropriate

way Fullerenes work by the same mechanism and have also been commonly utilized

bull Wires

bull The sole purpose of molecular wires is to electrically connect different parts of a molecular

electrical circuit As the assembly of these and their connection to a macroscopic circuit is still

not mastered the focus of research in single molecule electronics is primarily on the

functionalized molecules molecular wires are characterized by containing no functional

groups and are hence composed of plain repetitions of a conjugated building block Among

these are the carbon nanotubes that are quite large compared to the other suggestions but

have shown very promising electrical properties

Bra-ket Notation



08-11-2013

12

Quantum superposition

bull The superposition principle plays the most important role in all consideration of quantum

information and in most experiments of quantum mechanics

bull Double slit experiment

bull The essential ingredients of double slit experiment are a source a double slit assembly and an

observation screen on which we observe interference fringes According to



08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT

bull qbit is stands for quantum bit it is the basic unit of information in a quantum computer

same as bit which is the basic unit of information in classical computer

bull In a quantum computer a number of elemental particles such as electrons or photons can

be used with either their charge or polarization acting as a representation of 0 andor 1

bull Each of these particles is known as a qubit the nature and behavior of these particles (as

expressed in quantum theory) form the basis of quantum computing

bull Bit Vs Qbit

bull A bit is the basic unit of computer information Regardless of its physical realization a bit is

always understood to be either a 0 or a 1

bull An analogy to this is a light switch- with the off position representing 0 and the on position

representing 1

bull A qubit has some similarities to a classical bit but is overall very different

bull Like a bit a qubit can have two possible valuesmdashnormally a 0 or a 1 The difference is that

whereas a bit must be either 0 or 1 a qubit can be 0 1 or a superposition of both

bull Quantum superposition refers to the quantum

mechanical property of a particle to occupy all of its

possible quantum states simultaneously

bull Due to this property to completely describe a particle

one must include a description of every possible state

and the probability of the particle being in that state

bull In above figure second row shown the qbit representation of decimal 5 Third row shows the

qbit may represent superposition of decimal 4 and decimal 5



08-11-2013

15

bull Since the Schroumldinger equation is linear a solution that takes into account all possible

states will be a Linear combination of the solutions for each individual state This

mathematical property of linear equations is known as the superposition principle

bull Representation of qbit

bull As is the tradition with any sort of quantum states Dirac or bra-ket notation is used to

represent them This means that the two computational basis states are conventionally

written as and (pronounced ket 0 and ket 1)

bull Qbit states

bull A pure qubit state is a linear superposition of those two states This means that the qubit

can be represented as a linear combination of |0gt and |1gt

bull where α and β are probability amplitudes and can in general both be complex numbers

bull When we measure this qubit in the standard basis the probability of outcome |0gt is | α |2

and the probability of outcome |1gt is | β |2

bull Because the absolute squares of the amplitudes equate to probabilities it follows that α and

β must be represented by the equation



08-11-2013

16

Rough

bull state space of a single qubit register can be represented geometrically by the Bloch

sphere

bull The possible states for a single qubit can be visualised using a

Bloch sphere (see diagram)

bull Represented on such a sphere a classical bit could only be at the

North Pole or the South Pole in the locations where and are

respectively

bull The rest of the surface of the sphere is inaccessible to a classical

bit but a pure qubit state can be represented by any point on the

surface

bull For example the pure qubit state swould lie on the equator of the sphere on the positive y axis

bull The surface of the sphere is two-dimensional space which

represents the state space of the pure qubit statesbull This state space has two local degrees of freedom

bull It might at first sight seem that there should be four degrees of

freedom as α and β are complex numbers with two degrees of

freedom each However one degree of freedom is removed by the

constraint

bull Another the overall phase of the state has no physically observable

consequences so we can arbitrarily choose α to be real leaving just

two degrees of freedom

bull It is possible to put the qubit in a mixed state a statistical

combination of different pure states Mixed states can be

represented by points inside the Bloch sphere



08-11-2013

17

bull Kind of operations

bull There are various kinds of physical operations that can be performed on pure qubit

states

bull Unitary transformation These correspond to rotations of the Bloch sphere

bull Standard basis measurement It is an operation in which information is gained

about the state of the qubit With probability | α |2 the result of the measurement will

be and with probability | β |2 it will be Measurement of the state of the qubit

alters the values of α and β For instance if the state is measured α is changed to

1 (up to phase) and β is changed to 0 Note that a measurement of a qubit state

entangled with another quantum system transforms a pure state into a mixed state

Physical representation



08-11-2013

18

Single qbit transformation (Quantum GATE)Beam splitter

The beam splitter splits the laser into two separate beams and also recombine s the beams after they strike the mirrors



08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE

ndash So we have discussed only single qbit gates that is which involve one bit only

ndash Of greatest importance of q computation applications are two qubit gates where the evolution of one

bit is conditional upon the state of the other qubit so the simplest of these gates is the quantum

controlled NOT gate

ndash the controlled NOT gate (or CNOT) acts on 2 qubits and performs the NOT operation on the second

qubit only when the first qubit is |1gt and otherwise leaves it unchanged It is represented by the

matrix

ndash The action of quantum controlled NOT gate can be described by



08-11-2013

23

bull Controlled Not GATE can be represented by matrix

bull Controlled U GATE

bull if U is a gate that operates on single qubits with matrix representation

QUANTUM CIRCUIT MODEL

bull In quantum information theory a quantum circuit is a model for quantum computation in

which a computation is a sequence of quantum gates And This structure is referred to

as an n-qubit register

bull Proposed Models of quantum computation

1 Quantum Dot Cellular Automata

2 Quantum Gate Array

3 Quantum Turing Machine



08-11-2013

24

bull Quantum gate array

bull Important feature of computer is that they can be programmable so in case of programmable

quantum computer device would have to have the features that

bull It should consist of a fixed gate array with a data register and program register

bull And the array should work in such a way that the state of the program register

emcodes the unitary operator u that is applied to the state of data register

bull So we can say that ldquoQuantum gate array are fixed gate arrays acting on data register and

program register together with a final fixed projective measurement on the composite

systemrdquo

bull Suppose that we are given a quantum system prepared in the same state q and an operator

O by specifying its expansion in a basis of the space of operators so our task is to compute

the expectation value of O in the state q Hence ldquoQuantum gate array is a programmable

circuit that evaluates such expectation values by measuring the polarization of single qubitrdquo

Inputs of such circuits are data register program register and auxiliary qubit

bull QUANTUM TURING MACHINE

bull Turing machine is an idea of computing machine which moved from one state to another using a precise

finite set of rules given by finite table and depending on a single symbol it read from a tape

bull First turing machine which was a hypothetical computer consist of the following

ndash An infinite tape on which symbol may be read or written

ndash The machine travels right or left along the tape following a program

ndash At each step the machine writes to the tape travels either left or right and changes states according

to a set of internal states

ndash The set of symbols and set of internal states are both finite states



08-11-2013

25

Application of quantum mechanical system

bull Quantum CRYPTOGRAPHY

bull Cryptography is the method of hiding the secrate information It is the greek word which means

ldquohidden secraterdquo There are two main tasks of cryptography

bull Encryption

bull Decryption

bull Encryption is the method of converting information from a readable state to nonsense while

decryption is the method of converting the nonsense to the readable state

bull The user retain the ability to decrypt the data or information by the key which is generated at

the time of encryption and therefore by the use of encryption the user can avoid unwanted

person being able to read it

bull The quantum cryptography describes the use of quantum mechanical effects like quantum

communication and quantum computing to perform cryptographic task or to break

cryptographic systems

bull The well known example of quantum cryptography are the use of quantum communication to

secure exchange the key which is known as quantum key distribution and the use of quantum

computes that would allow the breaking of various popular public-key encryption

bull Quantum mechanical computations for simulation

bull The Quantum Mechanical computation systems can also be used on a very large scale

molecular systems to reduce the noise using self consistent field method where self consistent

field method is the method which is used in simulation of molecules to minimize the energy so

that the noise can be minimized

bull In a large molecular system we cannot perform the simulation or computing task because the

energy value of the large molecules is high and therefore with high energy value the large

quantity of noise is also present in the system

bull PROPAGATOR

bull In quantum mechanics and quantum field theory the propagator gives the probability

amplitude for a particle to travel from one place to another in a given time or to travel with a

certain energy and momentum

bull Propagators are used to represent the contribution of virtual particles on the internal lines of

Feynman diagrams



08-11-2013

26

bull Let us take an example for quantum mechanical system application propagate and

cryptography

bull Suppose there are two users John and Mick and John wants to send the secrete information

to Mick then John will first encrypt the data from readable state to nonsense by using a key

which is send via a quantum communication route to Mick

bull This quantum communication route is known as propagator

bull After that the John send the nonsense through any chipper media to Mick

bull After receiving the nonsense Mick will decrypt the information with the help of that key

Superdense coding

bull Suppose Alice wishes to send Bob two classical bits of information

bull Superdense coding is a way of achieving this task over a quantum channel requiring only

that Alice send one qubit to Bob

bull Alice and Bob must initially share the Bell state

bull Suppose Alice is in possession of the first qubit and Bob the second qubit

bull Alice performs one of four 1-qubit gates depending on the 2 classical bits she wishes to

communicate to Bob

bull For convenience we remind you again of the definitions of the Pauli gates



08-11-2013

bull If Alice wishes to send the bits 00 to Bob she does nothing to her qubit (or equivalently

applies the identity gate I )

bull If she wishes to send 01 she applies the X gate to her qubit

bull If she wishes to send 10 she applies the Z gate

bull and if she wishes to send 11 she applies Z 983223 X (ie she applies the X gate followed by the Z

gate)

bull The following list summarizes the resulting joint 2-qubit state in each case

bull The outcome of the Bell measurement reveals to Bob which Bell state he possesses and so

allows him to determine with certainty the two classical bits Alice wanted to communicate to

him The superdense coding protocol is il lustrated in Figure 51



08-11-2013

2

Introduction to Nanocomputer architecture

bull Nanotechnology holds the promise of putting a trillion molecular-scale devices in a square

centimeter How does one assemble a trillion devices per square centimeter Moreover

this needs to be done quickly inexpensively and sufficiently reliably What does one do

with a trillion devices

bull If we assume that one can make them (and they actually work) how can this massive

amount of devices be harnessed for useful computation These questions highlight the

need for innovative nanoelectronic circuit architectures

bull Recent accomplishments include the fabrication of molecular circuits that are capable of

performing logic operations

bull So the Nanocomputer architecture is based on the QCA single electron circuit

molecular circuit ets

Quantum Dot Cellular Automata

bull For the purpose of quantum computing a molecular structural model has been proposed

that utilizes quantum dots is termed as quantum cel lular automata(QCA) in which four

quantum dots in square array are placed in a cell such that electrons are able to tunnel

between the dots but are unable to leave the cell

bull When two excess electrons are placed in the cell coulomb repulsion will force the electron

to occupy dots on opposite corners

bull Two ground states are energetically equivalent and can be labeled logic lsquo1rsquoand lsquo0rsquo

respectivelyFIGURE 1 The two possible ground-state

polarizations denoted ldquo0rdquo and ldquo1rdquo of a four-dot

QCA cell

Flipping the logic state of one cell for instance by applying a negative potential to a lead

near the quantum dot occupied by an electron will result in the next door cell flipping

ground state in order to reduce coulomb repulsion

In this way a line of QCA cells can be used to do computation



08-11-2013

3














between electrons







closer





08-11-2013

4








P = minus1




cells

1 2



neighbor (P 2 )


a given value




P 1


partially polarized






08-11-2013

5

bull 13 QCA Logic








bull CORNER


bull Fan-Out



08-11-2013

6

bull Majority Gate






A B C Output

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1














08-11-2013

7
















computation process









signals




signals





08-11-2013

8


















08-11-2013

9























islands)











08-11-2013

10

Molecular Circuit









molecular scale


bull First




circuits

bull Second












08-11-2013

11

bull Transistor





bull Wires








Bra-ket Notation



08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

3














between electrons







closer





08-11-2013

4








P = minus1




cells

1 2



neighbor (P 2 )


a given value




P 1


partially polarized






08-11-2013

5

bull 13 QCA Logic








bull CORNER


bull Fan-Out



08-11-2013

6

bull Majority Gate






A B C Output

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1














08-11-2013

7
















computation process









signals




signals





08-11-2013

8


















08-11-2013

9























islands)











08-11-2013

10

Molecular Circuit









molecular scale


bull First




circuits

bull Second












08-11-2013

11

bull Transistor





bull Wires








Bra-ket Notation



08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

4








P = minus1




cells

1 2



neighbor (P 2 )


a given value




P 1


partially polarized






08-11-2013

5

bull 13 QCA Logic








bull CORNER


bull Fan-Out



08-11-2013

6

bull Majority Gate






A B C Output

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1














08-11-2013

7
















computation process









signals




signals





08-11-2013

8


















08-11-2013

9























islands)











08-11-2013

10

Molecular Circuit









molecular scale


bull First




circuits

bull Second












08-11-2013

11

bull Transistor





bull Wires








Bra-ket Notation



08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

5

bull 13 QCA Logic








bull CORNER


bull Fan-Out



08-11-2013

6

bull Majority Gate






A B C Output

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1














08-11-2013

7
















computation process









signals




signals





08-11-2013

8


















08-11-2013

9























islands)











08-11-2013

10

Molecular Circuit









molecular scale


bull First




circuits

bull Second












08-11-2013

11

bull Transistor





bull Wires








Bra-ket Notation



08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

6

bull Majority Gate






A B C Output

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1














08-11-2013

7
















computation process









signals




signals





08-11-2013

8


















08-11-2013

9























islands)











08-11-2013

10

Molecular Circuit









molecular scale


bull First




circuits

bull Second












08-11-2013

11

bull Transistor





bull Wires








Bra-ket Notation



08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

7
















computation process









signals




signals





08-11-2013

8


















08-11-2013

9























islands)











08-11-2013

10

Molecular Circuit









molecular scale


bull First




circuits

bull Second












08-11-2013

11

bull Transistor





bull Wires








Bra-ket Notation



08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

8


















08-11-2013

9























islands)











08-11-2013

10

Molecular Circuit









molecular scale


bull First




circuits

bull Second












08-11-2013

11

bull Transistor





bull Wires








Bra-ket Notation



08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

9























islands)











08-11-2013

10

Molecular Circuit









molecular scale


bull First




circuits

bull Second












08-11-2013

11

bull Transistor





bull Wires








Bra-ket Notation



08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

10

Molecular Circuit









molecular scale


bull First




circuits

bull Second












08-11-2013

11

bull Transistor





bull Wires








Bra-ket Notation



08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

11

bull Transistor





bull Wires








Bra-ket Notation



08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

12









08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

13



08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

14

Q-bitsbull QUBIT







bull Bit Vs Qbit




representing 1














08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

15








bull Qbit states










08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

16

Rough


sphere





respectively



surface







constraint









08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

17



states











08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

18





08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

19



08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

20

Phase Shifter



08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

21

Quantum GATE



08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

22

Controlled GATE




controlled NOT gate



matrix




08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

23














08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

24









systemrdquo

















08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

25





bull Encryption

bull Decryption




















bull PROPAGATOR





Feynman diagrams



08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013

26


cryptography







Superdense coding







communicate to Bob




08-11-2013






gate)







08-11-2013






gate)





Nanoelectronics and Nanophotonics_MNT-301 UNIT-3_(GGCT.pdf

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