PPT QUANTCOMP

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Overview Limit of todays Computer architecture

What is Quantum Computing ?

When will Quantum Computers be available ?

What comes after Quantum Computing ?

How does Quantum Computing Work ?

Projected benefits of Quantum Computing

Projected risks of Quantum Computing

Conclusion

Quantum ComputingAnd Quantum Computers

Why Quantum Computing ?

Quantum AlgorithmsQuantum Circuits

Quantum Gates

Todays Quantum Computers


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Theres a joke about personalcomputers that has been around since theycame in the market : You buy a newcomputer, take it home and just as youfinish unpacking it you see anadvertisement for a new computer thatmakes yours obsolete.

Speed has always been one ofthe prime objectives to be improved. Andweve moved from vaccume tubes totransistors to reduce the size and increasethe performance.

If you make a chart of the evolution of the computer in terms of processingpower, you would see that progress has been exponential. The man who first madethis famous observation is Gordon Moore, a co-founder of the microprocessor

company Intel.

Limit of todays Computer Architecture



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Moores observation is thatthe number of transistors on a 1-inch(2.5 centimeter) diameter of siliconchip doubles every 18 or 24 months.Its said to be a law but its more likean observation.

Even a small microprocessor chip today is as powerful as a full-sized chip was a few years ago. Advancements in circuit productionmake devices like smart phones and notebooks possible.

While Moore's originalobservation focused on technologicaladvances and the economics behindproducing circuits.

Thousands of transistors vs. years



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Just compare the very primitive computers and todays.

It means by making the semiconductor devices smaller, we can mountmore number of them in the same chip and implement more logic on the samechip and hence can get more processing power from the same sized chip. And

till today, we've keep doing that to increase the processing power ofmicroprocessors. But now we've already reduced the size of the devices tosuch an extent that its almost impossible to reduce the size further.

The current computer structure is beginning to reach its limits. Whatwill happen in next 20 years if processor development continues to supportMoores observation. The year 2020 or 2030 will find the circuits on a

microprocessor measured on an atomic scale.

ENIAC (1946) Todays Computers



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In the search for ever smaller and faster computational devices, and theresearches on computational power of biological systems such as the brain, oneis naturally led to consider the possibility of computational devices of the size ofcells, molecules, atoms, or of even smaller scales.

Why Quantum Computing ?

It has been pointed out that if trends over the last fortyyears continue, we may reach atomic-scale computation by theyear 2010. Transistors with gate lengths of 10nm can alreadybe fabricated.

Wave-like quantum properties of electrons becomeimportant on this length scale.

Transistors switchable by a single electron predicted by2015 or so.

Physicist Paul

The history of computer technology has involved a sequence of changesfrom one type of physical realization to another --- from gears to relays to valves totransistors to integrated circuits and so on. Quantum computing is the next logicaladvancement.

At such scales, quantum effects become importantwhether we want them or not. The natural laws that govern the

behavior of particles on extremely small scales.



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How is Quantum Mechanics different ? A classical system is always (in principle) in a definite state; we just

have to specify which one. We consider or want a classical bit to be in either 1 or0 state. The state of a quantum system can involve many different possibilities

simultaneously. Quantum bit or qubit is 0 and 1 simultaneously, superpositionof both.Quantum Mechanics and kets notation

Ket notation is mathematical representation of state of the quantum system.

Basis kets represent a complete set ofpossible states for system

Basis vectors represent a complete setof possible directions

x y r i j

Compare a two-dimensional vector:



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What is Quantum Computing ?

QC can be defined as a device for

computation that makes direct use of quantummechanical phenomena, such as superpositionand entanglement, to perform operations on data.The basic principle behind quantum computationis that quantum properties can be used torepresent data and perform operations on thesedata.

The Bloch Sphere

In the classical model of a computer themost fundamental building block, the bit, can onlyexist in one of two distinct states, a '0' or a '1'. Ina quantum computer the rules are changed. Not

only can a 'quantum bit', usually referred to as aqubit, exist in the classical '0' and '1' states, but it can also be in a superposition of both!In this coherent state, the bit exists as a '0' and a '1' in a manner which may at firstseem hard to accept. Let's consider a register of three classical bits: it would bepossible to use this register to represent any one of the numbers from 0 to 7 atany one time. If we then consider a register of three qubits, we can see that if each

bit is in the superposition or coherent state, the register can represent all thenumbers from 0 to 7 simultaneously!

Not 0 or 1 but 0 and 1.the superposition principle



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A processor that can use registers of qubits will in effect be able toperform calculations using all the possible values of the input registerssimultaneously. This phenomenon is called quantum parallelism, and is themotivating force behind the research being carried out in quantum computing.

Classical bit: 0 or 1Quantum bit: 0 1 Superposition of 0 and 1

(qubits)

A quantum computer performs manipulations on information representedas quantum bits, just as a classical computer performs manipulations on informationrepresented as classical bits.

If we consider a register of 3 classical bits, it would be possible torepresent the numbers from 0 to 7 at any one time.

000 , 001 , 010 , 011 , 100 , 101 , 110 , 111

Specifying general classical state requires three binary numbers

000 001 010 011 100 101 110 111a b c d e f g h Specifying general quantum state of N qubits requires 2

N numbers:



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How does Quantum Computing work ?

The qubit is the quantum analogue of the bit, the classical fundamental unitof information. It is a mathematical object with specific properties that can berealized physically in many different ways as an actual physical system. Just as theclassical bit has a state (either 0 or 1), a qubit also has a state. Yet contrary to theclassical bit, 0 and 1 are but two possible states of the qubit, and any linearcombination (superposition) thereof is also physically possible. In general, thus, thephysical state of a qubit is the superposition = 0 + 1 (where and arecomplex numbers). The state of a qubit can be described as a vector in a two-dimensional Hilbert space, a complex vector space . The special states 0 and 1are known as the computational basis states, and form an orthonormal basis for thisvector space. According to quantum theory, when we try to measure the qubit in thisbasis in order to determine its state, we get either 0 with probability or 1with probability . Since + = 1 (i.e., the qubit is a unit vector in theaforementioned two-dimensional Hilbert state), we may (ignoring the overall phasefactor) effectively write its state as = cos() 0 + e isin() 1 , where thenumbers and define a point on the unit three-dimensional sphere, as shownhere. This sphere is often called the Bloch sphere, and it provides a useful means tovisualize the state of a single qubit.

The Qubit



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Quantum Gates

The CNOT gate

Classical computational gates are Boolean logic gates that performmanipulations of the information stored in the bits.

In quantum computing these gates are represented by matrices, and canbe visualized as rotations of the quantum state on the Bloch sphere. As in the case of classical computing, where there exists a universal gate

(the combinations of which can be used to compute any computable function),namely, the NAND gate which results from performing an AND gate and then aNOT gate, in quantum computing it was shown (Barenco et al. , 1995) that any

multiple qubit logic gate may be composed from a quantum CNOT gate (whichoperates on a multiple qubit by flipping or preserving the target bit given the stateof the control bit, an operation analogous to the classical XOR , i.e., the exclusiveOR gate) and single qubit gates.

One feature of quantum gates that distinguishes them from classicalgates is that they are reversible: the inverse of a unitary matrix is also a unitary

matrix, and thus a quantum gate can always be inverted by another quantum gate.


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Quantum circuits are similar to classical computer circuits in that theyconsist of wires and logical gates . The wires are used to carry the information,

while the gates manipulate it (note that the wires do not correspond tophysical wires; they may

Quantum Circuits

correspond to a physical particle, aphoton, moving from one location toanother in space, or even to time-evolution). Conventionally, the input ofthe quantum circuit is assumed to be acomputational basis state, usually thestate consisting of all. The output stateof the circuit is then measured in thecomputational basis, or in any otherarbitrary orthonormal basis. The firstquantum algorithms (i.e. Deutsch-Jozsa,Simon, Shor and Grover) wereconstructed in this paradigm. Additionalparadigms for

quantum computing exist today that differ from the quantum circuit model in manyinteresting ways. So far, however, they all have been demonstrated to becomputationally equivalent to the circuit model, in the sense that anycomputational problem that can be solved by the circuit model can be solved bythese new models with only a polynomial overhead in computational resources.

D-WAVE Quantum Processor


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Quantum Algorithms Algorithm design is a highly complicated task, and in quantum

computing it becomes even more complicated due to the attempts to harnessquantum mechanical features to reduce the complexity of computationalproblems and to "speed-up" computation. Before attacking this problem, weshould first convince ourselves that quantum computers can be harnessed toperform standard, classical, computation without any "speed-up".

In some sense this is obvious, given the belief in the universal characterof quantum mechanics, and the observation that any quantum computation that isdiagonal in the computational basis, i.e., involves no interference between thequbits, is effectively classical.

Yet the demonstration that quantum circuits can be used to simulateclassical circuits is not straightforward. Indeed, quantum circuits cannot be useddirectly to simulate classical computation, but the latter can still be simulated on aquantum computer using an intermediate gate, namely the Toffoli gate.

This gate has three input bits and three output bits, two of which arecontrol bits, unaffected by the action of the gate. The third bit is a target bit that isflipped if both control bits are set to 1, and otherwise is left alone. This gate isreversible (its inverse is itself), and can be used to simulate all the elements ofthe classical irreversible circuit with a reversible one. Consequently, using thequantum version of the Toffoli gate one can simulate, although rather tediously,

irreversible classical logic gates with quantum reversible ones. Quantumcomputers are thus capable of performing any computation which a classical


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It has been shown in theory that a quantum computer will be able toperform any task that a classical computer can. However, this does notnecessarily mean that a quantum computer will outperform a classical computerfor all types of task. If we use our classical algorithms on a quantum computer, itwill simply perform the calculation in a similar manner to a classical computer. Inorder for a quantum computer to show its superiority, it needs to use newalgorithms which can exploit the phenomenon of quantum parallelism.


One of the embarrassments ofquantum computing is the fact that, so far, onlyone algorithm has been discovered, namelyShor's, for which a quantum computer issignificantly faster than any known classicalone. It is almost certain that one of the reasonsfor this scarcity of quantum algorithms is

related to the lack of our understanding of whatmakes a quantum computer quantum.

Shors algorithm

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Projected benefits of Quantum ComputingThis new conceptualization of computing power will result in three main

benefits :Increase in computing power

Advances in security Artificial IntelligenceThe sci-fi concept of teleportation.

Each of these opportunities can overcome the limitations of the currentcomputational concept.

Quantum Computation : increase in computing power

Utilizing quantum parallelism, quantum computers will well serve thepurpose of performing difficult mathematical calculations that are impossible using

semiconductor computers. Quantum Cryptology : advances in security

The expected capabilities of quantum computation promise greatimprovements in the world of cryptography. Ironically the same technology alsoposes current cryptography techniques a world of problems. The ability to break

the RSA coding system will render almost all current channels of communicationinsecure.


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The theories of quantum computation suggest that every physical object,even the universe, is in some sense a quantum computer. Ultimately thissuggests that computers will be capable of simulating conscious rational thought,maybe the quantum computer will be the key to achieving true artificialintelligence.

Artificial Intelligence

Teleportation

Teleportation is the capability to make an object or a person disintegratein one place while a perfect replica appears in another.

In physics, teleportation has never been taken seriously because of theuncertainty principle. According to the uncertainty principle, the duplicatingprocess will disturb or destroy the original objects; the more an object isduplicated, the more it is destroyed.

The detail information regarding how the duplication is made and how

the original object is destroyed is unknown. Therefore, it will reach a point whereone cannot extract enough information from the original to make a perfect replica.

However, scientists at IBM and elsewhere have discovered a way tomake a perfect replica using a distinctive feature of quantum mechanics calledEPR (Einstein-Podolsky-Rosen) effect.

Quantum computing provides at least a theoretical basis forteleportation.


Quantum Computing


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Projected Risks\Disadvantages of Quantum Computing Conceptually, it is believed that with quantum technology we will be able

to build microscopic machines such as a nanoassembler, a virtually universalconstructor that will not just take materials apart and rebuild them atom by atombut also replicate itself.

The bad news is that these HAL-like computing brains with capabilitiesexceeding those of humans, could redesign and replicate themselves at no cost,other than the loss of human dominance.

It sounds as terrifying as those scenarios in a science fiction film :TERMINATOR.


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Todays Quantum Computers

The technology needed to build a quantum computer is currently beyond ourreach. This is due to the fact that the coherent state, fundamental to a quantum computersoperation, is destroyed as soon as it is measurably affected by its environment. Attempts atcombating this problem have had little success, but the hunt for a practical solutioncontinues. Key technical challenge: prevent decoherence , or unwanted interaction with

environment Approaches: NMR, ion trap, quantum dot, Josephson junction, optical

The most advanced quantum computers have not gone beyond manipulating morethan 16 qubits, meaning that they are a far cry from practical application. Several keyadvancements have been made in quantum computing in the last few years.

1998 Los Alamos and MIT researchers managed to spread a single qubit across threenuclear spins in each molecule of a liquid solution of alanine (an amino acid used to analyzequantum state decay) or trichloroethylene (a chlorinated hydrocarbon used for quantumerror correction) molecules.

After that, there were several QCs developed from 3 to 12 qubits till 2006 by the scientists ofdifferent countries. 2007 Canadian startup company D-Wave demonstrated a 16-qubit quantum computer.The computer solved a Sudoku puzzle and other pattern matching problems. The companyclaims it will produce practical systems by 2008. Skeptics believe practical quantumcomputers are still decades away, that the system D-Wave has created isn't scalable.

Quantum computers must have at least several dozen qubits to be able to solve

real-world problems, and thus serve as a viable computing method.


Quantum Computing


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What comes after Quantum Computing ?

Once scientists can use atoms to complete complex computations, theday when a computer will be the size of 1 atom. These new machines can bedeployed in ways that are not available today. For example, a nanomachine can bebuilt and programmed to enter human cells to fight diseases or even resuscitatethose who have just died. Yet, this approach will not be available until scientists canmanipulate atoms using the quantum physics approaches of entanglement andsuperposition. In addition to smaller machines, scientistsalso claim that computers can now be stored incarbon-based beings, within DNA. Scientists havelong known that DNA could store information. Butonly when Charles Bennett, in 1973, drew attentionto the computational capability that is responsiblefor processing genetic information in DNA didresearchers begin to recognize the potential of abiological computer.

However, DNA computing is based on thefoundation of quantum computing : ability tomanipulate atoms.

DNA molecule

Quantum Computing


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Although the future of quantum

computing looks promising, we have only justtaken our first steps to actually realizing aquantum computer. There are many hurdleswhich need to be overcome before we can beginto appreciate the benefits they may deliver.Researchers around the world are racing to be

the first to achieve a practical system, a taskwhich some scientists think is futile..In comparison the progress in quantum

communications has been somewhat morefruitful. Companies like BT have actuallyachieved working

Conclusions


systems that are able to use quantum effects to detect eavesdropping on achannel. Whether or not such systems will prove practical remains to be seen.

Can we really build a useful quantum computer?

Who knows; in a quantum world, anything is possible!

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