THEORETICAL APPROACH TO MOLECULAR LEVEL QUANTUM COMPUTING full report
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quantum computing.docx (Size: 170.68 KB / Downloads: 84) A THEORETICAL APPROACH TO MOLECULAR LEVEL QUANTUM COMPUTING ABSTRACT: In this paper we are extending the boundaries of quantum registers which forms the basis for future quantum computing. The atomic excitation and relaxation paves the way for replacing the old conventional bits by qubits. Our paper elaborates the idea of implementing the molecular transistors without affecting molecular coherent property, which will be a pathway to the quantum computer castle, using nitrogen induced diamond as a temporary RAM. The experimental behavior of aluminium nano tubes and napthalocyanine makes the quantum processor to be fit for complex algorithms which cannot be processed by classical computers. Presented By: A.ABDUL KAREEM, A.HAJI MOHAMED, KCET, CUDDALORE I . INTRODUCTION The history of computer technology has involved a sequence of changes from one type of physical realization to another from gears to relays to valves to transistors to integrated circuits and so on. Todayâ„¢s advanced lithographic techniques can create chips with features only a fraction of micron wide. Soon they will yield even smaller parts and inevitably reach a point where logic gates are so small that they are made out of only a handful of atoms. On the atomic scale matter obeys the rules of quantum mechanics, which are quite different from the classical rules that determine the properties of conventional logic gates. So if computers are to become smaller in the future, new, quantum technology must replace or supplement what we have now. The point is, however, that quantum technology can offer much more than cramming more and more bits to silicon and multiplying the clockspeed of microprocessors. It can support entirely new kind of computation with qualitatively new algorithms based on quantum principles. Today simple quantum logic gates involving two qubits are being realized in laboratories. Current experiments range from trapped ions via atoms in an array of potential wells created by a pattern of crossed laser beams to electrons in semiconductors. The next decade should bring control over several qubits and, without any doubt, we shall already begin to benefit from our new way of harnessing nature. Shrinking size of a computer II.RUDIMENTARY QUBIT Quantum computing stores information in quantum states, which can be one, zero, or some probability of one and zero, called a superposition state. The value of a socalled qubits is not known until it is measured, whereupon it returns definite one or a zero. Bit versus qubit These so called qubits, are implemented using quantum mechanical two state systems; these are not confined to their two basic states but can also exist in superposition. A quantum mechanics property known as "quantum entanglement," says that a qubit can actually be in more than one state at once, which enhances the speed and performance of a quantum processor exponentially. From a physical point of view a bit is a physical system which can be prepared in one of the two different states representing two logical values  no or yes, false or true, or simply 0 or 1. Any classical register composed of three bits can store in a given moment of time only one out of eight different numbers. A quantum register composed of three qubits can store in a given moment of time all eight numbers in a quantum superposition. Once the register is prepared in a superposition of different numbers we can perform operations on all of them. The states presented so far, where each bit or higherlevel construct has a definite value, apply both to classical and quantum computers. However, quantum computers have a far richer set of possible states. Specifically, if are the possible states for a classical computer, the possible states of the corresponding quantum computer are all linear superpositions of these states, i.e., states of the form where is a complex number called the amplitude associated with the state . The physical interpretation of the amplitudes comes from the measurement process. When a measurement is made on the quantum computer in state , e.g., to determine the result of the computation represented by a particular configuration of the bits in a register, one of the possible classical states is obtained. Specifically, the classical state is obtained with probability . Furthermore, the measurement process changes the state of the computer to exactly match the result. That is, the measurement is said to collapse the original superposition to the new superposition consisting of the single classical state (i.e., the amplitude of the returned state is 1 and all other amplitudes are zero). This means repeated measurements will always return the same result. Quantum register  popular illustration of the idea III.THE THEORY OF QUANTUM COMPUTERS The key to quantum computing is the ability to manipulate and maintain quantum states. Unfortunately, these quantum states are hard to create, hard to manipulate, and very, very hard to stabilize. Quantum computers can perform many different calculations in parallel. A system with n qubits can perform 2n calculations at once. This has impact on the execution time and memory required in the process of computation and determines the efficiency of algorithms. De waveâ„¢s 16 bit quantum computer One of the interesting property of a quantum computer is coherence, which means that the states of multiple qubits change together at the same rate. Finally, the qubits are entangled, which means that the probability values of one qubit are correlated the values of other qubits. Changes to one qubit are reflected by changes to others and the measurement of one qubit restricts the values of the rest. If information is stored the value of one bit was correlated to that of another bit, then several algorithms will run faster than their classical counterparts. In case of algorithms for finding prime factors of large numbers, simulating quantum systems, and certain types of database searches. Thus the Quantum computing is a very hot topic in the world of physics at the moment because, for the first time, we can actually contemplate the sort of control required to make a quantum computer. It happens to also be true that a truly scalable quantum computer would have applications in the real world as wellâ€code breaking, and simulating quantum systems are two common examples. Functional quantum computers can be built, they will be valuable in factoring large numbers, and therefore extremely useful for decoding and encoding secret information Quantum computers are implemented along the same lines as classical computers. In principle we know how to build a quantum computer; we start with simple quantum logic gates and connect them up into quantum networks. A quantum logic gate, like a classical gate, is a very simple computing device that performs one elementary quantum operation, usually on two qubits, in a given time. Of course, quantum logic gates differ from their classical counterparts in that they can create and perform operations on quantum superpositions. The more interacting qubits are involved, the harder it tends to be the interaction that would display the quantum properties. The more components there are, the more likely it is that quantum information will spread outside the quantum computer and be lost into the environment, thus spoiling the computation. This process is called decoherence. Thus our task is to engineer submicroscopic systems in which qubits affect each other but not the environment. IV.SUPERPOSITION Superposition is not itself an observable quantity. Nevertheless, by changing the amplitude associated with different classical states, operations on the superposition can affect the probability with which various states are observed. This possibility is crucial for exploiting quantum computation, and makes it potentially more powerful than probabilistic classical machines, in which some choices in the program are made randomly. An important consequence of this interpretation results from the fact that probabilities must sum to one. Thus the amplitudes of any superposition of states must satisfy the normalization condition. The basic distinguishing feature of a quantum computer [2, 4, 11, 12, 18, 19, 29, 31, 35, 48, 51] is its ability to operate simultaneously on a collection of classical states, thus potentially performing many operations in the time a classical computer would do just one. Alternatively, this quantum parallelism can be viewed as a large parallel computer requiring no more hardware than that needed for a single processor. On the other hand, the range of allowable operations is rather limited. These superpositions can also be viewed as vectors in a space whose basis is the individual classical states and is the component of the vector along the i basis element of the space. Such a state vector can also be specified by its components as when the basis is understood from context. The inner product of two such vectors is where denotes the complex conjugate of . In matrix notation, this can also be written as where is treated as a column vector and is a row vector given by the transpose of with all entries changed to their complex conjugate values. For these vectors, the normalization condition amounts to requiring that . A two dimensional vector space of superpositions for a quantum bit. There are a number of proposals for implementing quantum bits, i.e., devices whose quantum mechanical properties can be controlled to produce desired superpositions of two classical values. superposition illustration A device consisting of n quantum bits allows for operations on superpositions of classical states. This ability to operate simultaneously on an exponentially large number of states with just a linear number of bits is the basis for quantum parallelism. A two dimensional vector space of superpositions for a quantum bit. There are a number of proposals for implementing quantum bits, i.e., devices whose quantum mechanical properties can be controlled to produce desired superpositions of two classical values. To complete this overview of quantum computers, it remains to describe how superpositions can be used within a program. There are two types of operations that can be performed on a superposition of states. Â¢ The first type is to run classical programs on the machine, and Â¢ The second allows for creating and manipulating the amplitudes of a superposition. In both these cases, the key property of the superposition is its linearity: an operation on a superposition of states gives the superposition of that operation acting on each of those states individually. As described below, this property, combined with the normalization condition, greatly limits the range of physically realizable operations. V.OPERATION A quantum computer can perform a classical program provided it is reversible, i.e., the final state contains enough information to recover the initial state. One way to achieve this is to retain the initial input as part of the output. To illustrate the linearity of operations, consider some reversible classical computation on these states, e.g., which produces a new state from a given input one. When applied to a superposition of states, the result is . Why is reversibility required Suppose the procedure f is not reversible, i.e., it maps at least two distinct states to the same result. For example, suppose . Then for the superposition linearity requires that giving , a superposition that violates the normalization condition. Thus this irreversible classical operation is not physically realizable on a superposition, i.e., it cannot be used with quantum parallelism. In contrast to this use of computations on individual states, the second type of operation modifies the amplitude of various states within a superposition. That is, starting from the operation, denoted by U, creates a new superposition . Because the operations are linear with respect to superpositions, the new amplitudes can be expressed in terms of the original ones by , or in matrix notation by . That is, linearity means that an operation changing the amplitudes can be represented as a matrix. To satisfy the normalization condition, Eq. 2, this matrix must be such that . In terms of the matrix U this condition becomes which must hold for any initial state vector with . To see what this implies about the matrix , suppose is the j unit vector, corresponding to the superposition where all amplitudes are zero except for . In this case which must equal one by Eq. 3. That is, the diagonal elements of must all be equal to one. For with , This must equal one by Eq. 3, and we already know that the diagonal terms equal one. Thus we conclude . A similar argument using , a superposition with an imaginary value for the second amplitude, gives . Together these conditions mean that A is the identity matrix, so , i.e., the matrix U must be unitary to operate on superpositions. Moreover, this condition is sufficient to make any initial state satisfy Eq. 3. This shows how the restriction to linear unitary operations arises directly from the linearity of quantum mechanics and Eq. 2, the normalization condition for probabilities. The class of unitary matrices includes permutations, rotations and arbitrary phase changes (i.e., diagonal matrices where each element on the diagonal is a complex number with magnitude equal to one). First quantum processor Reversible classical programs, unitary operations on the superpositions and the measurement process are the basic ingredients used to construct a program for a quantum computer. As used in the search algorithm described below, such a program consists of first preparing an initial superposition of states, operating on those states with a series of unitary matrices in conjunction with a classical program to evaluate the consistency of various states with respect to the search requirements, and then making a measurement to obtain a definite final answer. The amplitudes of the superposition just before the measurement is made determine the probability of obtaining a solution. The overall structure is a probabilistic Monte Carlo computation in which at each trial there is some probability to get a solution, but no guarantee. This means the search method is incomplete: it can find a solution if one exists but can never guarantee a solution doesn't exist. VI.ATOMIC REVOLUTION Atomicscale devices might be used as future computer chips, storage devices, sensors and for applications nobody has imagined yet. A. Magnetic anisotropy in individual atoms Anisotropy is an important property for data storage because it determines whether a magnet can maintain a specific orientation or not. This in turn allows the magnet to represent either a 1 or 0, which is the basis for storing data in computers. Two potential realizations for quantum bits based on nanometrescale magnetic particles of large spin S and highanisotropy molecular clusters. The bitvalue basis states 0 and 1 are the ground and first excited spin states Sz = S and S1, separated by an energy gap given by the ferromagnetic resonance frequency. When there is significant tunnelling through the anisotropy barrier, the qubit states correspond to the symmetric, 0 , and antisymmetric, 1 , combinations of the twofold degenerate ground state Sz = Ã‚Â±S. In each case the temperature of operation must be low compared to the energy gap, , between the states 0 and 1 . The gap in this can be controlled with an external magnetic field perpendicular to the easy axis of the molecular cluster. The states of different molecular clusters and magnetic particles may be entangled by connecting them by superconducting lines with Josephson switches, leading to the potential for quantum computing hardware. This fundamental measurement has important technological consequences because it determines an atomâ„¢s ability to store information. Previously, nobody had been able to measure the magnetic anisotropy of a single atom. Such a storage capability would enable nearly 30,000 feature length movies or the entire contents of YouTube â€œ millions of videos estimated to be more than 1,000 trillion bits of data â€œ to fit in a device the size of an iPod. Perhaps more importantly, the breakthrough could lead to new kinds of structures and devices that are so small they could be applied to entire new fields and disciplines beyond traditional computing. B. Molecular switches Switches inside computer chips act like a light switch to turn the flow of electrons on and off and, when put together, make up the logic gates, which in turn make up electrical circuits. Having ever smaller switches allows the circuits to be shrunk to ever smaller sizes, making it possible to pack more circuits into a processor and boosting speed and performance. Singlemolecule switch that can operate flawlessly without disrupting the molecule's outer frame , a significant step toward building computing elements at the molecular scale that are vastly smaller, faster and use less energy than today's computer chips and memory devices In addition to switching within a single molecule atoms inside one molecule can be used to switch atoms in an adjacent molecule, representing a rudimentary logic element. This is made possible partly because the molecular framework is not disturbed. switching within single molecules, but the molecules would change their shape when switching, making them unsuitable for building logic gates for computer chips or memory elements. The ability to switch a single molecule on and off, a basic element of computer logic, using two hydrogen atoms within a naphthalocyanine organic molecule. Napthalocyanine These molecular switches could one day lead to computer chips with speeds as fast as today's fastest supercomputers, but much smaller in size; with some speculating even building computer chips so small they could be the size of a speck of dust or fit on the tip of a needle. C.Molecular transistor Determining how a quantum transistor stacks up against a traditional electronic one in terms of performance is however considerably harder because of how the two paradigms differ as its "quantum superposition" can't be directly translated into a precise number of 01 or 10 transactions in standard electronics. By using a laser beam to impose the quantum state of a molecular transistor, It is demonstrated to control a second laser beam, which reflects the way in which a conventional transistor works. To connect two molecules in a way that the quantum mechanical superposition state of each molecule is exchanged in a coherent manner. Only that way the strength of the quantum computing principles can be fully taken advantage of. Singlemolecule optical transistor generates almost negligible amount of heat. When a single molecule absorbs one photon, there is some probability (quantum yield) that the molecule emits a photon out. The rest of the energy absorbed turns into heat in the matrix. For the case of the specific hydrocarbon molecule that we use, the quantum yield is near 100%. So almost no heat is generated VII. IDENTIFYING QUANTUM MEMORY Development of conventional siliconbased CMOS chips is approaching its physical limits, and the IT industry is exploring new, truly disruptive technologies to achieve further increases in computer performance. Modular molecular logic is a possible candidate, though still several years from reality. The next step is to build a series of these molecules into a circuit, then figure out how to network those together into a molecular chip. The individual molecules serving as switches or memory elements have been demonstrated to date. Most of these molecules are complex, threedimensional structures and change their shape when switching. Placing them on a surface while maintaining their function is extremely difficult, making them unsuitable as building blocks for computer logic. The switching within the molecule is welldefined, highlylocalized, reversible, intrinsic to the molecule, and does not involve changes in the molecular frame. Therefore, this molecule could be used as a building block for more complex molecular devices that serve as logic elements. As the shape of the molecule does not change during switching, single switches can be coupled in a controlled way. The switching process should also work with molecules embedded in more complex structures. The screening various molecules to discover that it would be suitable for molecular switches, in the case of naphthalocyanine, the tests being performed were not to observe switching but rather to examine molecular vibrations, since understanding vibrations of molecules is important for devices operating at the atomic level. During those tests, team members were surprised to observe results that were intriguing for switching at the molecular scale, and they shifted their focus from studying vibrations to studying switching, leading to this breakthrough. VIII. DIAMOND A DYNAMIC RAM Diamond is supposed to be a material made purely of carbon. Each carbon atom attaches itself to four other carbon atoms that sit at the apexes of an imaginary pyramid. However, if nitrogen is introduced during growth, it will become incorporated into the diamond. But nitrogen can only attach to three carbon atoms, so associated with every nitrogen is a gap where a carbon atom would normally sit. These vacancies distort the electronic structure of diamond so that each vacancy is associated with an electron that is free to move around the neighboring atoms. Moreover, that electron is more strongly coupled to the nuclear states of the surrounding atoms, meaning that, manipulating the state of the electron, then placing a nucleus in a welldefined state is made possible. Diamond crystal The mobility of the electrons, using them to act as a local communications channel between qubits. The qubits used are the spin orientation of two C13 nuclei that happened to be adjacent to a vacancy. Manipulating the state of the electron associated with the vacancy using microwaves, and then watching for the radio frequency response of the adjacent nuclei. It will be able to entangle the two nuclei in a controlled manner and, perhaps more surprisingly, that entanglement lasted for milliseconds. Furthermore, it was also possible to entangle the electron with the two nuclei; that threeway entanglement lasts for a few hundred microseconds. In diamond which is a pure carbon , the qubit state can be transfered to photonic qubits, then it should be possible to scale the entanglement up so that it can involve more than a single nitrogen vacancyâ€having the entanglement lasts for milliseconds helps in this regard. Furthermore, qubits based on nitrogen vacancies aren't too hard to scale, since it is a solidstate materialâ€no vacuum pumps required. The longevity of the entanglement should also enable the development of a refreshable quantum RAM. Opertion of a quantum processor IX. CONCLUSION Quantum computers harnessing the unusual rules of quantum mechanics, the principles governing nature's smallest particles might be used for applications such as fast and efficient code breaking, optimizing complex systems such as airline schedules, making counterfeitproof money, and solving complex mathematical problems. Quantum information technology in general allows for customdesigned systems for fundamental tests of quantum physics and asyetunknown futuristic applications. Quantum computers could also be used to search large databases in a fraction of the time that it would take a conventional computer. ACKNOWLEDGMENT Our sincere thanks to our senior professor Dr. Immanuvel .H for giving us a lot of encouragement on doing this project and implimentation. REFERENCES Nick Herbert 1985 quantum relativity beyond the new physics . D.Bhom and B.J.Hiley the undivided universe 1996. RobertM.White.Quantum theory of magnetism 2002. Wolf Gang YourGrav and Alwyn van Der.Morve perspectives in quantum theory. Ira N Levine Quantum Chemistry Fourth edition. Atam.P.Arya Fundamentals of Atomic Physics 2005. 



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