International Journal of Scientific Engineering and Applied Science (IJSEAS) - Volume-1, Issue-6, September 2015 ISSN: 2395-3470 www.ijseas.com
Understanding Quantum Computing
Dr. K J Sarma, SMIEEE; Dept of Humanities and Mathematics & Academic cell Malla Reddy Engineering College (Autonomous ), Secunderabad, India,
Abstract: It has been decided that Quantum estimated number of atoms in the universe and Computing (Q.C.) should be pursued, as it this enormous potential computational power is would be one of the priority research areas of the well worth harvesting.” M.A. Nielsen and I.L. future having a potential for computational Chuang [ 26 ] technology development and growth. Hence there is a need to motivate and involve The digital computers operate with the help of youngsters in research activity related to transistors. Digital computers require data to be quantum computing. There is a need to keep the encoded into binary digits (bits), each of which youngsters informed of the what, why, where, is always in one of two definite states (0 or 1), when, how of quantum computing. A review and the memory is made up of the bits. The of the origin and the progress of the binary digits for data encoding quantum developments in Quantum Computing is made computation uses qubits (quantum bits), which In this paper the author tried to review various can be in super-positions of states. aspects of the Quantum Computing like A Quantum Turing machine [40] is a theoretical Architecture, Operating system, Infrastructure model of such a computer, and is also known as required if any, links with other computing the universal quantum computer. Quantum technologies, Uses, Examples, Theoretical & computers share theoretical similarities with non Practical and class-room Applications, - deterministic and probabilistic computers. In Challenges, Algorithms, Security issues and other words a quantum Turing machine (QTM), Future trends. also a universal quantum computer, is an abstract machine used to model the effect of Key words: Quantum computing, Quantum a quantum computer. It provides a very simple mechanics, qubit, quantum information, model, which captures all of the power of quantum mechanics, Richard Feynman. quantum computation. Any quantum algorithm can be expressed formally as a 1. Introduction particular quantum Turing machine. Such Turing machines were first proposed in a Quantum computing is one of the hottest topics 1985 paper written by Oxford of 21 st century. This is a computational process University physicist David that uses the quantum mechanical phenomenon Deutsch suggesting quantum gates could different from the usual digital computers. function in a similar fashion to traditional digital Quantum computing studies computing with binary logic gates[41]. theoretical computation systems that make direct use of quantum-mechanical phenomena, Quantum Turing machines are not always used such as superposition and entanglement, to for analyzing quantum computation. perform operations on data. The quantum circuit is a more common model. “ It is very interesting and well worth noting, These models are computationally equivalent. that a quantum system of 500 qubits already Quantum Turing machines can be related to requires 2 500 amplitudes to fully describe its classical and probabilistic Turing machines in a quantum state. This number is larger than the framework based on transition matrices, shown
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by Lance Fortnow [42]. Iriyama et. al have been great developments in VLSI designs since developed a model of a Linear Quantum Turing the introduction of valve technology. In recent Machine (LQTM). This is a generalization of a times along with the thinking of optimization of classical QTM that has mixed states and that performance greater miniaturization of the allows irreversible transition functions. These systems also took a big leap [18]. It seems the allow the representation of quantum miniaturization has almost reached saturation. measurements without classical outcomes [43]. Also if transistors are reduced in size further it A quantum Turing machine with post would hinder the research in quantum selection was defined by Scott Aaronson, who mechanics. to hinder their performance. One showed that the class of polynomial time on must pay greater attention on this limitation as such a machine is equal to the classical Quantum computers share theoretical complexity class PP [44]. similarities with non-deterministic and probabilistic computers. This is similar to the The field of quantum computing was initiated by ability to be in more than one state the work of Yuri Manin in 1980, [2] Richard simultaneously. It may be noted that the field Feynman in 1982 [22], and David Deutsch [41]. of quantum computing was first introduced by A quantum computer with spins as quantum bits Richard Feynman in 1982 [22]. The Nobel was also formulated for use as a quantum space– prize-winning physicist Richard Feynman time in 1968. Experiments have been carried out thought of the idea of a 'quantum computer', a in which quantum computational operations computer that uses the effects of quantum were executed on a very small number of mechanics to its advantage as early as in qubits. Both practical and theoretical research 1982 [22]. For quite good length of time, the continues in an effort to develop notion of a quantum computer was primarily of quantum computers for civilian, business, trade, theoretical interest only. In the recent times and national security purposes, such quantum computers have received more as cryptanalysis. attention. This interest may also be due to the Large-scale quantum computers will be able to invention of an algorithm to factor large solve certain problems much more quickly than numbers, on a quantum computer, by Peter Shor any classical computers that use even the best (Bell Laboratories). By the use of this currently known algorithms, like integer algorithm, quantum computer is able to crack factorization using Shor's algorithm [30] or codes much more quickly than any ordinary the simulation of quantum many-body systems. computer. It is reported that quantum computer There are quantum algorithms, such as Simon's is capable of performing Shor's algorithm [ 24 ] algorithm, that run faster than any possible and is able to break current cryptography probabilistic classical algorithm.[8] When techniques in a matter of seconds. sufficient computational facility is available a classical computer could be made to simulate It is expected that Quantum computers will any quantum algorithm, as quantum someday replace silicon chips, just like the computation does not violate the Church–Turing transistor replaced the vacuum tube. It seems at thesis. the moment the technology required to develop such a quantum computer may take sufficiently 2. History & Genesis Of Quantum long time. In fact most research in quantum computing remained theoretical. The most Computers: advanced quantum computers have not gone 3. beyond manipulating more than 16 qubits,; In the following we trace the origin and the meaning that they are a far away from practical genesis of Quantum Computing. There have applications. But is expected that someday the 371
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quantum computers could perform faster Shor's Algorithm is a method for finding the calculations, which are time-consuming on prime factors of numbers (which plays an conventional computers. Many advancements intrinsic role in cryptography). The scientists of have been made in quantum computing in the IBM in 2001 used a 7-qubit computer to find the last few years. We would learn of some of the factors of 15 [24]. The computer correctly developments in research on quantum deduced that the prime factors were 3 and 5. computers. The scientists at the Institute of Optics in 2005, created the first qubyte or series of 8 qubits, In 1998 Los Alamos and MIT researchers using ion traps. managed to spread a single qubit across three nuclear spins in each molecule of a liquid In 2006 Scientists in Waterloo and solution of alkaline (an amino acid used to Massachusetts devised methods for quantum analyze quantum state or trichloro-ethylene (a control on a 12-qubit system and Quantum chlorinated hydrocarbon used for quantum error control becomes more complex as systems correction) molecules. Investigators used the employ more qubits. idea of entanglement, to study interactions The computer developed in 2007 by D-Wave between states as an indirect method for demonstrated a 16-qubit quantum computer analyzing the quantum information. which is used to solve Sudoku puzzle and other The quantum computer uses nuclear magnetic pattern matching problems. The D - Wave resonance (NMR) to manipulate particles in the Company claimed to produce practical systems atomic nuclei of molecules of trans-crotonic by 2008. But some of the pessimists believed acid, a simple fluid consisting of molecules that the practical quantum computers are still made up of six hydrogen and four carbon atoms. decades away. Also the system designed by D- The NMR is used to apply Wave is not scale-able, and that many of the electromagnetic pulses, which force the particles claims on D-Wave's Web site are simply to line up. These particles in positions parallel or impossible. The name quantum comes due to counter to the magnetic field allow the quantum quantum mechanics in its inner workings. So the computer to mimic the information-encoding name is not from the problems it is solving, but of bits in digital computers. This work was how it is solving them. carried out in 2000 March. The scientists at Los Alamos National Laboratory announced the There are several limitations on the computers. development of a 7-qubit quantum computer What they can and cannot depend on the laws within a single drop of liquid. of physics that governs them. The truely In August 2000 [47], the 5-qubit quantum fundamental laws of the universe are still not computer was designed to allow the nuclei of known. five fluorine atoms to interact with each other as The use of Deutschian [24] closed time like qubits and can be programmed by radio curve (D-CTC) is a form of time travel that (at frequency pulses and be detected by NMR least naively) appears to be allowed by general instruments similar to those used in hospitals. relativity. David Deutsch [18] suggested a Led by Dr. Isaac Chuang, the IBM team was version of these that preserves causality (think able to solve in one step a mathematical problem 12 monkeys - you can travel in time, but you that would take conventional computers repeated can't actually alter the past). Scott Aaronson and cycles. The problem of order-finding, involved John Watrous [2, 45] wrote an interesting paper finding the period of a particular function, a discussing the type of problems a computer built typical aspect of many mathematical problems with D - CTC could solve efficiently. It's related to cryptography. fascinating to see the interaction between computer science and the frontier of physics. 372
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A quantum computer maintains a sequence The contemporary way of 'generating', QC is to of qubits. A single qubit can represent a one, a take probabilistic computing, which allows zero, or any quantum superposition of those complex-valued probabilities, and require that two qubit states. A pair of qubits can be in any the L- 2 norm [55] of the probabilities sums to 1 quantum superposition of 4 states, and three rather than the L-1 norm. qubits in any superposition of 8 states. In general, a quantum computer with n qubits can It is believed that if a functional quantum be in an arbitrary superposition of up computers can be built, it may be valuable in to 2n different states simultaneously. This factoring large numbers. This may be compares to a normal computer that can only be extremely useful for decoding and encoding in one of these 2n states at any one time. secret information. Further such a system designed may bring revolutionary changes like, A qubit or quantum bit is a unit of quantum no information on the Internet would remain information - the quantum analogue of the safe. The currently available encryption classical bit. A qubit is a two-state quantum- procedures are simple, compared to the mechanical system, such as the polarization of a complicated methods of quantum computers. It single photon where the two states are vertical is thought that Quantum computers could also be polarization and horizontal polarization. In a used to search large databases in a fraction of classical system, a bit would have to be in one conventional computer time. It is expected that state or the other. However quantum mechanics quantum computers can be used to study several allows the qubit to be in a superposition of both issues related to quantum mechanics. states at the same time, a property which is It is well-known that quantum computing is fundamental to quantum computing. still in its early stages of development. Many The concept of the qubit was unknowingly scientists believe that the technology needed to introduced by Stephen Wiesner in 1983, in his create a practical quantum computer may take proposal for un-forgeable quantum money, sufficiently long time as Quantum computers which he had tried to publish for over a decade. must have at least several dozen qubits to be The coining of the term "qubit" is attributed able to solve real-world problems. to Benjamin Schumacher [46]. In the acknowledgments of his work, Schumacher states that the term qubit was invented in jest due to its phonological resemblance with an ancient unit of length called cubit, during a conversation with William Wootters. He described a way of compressing states emitted by a quantum source of information so that they require fewer physical resources to store. This procedure is now known as Schumacher compression. The bit is the basic unit of information. It is used to represent information by computers. Irrespective of the physical realization, a bit has two possible states typically thought of as 0 and 1, but more generally - and according to applications - interpretable as true and false, 4. Fundamental Aspects: night and day, or any other dichotomous choice. An analogy to this is a light switch - it’s off 373
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position can be thought of as 0 and it’s on position as 1. A qubit has a few similarities to a classical bit, but is overall very different. There are two possible outcomes for the measurement of a qubit—usually 0 and 1, like a bit. The difference is that whereas the state of a bit is either 0 or 1, the state of a qubit can also be a superposition of both [47]. It is possible to fully encode one bit in one qubit. However a qubit can hold even more information, for example up to two bits using Super-dense coding. One firm based at Cambridge believes that the The two states in which a qubit may be software will aid the commercialization of the measured are known as basis states (or emerging technology further, facilitating users basis vectors). As is the tradition with any sort in controlling the operations a quantum of quantum states, they are represented by Dirac computer can perform. - or "bra–ket"- notation. This means that the two computational basis states are conventionally QUBIT CONTROL: Microscopic particles can written as |0› and | 1› (pronounced "ket be programmed to control qubits in quantum 0" and "ket 1"). computers by using control devices. Ion traps use optical or magnetic fields (or a Qubit states: A quantum computer operates by combination of both) to trap ions. Optical setting the qubits in a controlled initial state that traps use light waves to trap and control represents the problem at hand and by particles. Quantum dots, made of manipulating those qubits with a fixed sequence semiconductor material and are used to of quantum logic gates. The sequence of gates to manipulate electrons. Semiconductor be applied is called a quantum algorithm. The impurities containing electrons are controlled by calculation ends with a measurement, collapsing using "unwanted" atoms found in semiconductor the system of qubits into one of the 2n pure material. Superconducting circuits allow states, where each qubit is zero or one. The electrons to flow with almost no resistance at outcome can therefore be at the most n classical very low temperatures [53]. bits of information. Quantum algorithms are Each qubit can assumes a wide range of values, often non-deterministic, in that they provide the and a moderate number of them can hold an correct solution only with a some known insane quantity of information. probability. Just 100 qubits can store 1,267,650,600,228,229,401,496,703,205,375 Quantum computers replace traditional bits that different numbers - many trillion times the are used in digital communications with storage capacity of all computers ever made. In quantum bits, or qubits. Potential applications other words, 100 qubits can simultaneously can be found in a variety of fields including represent all possible 100-bit numbers in their medicine and space missions. Qubits exist in a huge quantum state, unlike classical 100-bit state of superposition, meaning they can be in computer, which can represent just one. both states at once, rather than restricted to This vast ability means that quantum computers either binary state as traditional bits function. can provide immense power, many times faster than any classical computer.
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5. Definition The Quantum [50]. One of the problems quantum computers is that if one tries to look at the sub-atomic : Computer particles, which could bump them, and thereby The Turing machine, developed by Alan change their value. If he looks at a qubit in Turing in the 1930s, is a theoretical device superposition to determine its value, the qubit consisting of tape of unlimited length that is will assume the value of either 0 or 1, but not divided into small squares. Each square can both (similar to digital computer). In order to either hold a symbol (1 or 0) or be left blank. A make a practical quantum computer, scientists read-write device reads these symbols and have to devise ways of making measurements blanks giving the machine its instructions to indirectly to preserve the system's integrity. perform a certain program. In the case of a Entanglement provides a potential answer. In quantum turing machine the tape exists in a quantum physics, if one applies an outside quantum state, as does the read-write head. This force to two atoms, it can cause them to become means that the symbols on the tape can be either entangled, and the second atom can take on the 0 or 1 or a superposition of 0 and 1. In other properties of the first atom. So if left alone, an words the symbols are both 0 and 1 and all atom will spin in all directions. The instant it is points in between. While a normal Turing disturbed it chooses one spin, or one value At machine can only perform one calculation at a the same time, the second entangled atom will time, a quantum Turing machine can perform choose an opposite spin, or value. This allows many calculations at one go. scientists to know the value of the qubits without
actually looking at them. Today's computers, like a Turing machine work by manipulating bits that exist in one of the two states a 0 or a 1. Quantum computers aren't 6. Architecture: limited to two states; they encode information as quantum bits, or qubits, which can exist in A Layered framework for the quantum superposition. Qubits represent atoms, ions, computer Architecture is given below. photons or electrons and their respective control devices that are working together to act as computer memory and a processor. A quantum computer has the potential to be millions of times more powerful than today's most powerful supercomputers due to multiple figure-1 states. The superposition of qubits is what gives A review of the progress that has been made in quantum computers their inherent parallelism. developing architectures of quantum computing, According to physicist David Deutsch [48], this quantum computers is available [14, 53 ]. The parallelism allows a quantum computer to work highlight is the process of integrating the basic on a million computations at one go. A 30- elements that have already been developed, and qubit quantum computer would be equal to the introducing the challenges remain in delivering processing power of a conventional computer on the promise of quantum computing. that could run at 10 teraflops ( i.e. trillions of The most famous development to date in floating-point operations per second). Today's quantum algorithms is Shor's algorithm for typical desktop computers run at speeds factoring large numbers in polynomial time. measured in gigaflops (i.e. billions of floating- While the vernacular press often talks of point operations per second). factoring large numbers "in seconds", using a Quantum computers also utilize another aspect quantum computer. But in reality it is not of quantum mechanics known as entanglement possible to discuss the prospective performance of a system without knowing the physical and 375
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logical clock speed. The topology of the computer architecture must solve. Given the interconnect among the elements; the number of fragility of quantum data, how many qubits be logical quantum bits (qubits) is available in the kept "alive" long enough to complete a complex system, and the details of the algorithmic computation? The solution to this problem is implementation is given without specifying the the field of quantum error correction (QEC), architecture. Figure 1 illustrates the impact that began with studies demonstrating that arbitrarily architecture can have on the bottom-line accurate computation is theoretically possible viability of a quantum computer. The even with imperfect systems, but our concern architecture used can make the difference here is the design of subsystems for executing between an interesting and an immediate threat QEC, which can be called the quantum to all RSA ( due to Ron Rivest, Adi Shamir, computer micro- architecture. Recent progress and Leonard Adleman ) encryption processes. in experimentally demonstrated in building In developing a quantum computer architecture blocks and the implementation of QEC which we have much to learn from classical computer are the first two topics addressed in this article. architecture,. Foremost among these caveats is that the delicate nature of quantum information At the top of the stack, machines will be demands that memory elements be very active. designed for specific workloads, to run certain Second, long wires or long-distance connections algorithms that exist and computational inside a quantum computer are either complexity classes are believed to be nonexistent, requiring nearest neighbor, cellular inaccessible to classical computers. Without automaton-like transfer of data, or are at best these algorithms, there will be no economic poor quality, requiring much effort to transfer incentive to build and deploy machines. even a single qubit from place to place, using With context established at both the top and quantum teleportation and error management bottom of the stack, the progress that has been techniques. Thus, the principles of classical made toward integrated architectures, and a computer architecture can be applied, but the detailed example of the immense scale-up in size answers arrived at will differ from classical and slowdown in speed arising from the error architectures. correction needs of a full-scale investigation of Quantum computer architecture as a field digital quantum computer. We note that the remains in its infancy, but carries much promise process of writing this article has been made for producing machines that vastly exceed substantially easier by the appearance in the last current classical capabilities, for certain systems few years of excellent reviews on architecture. designed to solve certain problems. As we begin to design larger quantum computers, it 7. Developments must be recognized that large systems are not simply larger versions of small systems. The There are a number of quantum computing conceptual stack of subfields that must all models, distinguished by the basic elements in contribute to a scalable, real-world machine is which the computation is decomposed. The four divided into a set of layers where in the main models of practical importance are elements of this structure in turn, all leading to developed only in recent times. the central core of quantum computer a. The quantum gate array (computation architecture have been discussed. decomposed into sequence of few-qubit At the bottom of the stack we have the quantum gates), technologies for storing individual qubits, and b. The one-way quantum computer processing or transporting them to take part in a (computation decomposed into sequence larger computation. How small groups of qubits of one-qubit measurements applied to a will interconnect is the first problem quantum 376
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highly entangled initial state is called f. Solid-state NMR Kane quantum cluster state), computers (qubit realized by the nuclear c. The adiabatic quantum computer (i.e. spin state of phosphorus donors in computation decomposed into a slow silicon), continuous transformation of an initial g. Electrons-on-helium quantum Hamiltonian into a final Hamiltonian, computers (qubit is the electron spin), whose ground states contains the h. Cavity quantum electrodynamics solution), and (CQED) (qubit provided by the internal d. The topological quantum computer state of atoms trapped in coupled high- (computation decomposed into the finesse cavities), braiding of anyone in a 2D lattice). i. Molecular magnet Fullerene-based ESR quantum computer (where in qubit is The Quantum Turing machine is at theoretical based on the electronic spin of atoms or level but direct implementation of this model is molecules encased in fullerene yet to receive sufficient attention. All four structures), models of computation proved to be equivalent j. Optics-based quantum computer called to each other in the sense, that each can simulate Quantum optics (qubits realized by the other with no more than polynomial appropriate states of different modes of overhead. Of course many researchers are the electromagnetic field), pursuing practical implementing a quantum k. Diamond-based quantum computer (in computer\ using the models mentioned which qubit is realized by the electronic (depending on the physical system used to or nuclear spin of Nitrogen-vacancy realize the qubits): centers in diamond), a. Superconductor-based quantum l. Bose–Einstein condensate-based computers (including SQUID-based quantum computer. quantum computers) qubit implemented m. Transistor-based quantum computer – by the state of small superconducting string quantum computers with circuits (Josephson junctions). entrainment of positive holes using an b. Trapped ion quantum computer (qubit electrostatic trap, implemented by the internal state of n. Rare-earth-metal-ion-doped inorganic trapped ions), crystal based quantum computers (qubit c. Optical lattices (qubit implemented by realized by the internal electronic state internal states of neutral atoms trapped of dopants in optical fibers), in an optical lattice), electrically defined o. The large number of candidates or self-assembled quantum dots ( see demonstrates that the topic, in spite of Loss-DiVincenzo quantum computer ), rapid progress, is still in its infancy. But where in qubit given by the spin states at the same time, there is also a vast of an electron is trapped in the quantum amount of flexibility. dot), In 2005, researchers at Michigan built a d. Quantum dot charge is based on semiconductor chip that functioned as an ion semiconductor quantum computer (qubit trap. Such devices, produced by standard is the position of an electron inside a lithography techniques, may point the way to double quantum dot). scalable quantum computing tools. An improved e. Nuclear magnetic resonance on version was prepared in 2006. molecules in solution is a liquid-state In 2009, researchers at Yale University created NMR (qubit is provided by nuclear the first rudimentary solid-state quantum spins within the dissolved molecule), processor. The two-qubit superconducting chip 377
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was able to run elementary algorithms. Each of agreement to purchase a D-Wave-1 system. the two artificial atoms (or qubits) were made up Lockheed Martin and the University of Southern of a billion aluminum atoms but they acted like a California (USC). An agreement was made to single one that could occupy two different house the D-Wave- One Adiabatic Quantum energy states. Computer at the newly formed USC Lockheed Another team, working at the University of Martin Quantum Computing Center, part of Bristol, also created a silicon-based quantum USC's Information Sciences Institute campus in computing chip, based on quantum optics. The Marina del Rey. team was able to run Shor's algorithm on the During the same year, researchers working at the chip. Further developments were made in 2010. University of Bristol created an all-bulk optics Springer publishes a journal ("Quantum system which is able to run an iterative version Information Processing") devoted to the subject. of Shor's algorithm. They successfully managed In April 2011, a team of scientists from to factorize 21. Australia and Japan have finally made a In September 2011 researchers also proved that breakthrough in quantum called teleportation. a quantum computer can be made with Von They have successfully transferred a complex Neumann architecture (separation of RAM). set of quantum data with full transmission In 2012 IBM scientists said that they have made integrity achieved. Also if the qubits are several breakthroughs in quantum computing destroyed in one place, but instantaneously that put them "on the cusp of building systems resurrected in another, without affecting their that will take computing to a whole new level." super-positions. In April 2012 a multinational team of researchers from the University of Southern California, Delft University of Technology, the Iowa State University of Science and Technology, and the University of California, Santa Barbara, constructed a two-qubit quantum computer on a crystal of diamond doped with some manner of impurity, that can easily be scaled up in size and functionality at room temperature. Two logical qubit directions of electron spin and nitrogen kernels spin were used. A system which formed an impulse of microwave radiation of certain duration and the form was developed for the maintenance of protection against de-coherence. By means of
this computer Grover's algorithm for four Photograph of a chip constructed by D-Wave variants of search has generated the right answer Systems Inc., mounted on wire-bonded in a from the first trial in 95% of cases. sample holder. The D-Wave processor is designed to use 128 superconducting logic elements that exhibit controllable and tunable 8. Quantum Information And coupling to perform operations. Quantum Computing: In 2011, D-Wave Systems announced the first The research effort of exploring the commercial quantum annealer on the market by consequences of quantum mechanics for the name D-Wave One. The company claims information and computation began with that this system uses a 128 qubit processor Feynman's 1982 [ 22 ], proposal to build a chipset. In May 2011 D-Wave announced that computer that takes advantage of quantum Lockheed Martin Corporation entered into an 378
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mechanics has grown enormously since Peter size of the input). Specifically it takes time and Shor's 1994 [24 ] quantum factoring algorithm. quantum gates of order Extensive experimental and theoretical research O((log N)2(log log N)(log log log N)) efforts to build a quantum computer, have been using fast multiplication, demonstrating that the responsible in investigations related to quantum integer factorization problem can be efficiently information and quantum computing solved on a quantum computer and is thus in the complexity class is in BQP. This is Quantum Algorithms and Complexity: If a substantially faster than the most efficient perfectly functioning quantum computer were known classical factoring algorithm, the general built, which problems could it solve faster than number field sieve, which works in sub- conventional computers, and which problems do exponential time is about not admit any speedup? It studies complexity O (e1.9 (log N)1/3 (log log N)2/3). classes defined using quantum computers and The efficiency of Shor's algorithm is due to the quantum information which are computational efficiency of the quantum Fourier transform, models based on quantum mechanics. It studies and modular exponentiation by repeated the hardness of problems in relation to these squaring. complexity classes, and the relationship between Quantum Information theory: How can we quantum complexity classes and classical (i.e., communicate and compute using quantum non-quantum) complexity classes. information in the presence of noise? What are A complexity class is a collection of problems the properties of entanglement? which can be solved by some computational Measurement and Control: How can quantum model under resource constraints. For instance, information be useful in applications apart from the complexity class P is defined to be the set of computers and communication devices, such as problems solvable by a Turing clocks and precision measurements? machine in polynomial time. Similarly, one may Applications and Connections: How can ideas define a quantum complexity class using a from QI / QC contribute to areas as diverse as quantum model of computation,. Thus, the convex optimization, black holes and complexity class BQP is defined to be the set of condensed-matter physics? Quantum problems solvable by a quantum computer in Information and Quantum Computing Theory ( polynomial time with bounded error. QI & QC ) research at Center for Theoretical Two important quantum complexity classes Research ( CTR) of MIT. are BQP and QMA which are the bounded-error quantum analogues of P and NP. One of the Some of the notable contributions of theoretical main aims of quantum complexity theory is to physics group include the Quantum Adiabatic find out where these classes lie with respect to Algorithm and Quantum Walk Algorithms. classical complexity classes such as P, Efficient protocols for simulating quantum NP, PP, PSPACE and other complexity classes. channels (Harrow, Shor) and algorithms and Shor's algorithm, named after hardness results for testing entanglement mathematician Peter Shor, [24] is a quantum (Harrow) [52] have been carried out. An algorithm (an algorithm that runs on a quantum ongoing research at MIT in QI & QC includes computer) for integer factorization formulated in work on new quantum algorithms, efficient 1994. It solves the following problem: Given an simulations of quantum systems, connections to integer N, find its prime factors. convex optimization, understanding the role of de-coherence in excitonic transport (e.g. in On a quantum computer, to factor an integer N, photosynthesis) and many other topics. Some Shor's algorithm runs in polynomial time (the universities also included Quantum information time taken is polynomial in log N, which is the 379
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is included into the curriculum with a junior lab bounds. The speed with which it completes experiment on NMR quantum computing [56] . complex tasks when compared to regular PCs is one of the biggest advantages it brings. The 9. Operating System working of quantum computer means The first operating system for a quantum accomplishing simultaneous error detection of computer has been developed by researchers two quantum errors. which is signal for a significant step towards creating a practical version of the ultra powerful Researchers are working on significant machines. An operating system was developed activities to develop quantum computing by Cambridge Quantum Computing Lab technology that might enable the development of (CQCL), using a proprietary custom designed a Superfast quantum computer, though there has high speed supercomputer which accurately been less work done in the development of an simulates a quantum processor. Operating System that might control the quantum computers. It will have profound and The development of new OS “t | ket > “ is a far-reaching effects on a vast number of aspects major milestone. This OS has been facilitated of our daily lives. In the course of Polishing by CQCL's own proprietary custom designed Quantum Computing CQCL's new operating high-speed super computer and this allowed the system for the quantum computer comes almost company to accurately mimic how a quantum at the same time along with IBM; who brought processor will work. us even closer to a working with Superfast A quantum computer takes advantage of quantum computer by discovering a new method quantum interference. Consequently creating an for correcting two errors that a quantum immense advantage in improving computer can make. computational speed over conventional computers. This is also capable of carrying out One of the biggest issues that prevent us from massive parallel computations simultaneously. developing Superfast Quantum Computers is — It has significant applications for the global Quantum computing is greatly fragile. Even the economy, including financial markets, slightest fault can cause a major error to the insurance, intelligence, cyber-security, internet, computer. However, IBM researchers have medicinal and pharmaceutical research, defense, discovered a new way to detect both types of energy, database management, logistics and quantum computer errors, and revealed a new, communications. square quantum bit circuit design. IBM said it can be easily scaled up to make high- Quantum computing may be a reality much performance computers, according to the details earlier than originally anticipated. It will have published in Nature Communications. profound and far-reaching effects on a vast number of aspects of our daily lives. It is Traditional computers use the "bits" to represent expected that Quantum computers may be information as a 0 or a 1; therefore they are so holding revolutionary potential in a variety of much slower. On the other hand, Quantum fields due to their immense processing power. computers use "qubits" (quantum bits) to Governments, companies and organizations are represent information as a 0, 1, or both at the currently developing the technology in the belief same time. The major problem with qubits is that it could be the future of computing. that they sometimes flip without warning.
Working QC is getting closer: Even though it Qubits can suddenly flip from 0 to 1, which is can be extremely expensive, Quantum called a bit flip, or from 0+1 to 0-1, which is computing has been coming on leaps and called a phase flip. These flips are the actual 380
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culprits that create all kinds of errors. IBM's Although the speed does not seem very quantum circuit, consisting of four impressive, considering the inherent parallelism superconducting qubits on a one-quarter inch of each cubit gate, the overall processing speed square chip, allowing investigators to detect is likely to be very high. bit-flip as well as phase-flip quantum errors simultaneously. http://thehackernews.com/2015/05/os-quantum- 11. Future Of Quantum Computing computing.html#sthash.ovzDVYk1.dpuf.
It may be noted that, IBM has made greater 10. Comparison With Other progress with its simultaneous error detection to Technologies make a working quantum computer will be a Quantum Computing promises extraordinary reality in near future . CQC gave a report that computational speed for special class of the developments could affect our lives in a problems. Like DNA computing, quantum larger way when quantum computing will be a computing is suitable for problems that require reality [47]. massive parallel processing. Qubit is the equivalent of a bit in classical The massive amount of processing power computers. Two qubits can represent the generated by computer manufacturers and information in four different states, namely 00, algorithms developers has not yet been able to 01, 10 and 11. The difference from the classical quench our thirst for speed and computing computer becomes apparent when it comes to capacity. In 1947, Computer engineer Howard processing information. In a classical computer Aiken said that just six electronic one would need to enter these states to the digital computers would satisfy the computing digital system to get outputs one by one. In a needs of the United States. Some authors have quantum computer, all states enter the system made similar predictions about the amount of simultaneously and all outputs are generated at computing power that would support our the same time i.e. simultaneously. The outputs growing technological needs. It is reported that generated are in a superposed state and all Aiken didn't count on the large amounts of data available at the same time. generated by scientific research, the proliferation The power of quantum computing becomes of personal computers or the emergence of apparent when one considers large number of the Internet, which have only fueled our need for input qubits. Quantum gates can be connected more and more computing power. back to back and turned on and off to implement The number of transistors on complicated operations. Currently, there are only a microprocessor continues to double every 18 few problems that can take advantage of the months. By the year 2020, we may find the massive parallelism of quantum computers. circuits on a microprocessor which can be Computing with quantum computers require measured on an atomic scale. The next step initialization, processing and reading of cubits. will be to create to quantum computers is that Currently there are more than one way of they will harness the power of atoms and realizing cubits in hardware and this is likely to molecules to perform memory and processing increase in the near future. tasks. The currently available speed of a spin cubit Quantum computers are expected to have the gate made in silicon structure is in the order of potential to perform certain calculations 102 sec. and external operations dealing with significantly faster, than any silicon-based cubits require 105 sec. Linear density of cubits computer. We know that computers have been in semiconductors is currently 65 nm 14. around for the majority of the 20th century.
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Quantum computing was first theorized in less than 30 years ago, by a physicist at the Argonne National Laboratory. Paul Benioff is credited with first applying quantum theory to computers in 1981. Benioff theorized about creating a quantum Turing machine. The performance and quantum nature of the D- Wave-2 processor continues to be a topic of discussion with every new data release, and the performance figures that Google released in January-2014. The key question at the heart of the D-Wave is whether or not the system is actually performing quantum annealing. Theoretically, the D-Wave-2 processor could be a relatively According to Google, this sparse connectivity good simulation of a quantum computer. It may that’s allowing classical computers to keep pace be the best simulation ever built — but still, an with D-Wave’s quantum system. The company approximation of what the real thing would offer writes that, “For each solver, there are problems is yet to be perceived. The only way to for which the classical solver wins or at least determine whether or not the D-Wave performs achieves similar performance. But the inverse is true quantum annealing is to find a test case in also true. For each classical solver, there are which the D-Wave-2 performs far more better problems for which the hardware does much than the classical computers. better.” There are 9 ways quantum computing will The D-Wave - 2 is limited by what’s called change everything: “sparse connectivity,” as shown below. Lev Grossman [53] says that D-Wave’s machines are “so radical and strange, people are It may be noted that while each sub-group of still trying to figure out what it’s for and how to eight qubits is tightly linked to its adjacent use it.”. partners, the blocks themselves connect in far We live in the commercial age of Big Data, fewer places. Thus the limitation on the burying ourselves in information. We search performance of the quantum is annealed as it queries, genomes, credit-card purchases, phone limits the number of states that the quantum records, retail transactions, social media, computer can test. This is a separate problem geological surveys, climate data, surveillance from the number of qubits in the system (up to videos, movie recommendations and D-Wave 509 out of a possible 512 in this machine) . It’s just happens to be selling “a very shiny new an issue of how interconnected the 509 shovel.” functional qubits are. Technology will bring radical changes for the following areas, to name a few: 1. Safer airplanes—Lockheed Martin plans to use its D-Wave to test jet software that is currently too complex for classical computers. 2. Discover distant planets—Quantum computers will be able to analyze the vast amount of data collected by telescopes and seek out Earth-like planets. 3. Win elections— Campaigners will comb through reams of marketing information to best exploit individual 382
International Journal of Scientific Engineering and Applied Science (IJSEAS) - Volume-1, Issue-6, September 2015 ISSN: 2395-3470 www.ijseas.com
voter preferences. 4. Boost GDP—Hyper- unit of information but every parallel processing personalized advertising, based on quantum unit too. computation, will stimulate consumer spending. 5. Detect cancer earlier—Computational The physicist Ivan Deutsch has the task for the models will help determine how diseases past 20 years in designing the guts of a develop. 6. Help automobiles drive quantum computer. In a great Quanta Q&A he themselves—Google is using a quantum offered some hope in the form of old-school computer to design software that can distinguish computing: quantum simulations, not quite the cars from landmarks. 7. Reduce weather- real deal, but immensely powerful nonetheless. related deaths—Precision forecasting will give The key component is what Deutsch [19] calls people more time to take cover. 8. Cut back on the “qubit.” It’s a complete atom rather than a travel time—Sophisticated analysis of traffic single electron or other fundamental particle. It patterns in the air and on the ground will operates in a sort of fake or simulated quantum forestall bottlenecks and snarls. 9. Develop superposition in which it’s allowed to occupy more effective drugs—By mapping amino one of 16 different states, represented by energy acids, for example, or analyzing DNA- levels. Deutsch explanation using a full atom of sequencing data, doctors will discover and 16 possibilities is a fundamentally different than design superior drug-based treatments. a computer using the classical bit (on or off) or Quantum computing uses strange subatomic the quantum qubit (on and off). behavior to exponentially speed up processing. It could be a revolution, or it could be wishful 12. Limitations And Challenges For thinking. D- wave developers say that Quantum computers could represent an Quantum Simulators: The evolution of the analog simulation is not enormous new source of computing power--it digitized and the software cannot correct the has the potential to solve problems that would tiny errors which accumulate during the take conventional computers centuries, with calculation so we should error-correct noise on revolutionary consequences for fields ranging a universal machine. The analog device must from cryptography to nanotechnology, keep a quantum superposition intact long pharmaceuticals to artificial intelligence. enough for the simulation to run its course Of course Michael Byrne [57], on his article on without resorting to digital error correction. This “ The Near-Term Future Of Quantum is believed as a challenge for the analog Computing? Analog Simulations” also feels the approach to quantum simulation. progress in quantum computing is slow.
Physicists have performed quantum calculations With only few resources available than labs at, on small handfuls of qubits, the quantum analog IBM analog quantum simulators offer short- of the classical bit information carrier, but the term progress to academic researchers. Proper real prize remains distant. There is a reason for digital quantum computing is still limited to this: a quantum computer is really hard to do as about 10 qubits at a time. This is similar to a it has to do with the fragility of quantum train set inside a train set inside of an actual information (qubits), which, once disturbed, train. As reported so far no quantum error- become classical junk. It’s a hardware challenge. correcting algorithm exists for real-life scales. How do you protect a qubit - a single particle in The distance is still large . ” Deutsch offered, “I a superposition of different states - when it’s would love to see just one universal logical qubit very surroundings threaten to wipe it out? It’s that can be indefinitely be error corrected.” worse than that even, because wiping out one qubit means potentially wiping out the entire network of entangled qubits, nuking not just one 13. Conclusion: 383
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The recently developed new semiconductor essentially check their accuracy. By doing so, chip of IBM is bringing us one step closer to the the team was able to reduce the failure rate by a development of a practical quantum computer. factor of 8.5, according to their article in Nature. The chip integrated four qubits, the basis of quantum computing, in a two by two, 2-D grid. The difficultly is that simply observing a qubit Qubits are the bits that can exist as a 1 & a 0 to determine if it has “flipped” into an error state simultaneously (superposition state), offering via Even with this improvement, viable quantum quantum computers the possibility of making computing has a long way to go. Despite their simultaneous calculations. Quantum computers success, the team was only able to use the qubits to be developed may consist grids with in the classical manner of conventional bits, not hundreds or thousands of qubits working taking advantage of the superpositioning that is together in making calculations. IBM's chip is expected to provide the lion’s share of quantum supposed to be unique in the sense that it allows computing benefits. for the recognition of both kinds of quantum The quantum computer promises to deliver a errors known as: bit flips (when a qubit new level of computational power. A whole representing 0 changes to a 1, or vice versa) and new theory of computation being developed phase flips (the distortion of the superposition incorporates the strange effects of quantum state of a qubit). mechanics and considers every physical object to be some kind of quantum computer. A In 2015 march, Scott Wilsonson [ 33 ] suggests quantum computer thus produced will have the that Quantum Computing Takes Step forward, theoretical capability of simulating any finite A quantum computer chip – (Julian physical system and may even hold the key to Kelly/University of California, Santa Barbara) creating an artificially intelligent computer. Researchers at the University of California, The quantum computers power to perform Santa Barbara and Google have made a big leap calculations across a multitude of parallel toward realizing the goal of ultra-powerful universes gives it, ability to quickly perform quantum computers. Such devices could easily tasks which classical computers will never be break many current encryptions ciphers, which, able to practically achieve.. Some algorithms by proxy, could help calculate complex have already been invented which are proving to problems in minutes, rather than months. have huge implications on the world of cryptography. This is due to the commonly used The key to, and the power of, quantum cryptography techniques. A spinoff of quantum computing springs from that same instability, computing and quantum communication will however: by utilizing even more qubits in an allow information to be sent with secretly. error-correction scheme, valid results might be read from such computers, despite relatively One very important feature of electromagnetic high rates of de-coherence. Although the amount signals is measurability. This makes easy to of errors experienced in most quantum read all the parameters of a signal without computing devices far exceeds the scope of any introducing changes to it. This is the exact conventional error correction mechanism, reason why almost all techniques are equipped throwing more qubits at the problem is exactly with encryption. This protects transmitted the solution that Google has come up with. information from being read or altered by a third Working with an array of five qubits to hold party. The communicating parties don’t have data, the team inserted an additional four qubits another channel to talk, and cryptosystem next to them to devote exclusively to error developers brilliantly solved a very complicated correction. The four error-correcting qubits are problem as to, how to negotiate a secret allowed to observe the data qubits and encryption key when all communication might 384
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