QUANTUM COMPUTER
1. Introduction:
Ever since 1980 when quantum theory was applied to the classical Turing machine, the development of a quantum computer was pondered. Not only can these kinds of computers run 1,000,000,000 times faster than current silicon based computers, but they can theoretically run with no energy consumption. These computers will obsolete the silicon chip much as the transistor did the vacuum tube. Consequently, silicon chip and computer manufacturers, the
The paper discusses an overview of the quantum computing world, and what it means to the computing industry. It discusses the inevitability of quantum computers, how they originated, and what is different about them from classical computers, using the principles of superposition, entanglement, and quantum teleportation as examples. This paper is intended to be accessible to the general reader, so it will explain the basics of a few quantum computer features at the risk of over-simplification, and the paradoxical effects quantum theory produces in a practical world.
This author has not built nor operated a quantum computer, so he relies heavily on the scientific literature, and the only book so far published on the topic, "Explorations in Quantum Computing", by Colin Williams and Scott Clearwater (see bibliography at bottom).
2. History of Quantum Computer:
Quantum theory is not new. It started with Max Planck’s discovery of the energy quantum (Nobel prize in 1918), and Einstein’s discovery of the photon (Nobel prize in 1921). We might trace the invention of the modern computer back to 1956, when Bardeen, Brattain, and Shockley won the Nobel Prize for the invention of the transistor. The idea of a quantum computer originated in 1980 when P. Benioff thought about the now-classic Turing machine (developed in 1935 by Alan Turing) in terms of quantum states. Whereas the convention Turing machine computes by punching holes in a linear strip of paper, the Benioff’s Quantum Turing Machine (QTM) has strips of paper with multiple paths, each one with a probability of traversal. The QTM has exponentially many paths, not all equally probably, but all possible.
Two years later, Richard Feynman showed that because of these diverse paths a classical computer would slow down exponentially in attempting to traverse an exponentially-growing number of paths; that is, a classical computer would not be able to simulate quantum processes. Berthiaume & Brassard proved in 1994 that QTM’s are theoretically faster than Turing machines, part due to the parallelism of quantum computing; Shor was able to demonstrate that fact that same year by factoring large integers in polynomial time. Shor’s algorithm was the first significant problem solved by a quantum approach to excel classical computers.
Grover showed in 1996 a quantum algorithm to search unsorted databases in the square root of the time it would take a classical computer to find an entry. *** has said that to search for your name in the entire text of the Library of Congress would take classical computers about 100 years, but a quantum computer could find your name in a little under half a second. Grover’s algorithm and the law of super-positioning makes this possible. (Super-positioning is discussed later in this paper.),
The Turing machine, designed around a machine traversing a strip of paper, is hard to use as a focus to manipulate new ideas in programming and electronics. In 1993,
These algorithms are constructed and proved in theory, but last summer (June, 1998), Gershenfeld and Chuang built the first quantum computer at MIT. It was based on the principles of Nuclear Magnetic Resonance (NMR). There are other types of quantum computers that may be built, but it is characteristic in that it uses molecules in a liquid CPU of chloroform for logic gates. Their prototype is discussed later in this paper.
In December of last year, Anton Zeilinger made a fantastic accomplishment. He was able to quantum teleport a beam of light about three feet across his laboratory. This feat was achieved using a principle called quantum entanglement, both of which are explained later in this paper.,,
The idea of a computational device based on quantum mechanics was first explored in the 1970's and early 1980's by physicists and computer scientists such as Charles H. Bennett of the IBM Thomas J. Watson Research Center, Paul A. Benioff of Argonne National Laboratory in Illinois, David Deutsch of the University of Oxford, and the late Richard P. Feynman of the California Institute of Technology (Caltech). The idea emerged when scientists were pondering the fundamental limits of computation. They understood that if technology continued to abide by Moore's Law, then the continually shrinking size of circuitry packed onto silicon chips would eventually reach a point where individual elements would be no larger than a few atoms. Here a problem arose because at the atomic scale the physical laws that govern the behavior and properties of the circuit are inherently quantum mechanical in nature, not classical. This then raised the question of whether a new kind of computer could be devised based on the principles of quantum physics.
Feynman was among the first to attempt to provide an answer to this question by producing an abstract model in 1982 that showed how a quantum system could be used to do computations. He also explained how such a machine would be able to act as a simulator for quantum physics. In other words, a physicist would have the ability to carry out experiments in quantum physics inside a quantum mechanical computer.
Later, in 1985, Deutsch realized that Feynman's assertion could eventually lead to a general purpose quantum computer and published a crucial theoretical paper showing that any physical process, in principle, could be modeled perfectly by a quantum computer. Thus, a quantum computer would have capabilities far beyond those of any traditional classical computer. After Deutsch published this paper, the search began to find interesting applications for such a machine.
Unfortunately, all that could be found were a few rather contrived mathematical problems, until Shor circulated in 1994 a preprint of a paper in which he set out a method for using quantum computers to crack an important problem in number theory, namely factorization. He showed how an ensemble of mathematical operations, designed specifically for a quantum computer, could be organized to enable a such a machine to factor huge numbers extremely rapidly, much faster than is possible on conventional computers. With this breakthrough, quantum computing transformed from a mere academic curiosity directly into a national and world interest.
3. What is Different about Quantum Computers?
There is much that is different between quantum computers and classical computers. This paper will address only two: superpositioning to support the explanation of quantum circuits, and entanglement to support the explanation of quantum teleportation..
1. Superpositioning:
Superpositioning is a big word for an old concept: that two things can overlap each other without interfering with each other. In classical computers, electrons cannot occupy the same space at the same time, but as waves, they can.
2. Superposition in waves:
Take example of two super-imposed waves A and B. If I were to add these waves together numerically, S = A + B, the result would be a wave that looks like neither of its components. However, one could retrieve either wave be subtracting out the other, as shown. (The wave form S, is shown as dotted to indicate that it is only the apparent wave form; the actual wave form is the combination of two different waves. In the quantum world, the combined wave form is a set of amplitude probabilities.)
3. Superposition in link list pointers:
For an example germane to computer programming, one may look at a data structure called a linked list. Each date node in the list contains a reference, or pointer, to the next data node. The program traverses the list by jumping to the next data node indicated by the pointer. In a doubly-linked list, the data node contains two pointers, one for traversing to the top of the list, and another for traversing to the bottom of the list.
Another way of implementing a doubly-linked list is to use a single pointer space that contains the exclusive-or (XOR) or the two adjacent pointers. Figure 2 shows a link list node with pointer S that is the XOR of reference a (before) and reference B (after). To traverse the link list upward, the program XORs the current pointer (S) with the one it just left (B), and the result is the pointer of the next node (A). The same process works when traversing down the list. This superpositioning of node pointers is analogous to the water wave superposition example above, and is how the quantum states are maintained simultaneously in a quantum bit.
4. State Vectors:
A state vector is a mathematical name for the superpositioning of all the probabilities that a quantum bit may find itself in. These probabilities are not all equal. One may think of this as a vector of the probabilities drawn in a two-dimensional coordinate system of the Complex plane, that is, coordinates of the form x+iy, where x is a coordinate on the Real number line, and y is a coordinate on the Imaginary number line.
Classical bits are either vectors of 0 or 1 and have no Imaginary component. Quantum bits, or "qubits", have both components. If the probabilities were equal, the vector could be represented as 45 degrees from vertical; if the probability of 1 were twice that of 0, the vector could be represented as 30 degrees from vertical. This vector represents the superposition of the probability of 1 and the probability of 0 simultaneously. In this way, the state vectors of classical bits are "collapsed" qubit state vectors.
It is an important side note that any physical quantity that is expressed by an Imaginary number cannot be measured directly, and any physical quantity that is expressed by a Complex number can be measured only on its Real number component. Because of this, qubits cannot be measured directly. Any measurement of a qubit will break superposition and collapse its state vector to a classical bit, just as subtracting a component wave or XOR’ing a pointer, will produce a different result. In performing computation with qubits, it is important not to measure the qubits until the final answer is computed, or information can be lost or changed.
4. Inevitability of Quantum Computers:
As our technology rushes forward, several factors work together to push us toward the quantum computing world, and push out the classical silicon-based chips. These factors are: scaling in size, energy consumption, economics of building leading edge computers and new applications that are available with quantum computers that cannot be executed with classical computers. At the current rate of chip miniaturization, energy efficiency, and economics, the classical computer of the year 2020 (if it could happen at all), would contain a CPU running at 40 GHz (or 40,000 MHz), with 160 GB (160,000 MB) RAM, and run on 40 watts of power.
1. Scaling:
Our computing world is surrounded by breath-taking innovations, and many of them involve more powerful and smaller chips. Chip capacity has doubled every 18 months, according to
2. Energy:
The speed of chips is also rising exponentially. Faster, more densely-packed, and closer transistors cause thermodynamic problems. Advances in energy efficiency are required to keep the chips from melting during use. Fortunately, energy efficiencies are increasing, and the thermodynamic problems are being resolved. These energy advances are also pushing the physics of chips into the quantum realm.
Quantum computers are reversible; therefore there is theoretically no net energy consumption. Quantum reversibility means that quantum computers drive themselves forward in infinitesimal (reversible) steps, much the same way that molecules of perfume would diffuse from a perfume bottle. Quantum computer programs are not "run", but are said to "evolve," as they process the program’s inputs to outputs. Incidentally, reversibility also means that the inputs of a quantum computer can be implied from the outputs; the program can be run backwards to get the inputs.)
The argument for energy inevitability is a "carrot-and-stick" argument: the energy inefficiencies drive us away from classical computers and the appeal for energy-free (or at least, much reduced energy consumption) computing drives us toward quantum computers.
3. Economics:
Besides the energy factors at the micro level of computing, there are large-scale economic factors pushing us to a more energy-efficient means of computing: 5% of the entire national power production is consumed by computing machinery. With "fossil fuels continuing to dwindle, fission power in disfavor with the public, and fusion power still many decades away, the drain computers impose on our power supply could become significant."
The cost to build a semiconductor plant doubles every three years. By extrapolating that trend to the year 2020, a semiconductor plant will cost $1 trillion to build, which is 5% of the U.S. GNP. Based on Motorola’s sales figures, a similar company would need $10 trillion in annual sales to support that kind of construction.
5. Why do we study Quantum Computers?
The crietia whice a physics expriment must satisfy for the constuction of a quantum computer are summaried inthis points or in another word we can say that We are study the quantum computer because:
1)control over the hibrert space
2)initialization of the quantum computer
3)minimal decoherence
4)ability to perform quantum state
5)ability to perform stromg quantum measurement
` experiment in NMR(Nuclear Magnatic Resonamce)cavity quantum eletrodynemic and superconducting circuits are contemplated.
Difference between the Quantum Computer & Classical Computer:
A classical computer has a memory made up of bits. Each bit holds either a one or a zero. The device computes by manipulating those bits. For example, comprised of n-characters stored on the hard drive of a typical computer is accordingly described by a string of 8n zeros and ones.
Herein lays a key difference between your classical computer and a quantum computer. In a quantum computer, the fundamental unit of information called a quantum bit or qubit is not binary but rather more quaternary in nature. A qubit can hold a one, or a zero, or a superposition of one and zero. In other words, it can hold both a one and a zero at the same time. A quantum computer maintains a set of qubits. The quantum computer computes by manipulating those qubits.
6. The Structure of Quantum Computer:
A quantum computer can be implemented using any small particle that can have two states. Quantum computers might be built from atoms that are both excited and not excited at the same time. They might be built from photons of light that are in two places at the same time. They might be built from protons and neutrons that have a spin of "up" and "down" at the same time.
A microscopic molecule can contain many thousands of protons and neutrons. It might be used as a quantum computer with many thousands of qubits.
Quantum computer, according to Walther group:
The ion chain (pictured below) is trapped in the central part of the linear ion trap (top) and would form the register of a quantum computer.
In recent years it was recognized that by exploiting the laws of quantum mechanics, information may be processed in a far more effective way than on a purely classical basis. A system particularly well suited for quantum computing is a chain of ions in a linear ion trap. Quantum bits may be stored, for example, in two hyperfine ground states of each ion, while quantum logic transformations can is realized using the coupling provided by the quantized vibrational modes of the ions. A novel linear ion trap for demonstrating simple quantum logic gates in strings of 25Mg+ ions was developed. We have stored strings of a few laser cooled ions and we now work on methods for addressing individual ions in the chain by laser beams, as well as cooling the vibrational modes to the quantum mechanical ground state. Both are necessary requirements for performing even small quantum calculations. We plan to use the system to generate and investigate highly entangled quantum states of several ions in order to test fundamental predictions of quantum theory.
Hardware of the Quantum Computer:
In quantum circuits one of the basic building blocks is the CONTROLLED NOT GATE .it is a controlled version of the classical XOR agat made reversible by maintanig one of its input value.
In this diagram a solid dot represent a controlling connection o a gate and the large crossed circle represented the bit which is modified by gate. The controlled not gate works such that the value if A Input unchanged and toggle the B value if and only if the A input is set. Show truth table.
I/P O/P
A B A’ B’
0 0 0 0
0 1 0 1
1 0 1 1
1 1 1 0
The idea can be easily extended to multiple input bits. Simply the logical date of the control bits decides whether to toggle the final gate.
One more gate is used in quantum computer is butterfly gate:
These are the most interesting and important gate in quantum computing. Their job is to take a classic input and convert it into the superposition of the two possible states 0 and 1 and 50/50 chance of developing either a 1 or 0 as its output. It’s not a part of the classical computer.
QCE (Quantum Computer Emulator):
Quantum Computer Emulator (QCE) is a software tool that emulates various hardware designs of Quantum Computers. QCE simulates the physical processes that govern the operation of a hardware quantum processor, strictly according to the laws of quantum mechanics. QCE also provides an environment to debug and execute quantum algorithms under realistic experimental conditions. The software consists of a Graphical User Interface and the simulator itself. A few snapshots of the GUI are shown below:
the software is distributed as a self-extracting executable for Windows 98/NT4/2000/ME/ (XP with SP1). It also runs under Linux+VMware on Intel processor machines. Included in this package are several examples including order finding, number partitioning and various implementations of the Deutsch-Josza algorithm and Grover's database search on ideal and more realistic QC's, such as those used in the 2-qubit NMR Quantum Computer. Articles describing the internal working of the QCE and the examples are also included.
QCE offers in real-time animation of the qubits. Alternatively QCE can be used to generate data from which animations can be building. Some results for time evolution of a 2-qubit QC for the case of an ideal and a NMR QC are shown below.
It can be very difficult to take a large number and find all its prime factors. This integer factorization problem is believed to be difficult for an ordinary computer. A quantum computer could solve this problem very quickly. If a number has n bits (is n digits long when written in the binary numeral system), then a quantum computer with just over 2n qubits can find its factors. It can also solve a related problem called the discrete log problem. This ability would allow a quantum computer to break many of the cryptographic systems in use today. Most of the popular public key ciphers could be quickly broken, including forms of RSA, ElGamal and Diffie-Hellman. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would be significant. The only way to make an algorithm like RSA secure would be to make the key size larger than the largest quantum computer that can be built. It seems likely that it will always be possible to build classical computers that have more bits than the number of qubits in the largest quantum computer. If that's true, then algorithms like RSA could be made secure.
If a quantum computer were based on the protons and neutrons in a molecule, it might be too small to see, but could factor integers with many thousands of bits. A classical computer running known algorithms could also factor those integers. But to do it before the sun burns out, it would have to be larger than the known universe. That would be somewhat inconvenient to build.
Perhaps not as surprisingly, quantum computers could also be useful for running simulations of quantum mechanics. The speedup could be just as large as for factoring. This could be of great practical benefit to many physicists.
This dramatic advantage of quantum computers is currently known to exist for only those three problems: factoring, discrete log, and quantum physics simulations. However, there is no proof that the advantage is real: an equally fast classical algorithm may still be discovered (though this is considered unlikely). There is one other problem where quantum computers have a smaller, though significant (quadratic) advantage. It is quantum database search, and can be solved by Grover's algorithm. In this case the advantage is provable. This establishes beyond doubt that (ideal) quantum computers are superior to classical computers.
Suppose there is a problem, such as finding the password that decrypts a file. The problem has these four properties:
· The only way to solve it is to guess answers repeatedly and check them
· There are n possible answers to check
· Every possible answer takes the same amount of time to check
· There are no clues about which answers might be better. Generating possibilities randomly is just as good as checking them in some special order
For problems with all four properties, it will take an average of n/2 guesses to find the answer using a classical computer. The time for a quantum computer to solve this will be proportional to the square root of n. That can be a very large speedup, reducing some problems from years to seconds. It can be used to attack symmetric ciphers such as 3DES and AES. But it is also easy to defend against. Just double the size of the key for the cipher. There are also more complicated methods for secure communication, such as using quantum cryptography.
There are currently no other practical problems known where quantum computers give a large speedup over classical computers. Research is continuing, and more problems may yet be found.
7. An introduction to Quantum Computing:
As we know that computers have become more compact and considerably faster in performing their task, the task remains the same: to manipulate and interpret an encoding of binary bits into a useful computational result. A bit is a fundamental unit of information, classically represented as a 0 or 1 in your digital computer. Each classical bit is physically realized through a macroscopic physical system, such as the magnetization on a hard disk or the charge on a capacitor. A document, for example, comprised of n-characters stored on the hard drive of a typical computer is accordingly described by a string of 8n zeros and ones. Herein lays a key difference between your classical computer and a quantum computer. Where a classical computer obeys the well understood laws of classical physics, a quantum computer is a device that harnesses physical phenomenon unique to quantum mechanics (especially quantum interference) to realize a fundamentally new mode of information processing.
In a quantum computer, the fundamental unit of information (called a quantum bit or qubit), is not binary but rather more quaternary in nature. This qubit property arises as a direct consequence of its adherence to the laws of quantum mechanics which differ radically from the laws of classical physics. A qubit can exist not only in a state corresponding to the logical state 0 or 1 as in a classical bit, but also in states corresponding to a blend or superposition of these classical states. In other words, a qubit can exist as a zero, a one, or simultaneously as both 0 and 1, with a numerical coefficient representing the probability for each state. This may seem counterintuitive because everyday phenomenon is governed by classical physics, not quantum mechanics -- which takes over at the atomic level. This rather difficult concept is perhaps best explained through an experiment. Consider figure a below:
Here a light source emits a photon along a path towards a half-silvered mirror. This mirror splits the light, reflecting half vertically toward detector A and transmitting half toward detector B. A photon, however, is a single quantized packet of light and cannot be split, so it is detected with equal probability at either A or B. Intuition would say that the photon randomly leaves the mirror in either the vertical or horizontal direction. However, quantum mechanics predicts that the photon actually travels both paths simultaneously! This is more clearly demonstrated in figure b.
In an experiment like that in figure a, where a photon is fired at a half-silvered mirror, it can be shown that the photon does not actually split by verifying that if one detector registers a signal, then no other detector does. With this piece of information, one might think that any given photon travels vertically or horizontally, randomly choosing between the two paths. However, quantum mechanics predicts that the photon actually travels both paths simultaneously, collapsing down to one path only upon measurement. This effect, known as single-particle interference, can be better illustrated in a slightly more elaborate experiment shown in fig.B.
In figure b, in this experiment, the photon first encounters a half-silvered mirror, then a fully silvered mirror, and finally another half-silvered mirror before reaching a detector, where each half-silvered mirror introduces the probability of the photon traveling down one path or the other. Once a photon strikes the mirror along either of the two paths after the first beam splitter, the arrangement is identical to that in figure a, and so one might hypothesize that the photon will reach either detector A or detector B with equal probability. However, experiment shows that in reality this arrangement causes detector A to register 100% of the time, and never at detector B! How can this be?
Answer:-
If a single photon travels vertically and strikes the mirror, then, by comparison to the experiment in figure a, there should be an equal probability that the photon will strike either detector A or detector B. The same goes for a photon traveling down the horizontal path. However, the actual result is drastically different. The only conceivable conclusion is therefore that the photon somehow traveled both paths simultaneously; creating interference at the point of intersection that destroyed the possibility of the signal reaching B. This is known as quantum interference and results from the superposition of the possible photon states, or potential paths. So although only a single photon is emitted, it appears as though an identical photon exists and travels the 'path not taken,' only detectable by the interference it causes with the original photon when their paths come together again. If, for example, either of the paths are blocked with an absorbing screen, then detector B begins registering hits again just as in the first experiment! This unique characteristic, among others, makes the current research in quantum computing not merely a continuation of today's idea of a computer, but rather an entirely new branch of thought. And it is because quantum computers harness these special characteristics that give them the potential to be incredibly powerful computational devices.
The potential and power of Quantum Computing:-
In a traditional computer, information is encoded in a series of bits, and these bits are manipulated via Boolean logic gates arranged in succession to produce an end result. Similarly, a quantum computer manipulates qubits by executing a series of quantum gates, each a unitary transformation acting on a single qubit or pair of qubits. In applying these gates in succession, a quantum computer can perform a complicated unitary transformation to a set of qubits in some initial state. The qubits can then be measured, with this measurement serving as the final computational result. This similarity in calculation between a classical and quantum computer affords that in theory, a classical computer can accurately simulate a quantum computer. In other words, a classical computer would be able to do anything a quantum computer can. So why bother with quantum computers? Although a classical computer can theoretically simulate a quantum computer, it is incredibly inefficient, so much so that a classical computer is effectively incapable of performing many tasks that a quantum computer could perform with ease. The simulation of a quantum computer on a classical one is a computationally hard problem because the correlations among quantum bits are qualitatively different from correlations among classical bits, as first explained by John Bell. Take for example a system of only a few hundred qubits, this exists in a Hilbert space of dimension ~1090 that in simulation would require a classical computer to work with exponentially large matrices (to perform calculations on each individual state, which is also represented as a matrix), meaning it would take an exponentially longer time than even a primitive quantum computer.
Richard Feynman was among the first to recognize the potential in quantum superposition for solving such problems much much faster. For example, a system of 500 qubits, which is impossible to simulate classically, represents a quantum superposition of as many as 2500 states. Each state would be classically equivalent to a single list of 500 1's and 0's. Any quantum operation on that system --a particular pulse of radio waves, for instance, whose action might be to execute a controlled-NOT operation on the 100th and 101st qubits-- would simultaneously operate on all 2500 states. Hence with one fell swoop, one tick of the computer clock, a quantum operation could compute not just on one machine state, as serial computers do, but on 2500 machine states at once! Eventually, however, observing the system would cause it to collapse into a single quantum state corresponding to a single answer, a single list of 500 1's and 0's, as dictated by the measurement axiom of quantum mechanics. The reason this is an exciting result is because this answer, derived from the massive quantum parallelism achieved through superposition, is the equivalent of performing the same operation on a classical super computer with ~10150 separate processors (which is of course impossible)!!
Early investigators in this field were naturally excited by the potential of such immense computing power, and soon after realizing its potential, the hunt was on to find something interesting for a quantum computer to do. Peter Shor, a research and computer scientist at AT&T's Bell Laboratories in
Encryption, however, is only one application of a quantum computer. In addition, Shor has put together a toolbox of mathematical operations that can only be performed on a quantum computer, many of which he used in his factorization algorithm. Furthermore, Feynman asserted that a quantum computer could function as a kind of simulator for quantum physics, potentially opening the doors to many discoveries in the field. Currently the power and capability of a quantum computer is primarily theoretical speculation; the advent of the first fully functional quantum computer will undoubtedly bring many new and exciting applications.
Obstacle and research of Quantum Computer:
The field of quantum information processing has made numerous promising advancements since its conception, including the building of two- and three-qubit quantum computers capable of some simple arithmetic and data sorting. However, a few potentially large obstacles still remain that prevent us from "just building one," or more precisely, building a quantum computer that can rival today's modern digital computer. Among these difficulties, error correction, decoherence, and hardware architecture are probably the most rmidable. Error correction is rather self explanatory, but what errors need correction?
The answer is primarily those errors that arise as a direct result of decoherence , or the tendency of a quantum computer to decay from a given quantum state into an incoherent state as it interacts, or entangles, with the state of the environment. These interactions between the environment and qubits are unavoidable, and induce the breakdown of information stored in the quantum computer, and thus errors in computation. Before any quantum computer will be capable of solving hard problems, research must devise a way to maintain decoherence and other potential sources of error at an acceptable level.
Thanks to the theory (and now reality) of quantum error correction, first proposed in 1995 and continually developed since, small scale quantum computers have been built and the prospects of large quantum computers are looking up. Probably the most important idea in this field is the application of error correction in phase coherence as a means to extract information and reduce error in a quantum system without actually measuring that system. In 1998, researches at Los Alamos National Laboratory and MIT led by Raymond Laflamme managed to spread a single bit of quantum information (qubit) across three nuclear spins in each molecule of a liquid solution of alanine or trichloroethylene molecules. They accomplished this using the techniques of nuclear magnetic resonance (NMR). This experiment is significant because spreading out the information actually made it harder to corrupt. Quantum mechanics tells us that directly measuring the state of a qubit invariably destroys the superposition of states in which it exists, forcing it to become either a 0 or 1. The technique of spreading out the information allows researchers to utilize the property of entanglement to study the interactions between states as an indirect method for analyzing the quantum information. Rather than a direct measurement, the group compared the spins to see if any new differences arose between them without learning the information itself. This technique gave them the ability to detect and fix errors in a qubit's phase coherence, and thus maintain a higher level of coherence in the quantum system. This milestone has provided argument against skeptics, and hope for believers. Currently, research in quantum error correction continues with groups at Caltech (Preskill, Kimble), Microsoft, Los Alamos, and elsewhere.
At this point, only a few of the benefits of quantum computation and quantum computers are readily obvious, but before more possibilities are uncovered theory must be put to the test. In order to do this, devices capable of quantum computation must be constructed. Quantum computing hardware is, however, still in its infancy. As a result of several significant experiments, nuclear magnetic resonance (NMR) has become the most popular component in quantum hardware architecture. Only within the past year, a group from Los Alamos National Laboratory and MIT constructed the first experimental demonstrations of a quantum computer using nuclear magnetic resonance (NMR) technology. Currently, research is underway to discover methods for battling the destructive effects of decoherence, to develop optimal hardware architecture for designing and building a quantum computer, and to further uncover quantum algorithms to utilize the immense computing power available in these devices. Naturally this pursuit is intimately related to quantum error correction codes and quantum algorithms, so a number of groups are doing simultaneous research in a number of these fields. To date, designs have involved ion traps, cavity quantum electrodynamics (QED), and NMR. Though these devices have had mild success in performing interesting experiments, the technologies each have serious limitations. Ion trap computers are limited in speed by the vibration frequency of the modes in the trap. NMR devices have an exponential attenuation of signal to noise as the number of qubits in a system increases. Cavity QED is slightly more promising; however, it still has only been demonstrated with a few qubits. Seth Lloyd of MIT is currently a prominent researcher in quantum hardware. The future of quantum computer hardware architecture is likely to be very different from what we know today; however, the current research has helped to provide insight as to what obstacles the future will hold for these devices.
8. Implementation of a Quantum Computer:
In a linear Paul traps:
Here is a short outline of the ideas of I.Cirac and P.Zoller (see references) for the realization of a quantum computer. There are five important prerequisites for a possible quantum computer:
- A quantum system consisting of many quantum bits.
- 100% preparation of a quantum system before the computation.
- Strong interaction between the quantum bits.
- Coherent evolution of the system while computing (i.e. weak interaction with the outside world).
- 100% readout of the quantum system.
In theory, these requirements are quite well fulfilled in a linear Paul trap. A certain number of ions are stored in a chain configuration. These ions are the carriers of the quantum bits, i.e. their internal electronic structure is used to implement a two level system (just like a spin 1/2 system). These 'qbits' can be prepared from the outside world by shining laser light on them, they are strongly coupled to each other via their common oscillatory motion in the longitudinal direction of the trap (Coulomb repulsion), and they interact only weakly with the environment. The process of computation which involves the individual manipulation of the qbits can be done with laser pulses. Finally, the state of the system can be read out after the computation by again using lasers and by detecting the fluorescence on sensitive cameras.
In detail: Some ions are trapped in a linear Paul trap. The geometry of this trap is such that there is one direction (the longitudinal direction) in which the trapping potential is rather weak and that in the two other directions (the transversal directions) the trapping potential is rather strong. This forces the ions to be positioned along the longitudinal direction, and they keep a certain distance from each other due to the Coulomb repulsion (approximately 10 to 20 microns in our trap). Together they swing back and forth along this line with typical frequency of about 200 kHz. Considering the center of mass motion of these ions this oscillation is nothing else but a harmonic oscillator in one dimension (see any book on quantum mechanics concerning a quantum mechanical harmonic oscillator).
If now these ions are laser cooled (typical temperature: micro Kelvins) it is appropriate to consider the quantum mechanical behavior of this chain of ions. For example, after Doppler cooling the state of oscillation is a thermal state with a certain temperature in the milli Kelvin regime. A second cooling stage is neccessary to cool the ions even further (e.g. sideband cooling or Raman sideband cooling) so that finally they occupy only the lowest state of harmonic oscillator ladder. This is then a truely pure state and it is starting point for the quantum computation.
The actual process of quantum computation consist of a coherent (i.e. according to the Schrödinger equation of quantum mechanics) evolution of the system where the internal electronic degrees of freedom of the ions (see e.g. Calcium ) are the qbits which interact with a) laserlight from outside and b) interact with each other via their common oscillatory motion. To illustrate, look at one of the ions in the chain where we want to assume that the ion and the chain are in the quantum mechanical ground state. A laser pulse (say pi/2-pulse) on the blue sideband of the qbit-transition aimed at this ion excites the ion and also adds a quantum of motion of the harmonic oscillator with probability 1/2. A pi/2-laser pulse on the red sideband of the qbit-transition aimed at another ion then takes away the quantum of motion and also excites this ion (again, with probability 1/2). According to quantum mechanics, we thus end up with two ions of the chain whose internal degrees of freedom are correlated ('entangled'), while the oscillatory motion of the chain is left in the ground state. Together with on-resonance laser pulses on single ions these blue and red detuned pulses are all you need for implementing some quantum computational algorithm. Certainly, during the computation the laser has to have a definite phase, i.e. must preserve coherence. In addition, the oscillatory motion must not decay (which is the case for ion traps to a good approximation).
Finally, the state of the quantum bits can be read out with the help of an additional strong transition. This is the usual way how the state of a two level system is measured on a single trapped ion.
Obvious drawbacks of an ion trap quantum computer:
- The chain of ions cannot be arbitrarily long, i.e. the number of qbits is limited to the order of 10-100 for experimental reasons.
- Coherence time limited by interaction with environment (so far not possible to regenerated decaying qbits, though progress on the theoretical side is impressive).
- Quantum system to complicate i.e. needs to much infrastructure (vacuum vessel, lasers etc.).
Major experimental difficulties of the scheme above at the present time:
- Preparation of the state to start with. Here, it is necessary to cool a chain of ions into the ground state of their oscillatory motion. Laser cooling of a single ion to its oscillatory ground state has already been achieved (see 3rd reference) in three dimensions, but ground state laser cooling of more than one ion still needs to be shown.
- Addressing individual ions with laser beams. Since the spacing between adjacent ions is on the order of 10 microns, aiming a laser beam at only one ion is not an easy task.
Model Quantum Computer and Quantum Code:
In this section we describe a simple model for a quantum computer based on a classical computer instructing a machine to manipulate a set of spins. This model has some intrinsic limitations which make designing algorithms in a high-level language somewhat tricky. We discuss some of the rules for writing such quantum computer code as a high-level language and give an example.
Consider the following model for the operation of a quantum computer: Several thousand spin-1/2 particles (or two-level systems) are initially in some well defined state, such as spin-down. A classical machine takes single spins or pairs of spins and entangles them (performing an elementary one-bit operation Uө or the two-bit XOR gate); see Fig. 9a, b and c. These stages are repeated on different pairs of spins according to the instructions of a conventional computer program. Since the spins are entangled, we must not look at the spins at intermediate stages: We must keep the quantum superposition intact. Furthermore, nothing else may interfere with the spins which could destroy their orientation or interrupt their unitary evolution. Once this well-defined cycle of manipulation is complete the orientations of the spins are measured (Fig. 9d). This set of measured orientations is the output of the computation.
Fig. 9 Model quantum computer as pictured by Shor. Initially all particles are spin-down. Stage a) a classical machine takes a single or pair of spins and in stage b) it performs a selected one-bit or two-bit operation; in stage c) the ``entangled'' particles are returned to their original locations. These three stages are repeated many times in accord with the instructions given by an ordinary classical computer. When this cycle is complete stage d) consists of measuring the state of the particles (leaving them in some particular bit-string); this bit-string is the result of the computation.
Given this paradigm for a quantum computer, what might its high-level language (its computer code) look like? The most serious difficulty that must be dealt with is that the quantum information is manipulated by a conventional computer in a completely blind manner---without any access to the values of this quantum information. This means that the program cannot utilize ``shortcuts'' conditional on the value of a quantum variable (or register or bit). For example, loops must be iterated through exactly the same number of times independent of the values of the quantum variables. Similarly, conditional branches around large pieces of code must be broken down into repeated conditions for each step. In addition, each instruction performed upon the quantum bits must be logically reversible. Thus, ordinary assignments of a value to a variable, such as
| a) = n, are not legal and must instead be performed as increments on an initially zeroed variable, such as | a) = | a) + n.
An example of such code that could run on this machine might look like this:
Do 10 k = 1, worstdiv
| a) = | a) - n
If (| a) >= 0) | q) = | q) + 1
10 continue
Do 20 k = 1, worstdiv
If (k > | q)) | a) = | a) + n
20 continue
This code fragment could be used to calculate the quotient and the remainder, placed in |q) and |a) , respectively, for the division of |a) by n; the constant worstdiv is the worst-case number of times the loop must be traversed. Here |q) is initially zero. Each instruction here is either a conventional computer instruction or one involving some quantum variables. The former are direct instructions for the external computer, while the latter must be interpreted as a sequence of manipulations to be performed upon the quantum bits. As it stands, this code is not reversible (neither is it very efficient), e.g., the label 10 gives no specification of which routes might be used to get to it.
9. How does a quantum computer work?
The computer sitting on your desk works by manipulating bits, digits that are binary -- that is, that can either represent a zero or one. Everything from numbers and letters to the status of your modem or mouse are all represented by a collection of bits in combinations of ones and zeros. These bits correspond very nicely with the way classical physics represents the world. Electrical switches can be on or off, objects are in one place or they're not, etc. Quantum computers aren't limited by the binary nature of the classical physical world, however -- they depend on observing the state of quantum bits or qubits that might represent a one or a zero, might represent a combination of the two or might represent a number expressing that the state of the qubit is somewhere between 1 and 0.
According to quantum physics, a subatomic particle can't be absolutely said to exist: It exhibits a statistical probability to exist in a particular place and time, but there's no way of knowing whether it's there or not until you observe it, at which point all the probabilities collapse down into a definite state. In fact, there are those who say that it both exists and doesn't exist until it's observed at which time the observer sets a particular observed state into concrete existence. According to some theorists, this means that there must be an infinite number of alternative universes since there's no other way to account for the states that aren't observed by a particular observer, but since we don't have any way of getting at the other universes; they don't really help building a computer.
Researchers at IBM have built quantum computers by using nuclear magnetic resonance (NMR) techniques to measure and manipulate the spin of individual atoms. Radio-frequency energy bursts can begin the "computing" process by changing the energy level of an atom, which might then interact with other atoms in a controlled manner, to establish the patterns of quantum computing that correspond to answers that might be gathered through normal computers.
There are several reasons that researchers are working so hard to develop a practical quantum computer. First, atoms change energy states very quickly -- much more quickly than even the fastest computer processors. Next, given the right type of problem, each qubit can take the place of an entire processor -- meaning that 1,000 ions of, say, barium, could take the place of a 1,000 processor computer. The key is finding the sort of problem a quantum computer is able to solve.
It's unlikely that you'll ever have a large quantum computer on your desk, because they aren't well suited for tasks like word processing and e-mail. Large-scale cryptography, on the other hand, is ideal for quantum computing, as is modeling and indexing very large databases. It is for these large-scale applications that scientists continue to work on quantum computer.
Though scientists and engineers have demonstrated a number of small-scale quantum computers, developers face several profound difficulties in building commercially viable quantum computers. The most pressing problem is that it's difficult to hold a single ion in a steady state while you observe its manipulated energy levels and spin directions. Right now, doing so often involves using lasers to cool ions to a point very near absolute zero. That's after you've separated a single atom from a group and herded it into place. So far, the demonstrations have generally involved between two and five atoms. There's also the issue of observing the atom and collapsing the probabilities into a single state -- that destroys the "both or between" states that are so valuable. The NMR technique used by IBM is one way to try to observe the effects of the ion's state without directly observing it and therefore collapsing the probabilities.
Scientists at Los Alamos National Labs, IBM, CalTech and
10. Latest technology of Quantum Computers:
The Centre for Quantum Computer Technology is an Australian multi-university collaboration undertaking research on the fundamental physics and technology of building, at the atomic level, a solid state quantum computer in silicon together with other high potential implementations. The objective is underpinned by a vigorous semiconductor research program that includes a sophisticated quantum measurement capability at ultra-low temperatures.
Established in January 2000 through funds from the Australian Research Council and participating institutions, the Centre has eight nodes at the
Silicon Quantum Computer:
Quantum computer - a new kind of computer far more powerful than any that currently exist - could be made today, says Thaddeus Ladd of
The microelectronics industry has decades of experience of controlling and fine-tuning the structure and properties of silicon. These skills would give a silicon-based quantum computer a head start over other schemes for putting one together.
Quantum and conventional computers encode, store and manipulate information as sequences of binary digits, or bits, denoted as 1s and 0s. In a normal computer, each bit is a switch, which can be either 'on' or 'off'.
In a quantum computer, switches can be on, off or in a superposition of states - on and off at the same time. These extra configurations mean that quantum bits, or qubits, can encode more information than classical switches.
That increase in capacity would, in theory, make quantum computers faster and more powerful. In practice it is extremely difficult to maintain a superposition of more than a few quantum states for any length of time. So far, quantum computing has been demonstrated with only four qubits, compared with the billions of bits that conventional silicon microprocessors handle.
Several quantum-computing demonstrations have used nuclear magnetic resonance (NMR) to control and detect the quantum states of atoms floating in solution. But this beaker-of-liquid approach is unlikely to remain viable beyond ten or so qubits.
Many researchers suspect that making a quantum computer with as many qubits as a Pentium chip has transistors will take the same kind of technology, recording the information in solid-state devices.
Chip off the old block:
In 1998, Bruce Kane of the
The device proposed by Ladd and his colleagues is similar, but more within the reach of current technical capabilities. They suggest that qubits could be encoded in an isotope of silicon called silicon-29, or 29Si.
Itoh's group in
Crucially, each qubit would be stored not just in a single 29Si atom but in many thousand copies, one in each 29Si chain. This would avoid the problem of making measurements on single atoms. The readout could be performed using magnetic resonance force microscopy, which detects the oscillations of a thin bridge in which the rows of silicon atoms are embedded.
The details are subtle, but the point, the researchers say, is that the device is feasible without "unrealistic advances in fabrication, measurement, or control technologies". All they have to do now is build it.schemes.
Quantum computer data readable Evan as cooper pair:
Researchers in
This is true even though the signal consists only of the presence or absence of two electrons, a so-called Cooper pair.
Göran Johansson at the Department of Microelectronics and Nanoscience, Chalmers University of Technology, reports that the Chalmers research team of which he is a member has been able to produce readouts of superconductor quantum computers.
The key to success lies in being able to meter tiny charges before they move on.
Different research teams are studying different problems involving quantum computers. Research is pursuing many paths at the same time.
“But even very simple quantum computers are still at least ten years down the road,” says Göran.
The Chalmers research team, led by Per Delsing, together with their colleagues at Yale, may already be the best in the world when it comes to the rapid metering of charges with the aid of so-called monoelectron transistors.
Working with theoreticians from their Chalmers colleague Göran Wendin’s team, they have now shown that it is possible to register a quantum bit rapidly enough to retrieve the information before it is destroyed by the metering itself.
Delsing’s and Wendin’s research teams are part of an EU consortium, SQUBIT, coordinated by Chalmers University of Technology in
The French node at CEA, Saclay, has just presented a superconductor circuit representing a quantum bit with an extremely long lifetime, a world record for this type, and has tremendous potential to expand this into a small basic quantum computer with 5-10 quantum bits within ten years.
“Chalmers has just applied for EU funding to extend our collaboration and to actually build an elementary quantum computer. What’s more, we plan to take part in an even bigger effort within the EU’s seventh framework program in quantum informatics, quantum computers, and nanotechnology,” adds Göran Wendin.
Quantum computers are a new type of computers based on the laws of physics at the atomic level, so-called quantum physics. The principle is the same as that of Schrödinger’s famous cat, which is both dead and alive until you open the lid and check. The bits in a quantum computer are both zero and one, until you read them.
11. Application of Quantum Computer:
1. Encryption Technology:
The speed of quantum computers also jeopardizes the encryption schemes that rely on impracticably-long times to decrypt by brute force methods. Encryption schemes that may take millions of years to guess and check are now vulnerable to quantum computers that may reach a solution within one year. Many governments, included ours, use such encryption schemes for national security. They are very interested in any technology that puts that at risk. As a result, the Office of Naval Research, the CIA, and DARPA, are sinking huge funds into quantum computer research. DARPA is funding $5 million for a Quantum Information and Computing Institute, and the CIA is funding an unknown amount for factoring of large integers, a fundamental part of encryption technology.
2. Ultra-secure and Super-dense Communications:
It is possible to transmit information without a signal path by using newly-discovered quantum principles, quantum teleportation. There is no way to intercept the path and extract information. Ultra-secure communication is also possible by super-dense information coding, which is a new technology in its own right. Quantum bits can be used to allow more information to be communicated per bit than the same number of classical bits.
3. Improved Error Correction and Error Detection:
Through similar processes that support ultra-secure and super-dense communications, the existing bit streams can be made more robust and secure by improvements in error correction and detection. Recovering informational from a noisy transmission path will also be a lucrative and useful practice.
4. Molecular Simulations:
Richard Feynman showed in 1982 that classical computers cannot simulate quantum effects without slowing down exponentially; a quantum computer can simulate physical processes of quantum effects in real time. Molecular simulations of chemical interactions will allow chemists and pharmacists to learn more about how their products interaction with each other, and with biological processes such as how a drug may interact with a person’s metabolism or disease. Pharmaceutical research offers a big market to such applications.
5. True Randomness:
Classical computers do not have the ability to generate true random numbers. The random number generators on today’s computers are pseudo-random generators—there is always a cycle or a trend, however subtle. Pseudo-random generators cannot simulate natural random processes accurately for some applications, and can not reproduce certain random effects. Quantum computers can generate true randomness, thus give more veracity to programs that need true randomness in their processing. Randomness plays a significant part of applications with a heavy reliance on statistical approaches, for simulations, for code making, randomized algorithms for problems solving, and for stock market predictions, to name a few.
With the global forces of computer competition, encryption technology for national security, new applications, and the thermodynamics of computer systems changing as they are, there is a rush toward the new quantum technology to produce the first viable quantum computer. The world is moving toward a place that no classical computer has gone before, nor can go.
The other applications of quantum computer are:
v cryptography: perfectly secure communication
v searching: especially algorithmic searching
v factorization: large numbers very rapidly
v simulating: quantum computer system efficiently
v quantum computers will very likely be used for encryption problem
v they will find a home in modeling quantum chemistry problem
12. Advantages & Disadvantages of Quantum Computer:
ADVANTAGES:
Fast computing more memory easy to solve a complex problem or sum which is not possible in classical computer
DISADVANTAGES:
v more complex in design
v higher cost
v till it is not use in practice
13. Conclusion:
After the all these points the only conclusion is that the quantum computer is very new technology or in other word we can say that it is very advance technology of a new generation Which is very faster to do any work and capable to solve any complex problem and more powerful device to compare of today’s classical computer.
This paper skimmed the marvelous ideas of quantum computing, its concepts, and how quantum theory allows technological jumps in the computer industry that will revolutionize the practical computing world. Quantum computes are coming, and they will require a new way of looking at computing. Applications that can not be done now are easily possible with quantum computers. The spin-off concepts, like quantum teleportation, open vistas only imagined before. Computer science is still immature for it’s barely 80 years, and this radical divergence from the traditional development path is one indicator that. Who knows what the next 870 years will bring?
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