Quantum computer is the key to controlling complex processes. If its hardware, in general is successfully created on the basis of the physical baggage of the 20th century, the mathematical software is fundamentally lagging behind. Feynman's user interface in the form of quantum gate arrays, cannot be used for the control because it gives the solution of the Schrödinger equation with quadratic slowdown compared to the real process. The software must then imitate the real process using appropriate program primitives written as the programs for classical supercomputer. The decoherence will be reflected by some constant - the number of basic states that can fit into the limited of memory available to software. The real value of this constant can be found in the experimental realization of Grover search algorithm. Rough estimates of this constant are given based on the simplest processes of quantum electrodynamics and nuclear decay.
Quantum computer is the key to controlling complex processes. If its hardware, in general is successfully created on the basis of the physical baggage of the 20th century, the mathematical software is fundamentally lagging behind. Feynman's user interface in the form of quantum gate arrays, cannot be used for the control because it gives the solution of the Schrödinger equation with quadratic slowdown compared to the real process. The software must then imitate the real process using appropriate program primitives written as the programs for classical supercomputer. The decoherence will be reflected by some constant - the number of basic states that can fit into the limited of memory available to software. The real value of this constant can be found in the experimental realization of Grover search algorithm. Rough estimates of this constant are given based on the simplest processes of quantum electrodynamics and nuclear decay.
Quantum computing is based on the exploitation of quantum effects to perform some important computations more efficiently than ever possible on classical computers. Well known quantum algorithms are Shors polynomial time factoring algorithm and Grovers data base search scheme. Their potential is due to the parallelism of a quantum computation increasing exponentially with the size of the computing device. IBM has succeeded in building a first working quantum computing device with up to 7 qubits based on NMR technology, however, the construction of large multi-qubit systems appears to become extremely difficult due to the loss of coherence of the quantum states. Like the design process of modern microprocessors which is carried out by means of sophisticated software, modelling and simulation of the entire QC device is even more relevant. Simulation is required in order to understand the functioning of quantum algorithms, to construct novel quantum algorithms, to write quantum programs, to teach quantum computing, to construct real quantum computers, to understand and fight de-coherence and to understand and control the influence of the environment. Since quantum parallelism increases exponentially with the size of the quantum computer, parallel supercomputers are required for realistic simulations. I intend to give an introduction into the simulation of quantum computers using conventional computers. The simulation is based on a generic physical model of quantum computer hardware. Issues like parallel gate level simulators, modelling of QCs, simulators for physical quantum computers are addressed.
Quantum computing is the delicate art of using a quantum-mechanical system to perform some kind of computation. Such a system differs in a number of significant ways from ordinary computers:• A quantum computer actually does a lot of computations at the same time, each solution is represented by a particular possible state. This is inherent to the physical properties of such a system.• Unless you are sure that you have reached the final (unique) solution, you can not "look" at the "values" of the variables in the computer program that is being run: since all solutions are possible at the same time, observing the values will influence the system and put it into one particular, but otherwise arbitrary, state.• All computations must be reversible, that is, a statement like "a = 5" can only appear in the initialization phase of a program, because the previous value will be lost. On the other hand, a statement like "a = a + 5" is reversible, since you can retrieve the original value.The properties of such a quantum computer make it possible to devise very efficient algorithms. One such algorithm, described by L. Grover (see the references), is searching in an unsorted array of items. With ordinary computers this can not be done more efficiently than in O (N) steps (an exhaustive search: each item is examined in the worst case), with this quantum algorithm, however, the number of steps needed is O (N 1/2 ).Devising quantum algorithms requires a thorough understanding of quantum mechanics, there is no doubt about that. Another question is: do we need quantum computers and special programming languages to program (or perhaps emulate) these algorithms? This article tries to show that, at least for the quantum search algorithm, a classical programming language like Fortran is quite fit (yes, the pun is fortunate).
The principles of quantum mechanics – superposition, entanglement, measurement, and decoherence – form the foundation of quantum computing. Qubits, which are abstract objects having a mathematical expression to implement the rules of quantum physics, are the fundamental building blocks of computation. Software is a key component of quantum computing, along with quantum hardware. Algorithms make up software, and they are implemented using logic gates and quantum circuits. These qualities make quantum computing a paradigm that non-physicists find difficult to comprehend. It is crucial to incorporate a conceptual framework of the principles upon which quantum computing is founded into this new method of creating software. In this paper, we present a kind of taxonomical view of the fundamental concepts of quantum computing and the derived concepts that integrate the emerging discipline of quantum software engineering. Because the systematic review's main goal is to identify the core ideas behind quantum computing and quantum software, we conducted a quasi-systematic mapping as part of the review process. The findings can serve as a starting point for computer science teachers and students to address the study of this field.
Why quantum computing? As we all know very well, conventional (electronic) computers have enormous power which, moreover, is constantly increasing. With their help gigantic quantities of data can be handled and evaluated. This is of crucial importance, for instance, in modern high energy physics experiments. On the other hand, computers can be used to model very complex systems with the aim of predicting, for example, future developments in our environment, notably climatic changes. Thanks to their incredible speed computers are, of course, destined to treat mathematical problems for which specific algorithms exist very efficiently. To mention a simple example, the digits of π are readily evaluated up to a very high order. Last, but not least, their potential to solve differential equations numerically, even when they are nonlinear, makes computers indispensable in modern research. So, one might ask, is there any reason to look for fundamentally new ways of computing as they are seemingly offered by quantum processes? What advantages can be expected when the laws of quantum mechanics, rather than those of classical physics, are exploited for computation? Two answers were given: first, the simulation of complex quantum systems on classical computers meets serious difficulties that might be overcome with the help of quantum computers. This idea was suggested in 1982 by R. Feynman, and in the 1990s it was indeed shown by several groups of researchers that quantum mechanical systems for which no efficient simulation on a classical computer is known can be efficiently simulated on a quantum computer.
Early researchers attempting to simulate complex quantum mechanical interactions on digital computers discovered that they very quickly consumed the computers’ available memory\nresources, because the state space of a quantum system typically grows exponentially with problem size. Consequently, Richard Feynman proposed in 1982 that perhaps the only way to simulate complex quantum mechanical situations was by simulating them on some quantum mechanical system. Quantum computers attempt to exploit this idea incorporating the special properties of quantum mechanics, such as the superposition of states and entanglement, into a computing device. Two key algorithms have been discovered which would run on this new type of computer, Shor’s factorization algorithm discovered in 1994, which provides an exponential speedup over classical algorithms and Grover’s search algorithm in 1996, which provides a quadratic speedup. Following this in 1999 Meyer initiated the field of quantum game theory by introducing quantum mechanical states into the framework of classical game theory. In this thesis, we firstly investigate the phase estimation procedure, due to its importance as the basis for Shor’s factorization algorithm, for which a new error formula is found using an improved symmetrical definition of the error. Unlike other existing error formulas which require approximations in their derivation, our result is obtained analytically. The work on the phase estimation procedure then motivates the development of computer software written in the Java programming language, which can simulate the common algorithms and visually display their behavior on a circuit board type layout. The software is found useful in verifying the new error formula described above and to test ideas for new algorithms. Being written in Java, it is envisaged that it could be placed online and used as a learning tool for new students to the field. We then investigate the second key algorithm of quantum computing, the Grover search algorithm. It is already known that the Grover search is an SU(2) rotation but the idea is extended by deriving the three generators in terms of the two non-orthogonal basis vectors, representing the solution and initial states. We then demonstrate that the Grover search is equivalent to the precession of the polarization axis of a spin- 1/2 particle in a magnetic field. At this point we introduce geometric algebra (GA), because of its efficient implementation of rotations and its associated visual representation, and hence ideal to describe the Grover search process. It was found to provide a simple algebraic solution to the exact Grover search problem as well providing a simple visual picture describing the general solution to Meyer’s quantum penny flip game, which is a simple two-player quantum game based on the manipulation of a single qubit and hence closely analogous to the Grover search process. We then extend the work on quantum games developing two-player, three-player and N player quantum games in the context of an EPR type experiment, which has the advantage of providing a sound physical basis to quantum games avoiding the common criticism of other quantum game frameworks regarding the proper embedding of the classical game. Using the algebraic approach of GA, we solve the general N player game, without requiring the use of matrices which become unworkable for large N. Games based on non-factorisable joint probabilities were then also developed which provided a more general framework for both classical and quantum games, and allows the field of quantum games to be accessible to nonphysicists, as it does not employ Dirac’s bra-ket notation. In summary, several new results in the field of Quantum computing were produced, including an improved error formula for phase estimation [JMCL11b], a general solution to Meyer’s quantum penny flip game [CILVS09] and a paper producing quantum games from non-factorisable joint probabilities [CIA10], as well as an EPR framework for quantum games [JMCL11a], refer attached papers.
The quantum computer, is a "supercomputer" that relies on the phenomena of quantum mechanics to perform operations on data. Object of suppositions, sometimes farfetched, quantum mechanics gave birth to the quantum computer, a machine capable of processing data tens of millions of times faster than a conventional computer. A quantum computer doesn't use the same memory as a conventional computer. Rather than a sequence of 0 and 1, it works with qubits or quantum bits. The quantum computer is a combination of two major scientific fields: quantum mechanics and computer science. Quantum mechanics, on which this computer is based, governs the movement of bodies in the atomic, molecular and corpuscular domains, is a theory whose logic is totally contrary to intuition and it is essential to use mathematics to fully grasp it. Quantum computing is the sub-domain of computer science that deals with quantum computers using quantum mechanical phenomena, as opposed to those of electricity exclusively, for so-called "classical" computing. The quantum phenomena used are quantum entanglement and superposition. The article examines some aspects related to the development, operation, advantages and difficulties, applications and future of the quantum computer.