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arXiv:1401.4507

Using Quantum Computers to Learn Physics

Nathan Wiebe

Published Jan 18, 2014• 1 citation
arXivHTMLPDF

Abstract

Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve using existing computers for even modestly large systems. Here I will show that quantum computers can sometimes be used to address such problems and that quantum computer science can assign formal complexities to learning facts about nature. Hence, computer science should not only be regarded as an applied science; it is also of central importance to the foundations of science.

DOI
10.48550/arxiv.1401.4507

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Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve using existing computers for even modestly large systems. Here I will show that quantum computers can sometimes be used to address such problems and that quantum computer science can assign formal complexities to learning facts about nature. Hence, computer science should not only be regarded as an applied science; it is also of central importance to the foundations of science.
Quantum theory is one of the most successful theories that have influenced the course of scientific progress during the twentieth century. It has presented a new line of scientific thought, predicted entirely inconceivable situations and influenced several domains of modern technologies. There are many different ways for expressing laws of science in general and laws of physics in particular. Similar to physical laws of nature, information can also be expressed in different ways. The fact that information can be expressed in different ways without losing its essential nature, leads for the possibility of the automatic manipulation of information. Quantum computing is a study area that focuses on developing computers based on the properties of “quantum theory” & “quantum physics”. Quantum theory defines the behavior & nature of energy and matter on the “atomic” and “subatomic” levels also known as the quantum levels. A quantum computer is a computational device that utilizes the phenomena of quantum mechanics with its quantum properties to structure & process data. A large-scale quantum computer is capable of performing operations in exponentially enormous speed compared to a classical computer. Development of such computers is considered a massive leap for mankind in computing abilities with huge performance gains for simulations or brute force for example. All ways of expressing information use physical system, spoken words are conveyed by air pressure fluctuations: “No information without physical representation”. Quantum computers are not meant to replace typical computers. In practice, they will be separate instruments used to solve complex, data-heavy problems, particularly those that make use of machine learning, where the system can make predictions and improve over time.
The following paper describes how quantum mechanics can be used to improve computation. The main challenge for a conventional computer is to solve an exponentially difficult problem and factoring a large number. In the course of this paper, the standard tools of computation, universal gates and machines are reviewed. These ideas are then applied first to conventional computers and then to quantum computers. A schematic model of a quantum computer is described as well as some of the subtleties in its programming.
At the beginning of the twentieth century it would be unthinkable, among european scientists, to separate natural science and philosophy. Physicists-philosophers were scientists such as Einstein, Bohr, Heisenberg, Schrödinger, among others, who refounded physics by laying the foundations of quantum mechanics and special and general relativity. In this paper we briefly review how some of these thinkers have looked at the issues of the value of science, the relationship between science and philosophy, and the importance of Greek philosophy to nuclear physics and quantum theory.
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.
In This Remarkable Treatise, Professor Schafer shares his conclusions from a lifelong search for evidence -- from quantum science -- of the existence of a transcendent part of physical reality. With a view as wide as the cosmos and as infinitesimal as the electron, he combines disciplinary thought from science, philosophy, religion, and ethics to address the educated generalist and layman with a profound look at existence. When modern science adopted objectivity and experimental testing as operational principles, the ensuing advances in the physical sciences first clashed with, and then destroyed, the world view of the ruling religious mythologies. A general disorientation resulted and a schism evolved in society, disconnecting the world of facts from the world of values. In a disastrous way the covenant which all religious mythologies claimed existed between humanity and nature was broken, and it seemed to many that life itself was rendered meaningless in the process. However, twentieth-century science has discovered -- in quantum phenomena -- a part of physical reality which, in contrast to the mechanical world of classical science, has all the characteristics of a transcendent reality Now the foundation of the material world is discovered to be nonmaterial, the constituents of real things are found to be not real in the same way as the things that they make, and non-local, faster-than-light influences are found to pervade a universe whose nature is mindlike. Braving controversy, Professor Schafer concludes that the discovery of the phenomena of quantum mechanics has established a new covenant -- between the human mind and the mindlike background of the universe -- one thatprovides a home again to the homeless and meaning to seemingly pointless life. In this new understanding of the world, the universe must be assumed to have a moral as well as a physical order, and facts and values derive, again, from a single source.
Quantum Physics is defined as “the study of matter and energy at the most fundamental level”. It has entirely transformed our perspective of the physical world and is also the foundation of numerous technological advancements. More specifically, quantum mechanics has been applied in sectors such as medicine and biology, with quantum computing emerging as the most prominent among them. [5] The primary objective of this study is to analyse the concepts of quantum computing, focusing on what quantum computers are, how they function, as well as outline and explain the differences between them and standard computational models (classic computers). Furthermore, their relation to the laws of physics will be discussed. Secondarily, this article aims to provide recent achievements, such as existing quantum computers and plans concerning the future so as to underline the role quantum physics will play, shaping the frontier of computation.