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Quantum Mechanics in Quantum Computing

M. Dean Johnson

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Mathematics (Option 1) with a minor in Physics. In his sophomore year, he participated in the studentfaculty colloquium, where he explored quantum computing with several other students and faculty. Quantum mechanics is a scientific theory that seeks to describe atomic and subatomic particles (or quantum particles) as well as the interaction among them. Such particles include electrons, protons, neutrons, and photons. In classical mechanics, a particle’s future state is described with certainty once its present state is known. At any given moment, its momentum and position are determined with certainty. In quantum mechanics, its future state is described probabilistically. Instead of a single momentum, a particle can assume a simultaneous range of momenta, and instead of a single position, it can take a simultaneous range of positions. Since the product of these ranges is no less than a specific positive universal constant, a decrease in the range of its position forces an increase in the range of momentum and vice versa. It

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Mathematics (Option 1) with a minor in Physics. In his sophomore year, he participated in the studentfaculty colloquium, where he explored quantum computing with several other students and faculty. Quantum mechanics is a scientific theory that seeks to describe atomic and subatomic particles (or quantum particles) as well as the interaction among them. Such particles include electrons, protons, neutrons, and photons. In classical mechanics, a particle’s future state is described with certainty once its present state is known. At any given moment, its momentum and position are determined with certainty. In quantum mechanics, its future state is described probabilistically. Instead of a single momentum, a particle can assume a simultaneous range of momenta, and instead of a single position, it can take a simultaneous range of positions. Since the product of these ranges is no less than a specific positive universal constant, a decrease in the range of its position forces an increase in the range of momentum and vice versa. It
The Quantum theory deals with the microscopic structure of the Universe that describes the finer details of nature at the subatomic domain.To a physicist, quantum mechanics is one of the three great pillars supporting our intuition of evocative, bewildering and fascinating natural World as we continuously struggle with the inescapable strangeness of the subatomic domain as if something strange is always afoot.It is well accepted fact that quantum mechanics is a physical theory that describes the way things behave at subatomic level which is quite dazzling in its precision and explanatory power.A test of quantum electrodynamics, the oldest and best understood of the modern quantum theory that involves measuring the way an electron behaves in the vicinity of a magnetic force. Many of the technological and social changes that have revolutionized our lives have actually risen out of the fundamental theoretical research carried out with only motivation to understand the World in a better way than ever. For example, the invention of transistor actually came with the fundamental theoretical research on the Uncertainty Principle which states that the uncertainty of the position of a particle times the uncertainty of its velocity is always a constant. If we double the certainty of the position of the particle, we have to make half the certainty of its velocity and vice versa. Quantum theory is perhaps the prime example of the infinitely esoteric in the sense that it describes a World in which a particle really can be in several places at once and it moves from one place to another by exploring the entire Universe simultaneously-the theory of simultaneity. The diverse and complex Universe is actually made of a few tiny particles according to the rules of quantum theory which is so simple that can be summarized on the back of an envelope. The more we understand about the elemental nature of the Universe, the simpler it looks. We have already discovered that everything in the diverse and complex Universe is nothing but the different assemblies of atoms, and the wide variety of atoms are constructed using the three building blocks at the sub-atomic domain i.e. subatomic particles: protons, neutrons and electrons. We have also discovered that protons and neutrons ate made up of combination of three entities called quarks. And that is where things stop as far as recent discovery is concerned. But the recent progress in particle physics inspiring the quest for the ultimate unified theory of physics that can describe everything in the Universe in one go. The discovery of Boson particle certainty will revolutionaries the Newton's mass concept and gravity into whole new looks. To an optimistic point of view, we must hope the best out of the progress in physics.
Abstract: Quantum computing is a modern calculation method that is based on the science of quantum mechanics. These phenomena include the bizarre behavior of particles at the atomic and subatomic levels, and the way that these particles can be in multiple states simultaneously. The field of computer science is a great mix of physics, math, and information theory. This technology provides high computing power, low power consumption, and exponential speed by controlling the behavior of small physical objects, such as atoms. Atoms, electrons, photons, etc. are all elements of the physical world. We would like to introduce the basics of quantum computing, and some of the ideas behind it. This article begins with the origins of the classical computer and discusses all the improvements and transformations that have been made due to its limitations thus far, then moves on to the basic operations of quantum computing and results in quantum properties such as superposition, entanglement, and interference.
Those defile the purity of mathematical and philosophical truthy who confound real quantities with their relations and sensible measures. —ISAAC NEWTON, Principia Before we say anything about quantum mechanics, let us take a quick look at the Newtonian (or ‘classical’) view of the physical universe. According to that view, nature consists of an enormous number of particles. When Newtonian physics is combined with the theory of the electromagnetic field, it becomes convenient to think of these particles as dimensionless (even if there is a kind of conceptual strain involved in trying to think of something as having a mass but not any size ), and as possessing electrical properties – negative charge, or positive charge, or neutrality. This leads to the well-known ‘solar system’ view of the atom – with the electrons whirling around the nucleons (neutrons and protons) just as the planets whirl around the sun. Out of atoms are built molecules; out of molecules, macroscopic objects, scaling from dust motes to whole planets and stars. These latter also fall into larger groupings – solar systems and galaxies – but these larger structures differ from the ones previously mentioned in being held together exclusively by gravitational forces. At every level, however, one has trajectories (ultimately that means the possibility of continuously tracing the movements of the elementary particles) and one has causality (ultimately that means the possibility of extrapolating from the history of the universe up to a given time to its whole sequence of future states).
Quantum physics joined the mainstream in the 1920s and 1930s with the general acceptance of the theories of Max Planck, Albert Einstein, Niels Bohr (1885-1962), Erwin Schrödinger (1887-1961), Werner Heisenberg (1901-1976), Paul Dirac (1902-1984), and many other established physicists. Quantum computing is based on quantum physics, with all of its special behaviors and unusual limits. Therefore, quantum computing deals with the behaviors of atomic and subatomic particles. These behaviors are irreducibly random and the measurement of particle characteristics simultaneously, such as position and momentum, to an arbitrary precision is impossible. That is, physical phenomena of small particles do not agree often with our classical intuition. The unusual behavior results from features of quantum mechanics called superposition and interference. In the early 1980s, Richard Feynman (1918-1988) noted that there seemed to be fundamental difficulties in simulating quantum mechanical systems on digital computers, and further suggested that having computers based on the principles of quantum mechanics would overcome those difficulties. Devices that perform quantum information processing are known as quantum computers.
Quantum mechanics is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Quantum mechanics is inescapable. Nearly all fields of modern physics, from elementary particles to the big bang, from semiconductors to solar energy cells, are related to quantum physics. Particles have characteristic trait of both particles and waves. The Schrodinger equation is the basic equation of quantum mechanics. The Schrodinger equation was established based on the quantization of energy conservation using quantum operators and the de Broglie relation. Wave function plays an important role in quantum mechanics. The probability interpretation assumes that the norm of the wave function measures the probability of the system in a particular coordinate or representation, in which the total probability is normalized.