Quantum computing

Quantum computing is the use of quantum-mechanical phenomena such as superposition and entanglement to perform computation. A quantum computer is used to perform such computation, which can be implemented theoretically or physically; the field of quantum computing is a sub-field of quantum information science, which includes quantum cryptography and quantum communication. Quantum Computing was started in the early 1980s when Richard Feynman and Yuri Manin expressed the idea that a quantum computer had the potential to simulate things that a classical computer could not. In 1994, Peter Shor shocked the world with an algorithm that had the potential to decrypt all secured communications. There are two main approaches to physically implementing a quantum computer analog and digital. Analog approaches are further divided into quantum simulation, quantum annealing, adiabatic quantum computation. Digital quantum computers use quantum logic gates to do computation. Both approaches use quantum qubits.

Qubits are fundamental to quantum computing and are somewhat analogous to bits in a classical computer. Qubits can be in a 0 quantum state, but they can be in a superposition of the 1 and 0 states. However, when qubits are measured they always give a 0 or a 1 based on the quantum state they were in. Today's physical quantum computers are noisy and quantum error correction is a burgeoning field of research. Quantum supremacy is the next milestone that quantum computing will achieve soon. While there is much hope and research in the field of quantum computing, as of March 2019 there have been no commercially useful algorithms published for today's noisy quantum computers. A classical computer has a memory made up of bits, where each bit is represented by either a one or a zero. A quantum computer, on the other hand, maintains a sequence of qubits, which can represent a one, a zero, or any quantum superposition of those two qubit states. In general, a quantum computer with n qubits can be in any superposition of up to 2 n different states..

A quantum computer operates on its qubits using measurement. An algorithm is composed of a fixed sequence of quantum logic gates and a problem is encoded by setting the initial values of the qubits, similar to how a classical computer works; the calculation ends with a measurement, collapsing the system of qubits into one of the 2 n eigenstates, where each qubit is zero or one, decomposing into a classical state. The outcome can, therefore, be at most n classical bits of information. If the algorithm did not end with a measurement, the result is an unobserved quantum state. Quantum algorithms are probabilistic, in that they provide the correct solution only with a certain known probability. Note that the term non-deterministic computing must not be used in that case to mean probabilistic because the term non-deterministic has a different meaning in computer science. An example of an implementation of qubits of a quantum computer could start with the use of particles with two spin states: "down" and "up".

This is true. A quantum computer with a given number of qubits is fundamentally different from a classical computer composed of the same number of classical bits. For example, representing the state of an n-qubit system on a classical computer requires the storage of 2n complex coefficients, while to characterize the state of a classical n-bit system it is sufficient to provide the values of the n bits, that is, only n numbers. Although this fact may seem to indicate that qubits can hold exponentially more information than their classical counterparts, care must be taken not to overlook the fact that the qubits are only in a probabilistic superposition of all of their states; this means that when the final state of the qubits is measured, they will only be found in one of the possible configurations they were in before the measurement. It is incorrect to think of a system of qubits as being in one particular state before the measurement; the qubits are in a superposition of states before any measurement is made, which directly affects the possible outcomes of the computation.

To better understand this point, consider a classical computer that operates on a three-bit register. If the exact state of the register at a given time is not known, it can be described as a probability distribution over the 2 3 = 8 different three-bit strings 000, 001, 010, 011, 100, 101, 110, 111. If there is no uncertainty over its state it is in one of these states with probability 1. However, if it is a probabilistic computer there is a possibility of it being in any one of a number of different states; the state of a three-qubit quantum computer is described by an eight-dimensional vector (

Michael Nielsen

Michael Aaron Nielsen is a quantum physicist, science writer, computer programming researcher living in San Francisco. In 2004 Nielsen was characterized as Australia's "youngest academic" and secured a Federation Fellowship at the University of Queensland, he worked at the Los Alamos National Laboratory, as the Richard Chace Tolman Prize Fellow at Caltech, a Senior Faculty Member at the Perimeter Institute for Theoretical Physics. Nielsen obtained his PhD in physics in 1998 at the University of New Mexico. With Isaac Chuang he is the co-author of a popular textbook on quantum computing. In 2007, Nielsen announced a marked shift in his field of research: from quantum information and computation to “the development of new tools for scientific collaboration and publication”; this work includes "massively collaborative mathematics" projects like the Polymath project with Timothy Gowers. Besides writing books and essays, he has given talks about Open Science, he was a member of the Working Group on Open Data in Science at the Open Knowledge Foundation.

In 2015 Nielsen published the online textbook Neural Networks and Deep Learning. The same year he joined the Recurse Center as a Research Fellow. Since 2017 Nielsen works as a Research Fellow at Y Combinator Research.. Nielsen, Michael A. Reinventing Discovery: The New Era of Networked Science. Princeton, N. J: Princeton University Press. ISBN 0-691-14890-2; this book is based on themes that are covered in his essay on the Future of Science. Nielsen, Michael A.. Neural Networks and Deep Learning. Determination Press

Classical physics

Classical physics refers to theories of physics that predate modern, more complete, or more applicable theories. If a accepted theory is considered to be modern, its introduction represented a major paradigm shift the previous theories, or new theories based on the older paradigm, will be referred to as belonging to the realm of "classical physics"; as such, the definition of a classical theory depends on context. Classical physical concepts are used when modern theories are unnecessarily complex for a particular situation. Most classical physics refers to pre-1900 physics, while modern physics refers to post-1900 physics which incorporates elements of quantum mechanics and relativity. Classical theory has at least two distinct meanings in physics. In the context of quantum mechanics, classical theory refers to theories of physics that do not use the quantisation paradigm, which includes classical mechanics and relativity. Classical field theories, such as general relativity and classical electromagnetism, are those that do not use quantum mechanics.

In the context of general and special relativity, classical theories are those that obey Galilean relativity. Depending on point of view, among the branches of theory sometimes included in classical physics are variably: Classical mechanics Newton's laws of motion Classical Lagrangian and Hamiltonian formalisms Classical electrodynamics Classical thermodynamics Special relativity and general relativity Classical chaos theory and nonlinear dynamics In contrast to classical physics, "modern physics" is a looser term which may refer to just quantum physics or to 20th and 21st century physics in general. Modern physics includes quantum relativity, when applicable. A physical system can be described by classical physics when it satisfies conditions such that the laws of classical physics are valid. In practice, physical objects ranging from those larger than atoms and molecules, to objects in the macroscopic and astronomical realm, can be well-described with classical mechanics. Beginning at the atomic level and lower, the laws of classical physics break down and do not provide a correct description of nature.

Electromagnetic fields and forces can be described well by classical electrodynamics at length scales and field strengths large enough that quantum mechanical effects are negligible. Unlike quantum physics, classical physics is characterized by the principle of complete determinism, although deterministic interpretations of quantum mechanics do exist. From the point of view of classical physics as being non-relativistic physics, the predictions of general and special relativity are different than those of classical theories concerning the passage of time, the geometry of space, the motion of bodies in free fall, the propagation of light. Traditionally, light was reconciled with classical mechanics by assuming the existence of a stationary medium through which light propagated, the luminiferous aether, shown not to exist. Mathematically, classical physics equations are those. According to the correspondence principle and Ehrenfest's theorem, as a system becomes larger or more massive the classical dynamics tends to emerge, with some exceptions, such as superfluidity.

This is why we can ignore quantum mechanics when dealing with everyday objects and the classical description will suffice. However, one of the most vigorous on-going fields of research in physics is classical-quantum correspondence; this field of research is concerned with the discovery of how the laws of quantum physics give rise to classical physics found at the limit of the large scales of the classical level. Today a computer performs millions of arithmetic operations in seconds to solve a classical differential equation, while Newton would take hours to solve the same equation by manual calculation if he were the discoverer of that particular equation. Computer modeling is essential for relativistic physics. Classic physics is considered the limit of quantum mechanics for large number of particles. On the other hand, classic mechanics is derived from relativistic mechanics. For example, in many formulations from special relativity, a correction factor 2 appears, where v is the velocity of the object and c is the speed of light.

For velocities much smaller than that of light, one can neglect the terms with c2 and higher that appear. These formulas reduce to the standard definitions of Newtonian kinetic energy and momentum; this is as it should be, for special relativity must agree with Newtonian mechanics at low velocities. Computer modeling has to be as real as possible. Classical physics would introduce an error as in the superfluidity case. In order to produce reliable models of the world, we can not use classic physics, it is true that quantum theories consume time and computer resources, the equations of classical physics could be resorted to provide a quick solution, but such a solution would lack reliability. Computer modeling would use only the energy criteria to determine which theory to use: relativity or quantum theory, when attempting to describe the behavior of an object. A physicist would use a classical model to provide an approximation before more exacting models are applied and those calculations proceed.

In a computer model, there is no need to use the speed of the object if classical physics is excluded. Low energy objects would be handled by quantum theory and high energy objects by relativity theory. Glossary of classical physics Semiclassical physics

Quantum mechanics

Quantum mechanics, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, describes nature at ordinary scale. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large scale. Quantum mechanics differs from classical physics in that energy, angular momentum and other quantities of a bound system are restricted to discrete values. Quantum mechanics arose from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, from the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others; the modern theory is formulated in various specially developed mathematical formalisms.

In one of them, a mathematical function, the wave function, provides information about the probability amplitude of position and other physical properties of a particle. Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, the laser, the transistor and semiconductors such as the microprocessor and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for many biological and physical phenomena are rooted in the nature of the chemical bond, most notably the macro-molecule DNA. Scientific inquiry into the wave nature of light began in the 17th and 18th centuries, when scientists such as Robert Hooke, Christiaan Huygens and Leonhard Euler proposed a wave theory of light based on experimental observations. In 1803, Thomas Young, an English polymath, performed the famous double-slit experiment that he described in a paper titled On the nature of light and colours.

This experiment played a major role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays; these studies were followed by the 1859 statement of the black-body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system can be discrete, the 1900 quantum hypothesis of Max Planck. Planck's hypothesis that energy is radiated and absorbed in discrete "quanta" matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, known as Wien's law in his honor. Ludwig Boltzmann independently arrived at this result by considerations of Maxwell's equations. However, it underestimated the radiance at low frequencies. Planck corrected this model using Boltzmann's statistical interpretation of thermodynamics and proposed what is now called Planck's law, which led to the development of quantum mechanics. Following Max Planck's solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect.

Around 1900–1910, the atomic theory and the corpuscular theory of light first came to be accepted as scientific fact. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, Pieter Zeeman, each of whom has a quantum effect named after him. Robert Andrews Millikan studied the photoelectric effect experimentally, Albert Einstein developed a theory for it. At the same time, Ernest Rutherford experimentally discovered the nuclear model of the atom, for which Niels Bohr developed his theory of the atomic structure, confirmed by the experiments of Henry Moseley. In 1913, Peter Debye extended Niels Bohr's theory of atomic structure, introducing elliptical orbits, a concept introduced by Arnold Sommerfeld; this phase is known as old quantum theory. According to Planck, each energy element is proportional to its frequency: E = h ν, where h is Planck's constant. Planck cautiously insisted that this was an aspect of the processes of absorption and emission of radiation and had nothing to do with the physical reality of the radiation itself.

In fact, he considered his quantum hypothesis a mathematical trick to get the right answer rather than a sizable discovery. However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis realistically and used it to explain the photoelectric effect, in which shining light on certain materials can eject electrons from the material, he won the 1921 Nobel Prize in Physics for this work. Einstein further developed this idea to show that an electromagnetic wave such as light could be described as a particle, with a discrete quantum of energy, dependent on its frequency; the foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wi

The Fabric of Reality

The Fabric of Reality is a 1997 book by the physicist David Deutsch. The text was published on August 1, 1997 by Viking Adult and Deutsch wrote a follow-up book entitled The Beginning of Infinity, published in 2011; the book expands upon its implications for understanding reality. This interpretation, which he calls the multiverse hypothesis, is one of a four-strand Theory of Everything. Hugh Everett's many-worlds interpretation of quantum physics, "The first and most important of the four strands". Karl Popper's epistemology its anti-inductivism and its requiring a realist interpretation of scientific theories, its emphasis on taking those bold conjectures that resist being falsified. Alan Turing's theory of computation as developed in Deutsch's "Turing principle", where Turing's Universal Turing machine is replaced by Deutsch's universal quantum computer. Richard Dawkins's refinement of Darwinian evolutionary theory and the modern evolutionary synthesis the ideas of replicator and meme as they integrate with Popperian problem-solving.

His theory of everything is emergentist rather than reductive. It aims not at the reduction of everything to particle physics, but rather at mutual support among multiverse, computational and evolutionary principles. Critical reception has been positive; the New York Times wrote a mixed review for The Fabric of Reality, writing that it "is full of refreshingly oblique, provocative insights. But I came away from it with only the mushiest sense of how the strands in Deutsch's tapestry hang together." The Guardian was more favorable in their review, stating "This is a deep and ambitious book and there were plenty of moments when I was out of my depth. But the sheer adventure of thinking not just out of the envelope but right out of the Newtonian universe is exhilarating." The Beginning of Infinity The 4 Percent Universe Simulated reality Solipsism

Computer

A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming. Modern computers have the ability to follow generalized sets of called programs; these programs enable computers to perform an wide range of tasks. A "complete" computer including the hardware, the operating system, peripheral equipment required and used for "full" operation can be referred to as a computer system; this term may as well be used for a group of computers that are connected and work together, in particular a computer network or computer cluster. Computers are used as control systems for a wide variety of industrial and consumer devices; this includes simple special purpose devices like microwave ovens and remote controls, factory devices such as industrial robots and computer-aided design, general purpose devices like personal computers and mobile devices such as smartphones. The Internet is run on computers and it connects hundreds of millions of other computers and their users.

Early computers were only conceived as calculating devices. Since ancient times, simple manual devices like the abacus aided people in doing calculations. Early in the Industrial Revolution, some mechanical devices were built to automate long tedious tasks, such as guiding patterns for looms. More sophisticated electrical machines did specialized analog calculations in the early 20th century; the first digital electronic calculating machines were developed during World War II. The speed and versatility of computers have been increasing ever since then. Conventionally, a modern computer consists of at least one processing element a central processing unit, some form of memory; the processing element carries out arithmetic and logical operations, a sequencing and control unit can change the order of operations in response to stored information. Peripheral devices include input devices, output devices, input/output devices that perform both functions. Peripheral devices allow information to be retrieved from an external source and they enable the result of operations to be saved and retrieved.

According to the Oxford English Dictionary, the first known use of the word "computer" was in 1613 in a book called The Yong Mans Gleanings by English writer Richard Braithwait: "I haue read the truest computer of Times, the best Arithmetician that euer breathed, he reduceth thy dayes into a short number." This usage of the term referred to a human computer, a person who carried out calculations or computations. The word continued with the same meaning until the middle of the 20th century. During the latter part of this period women were hired as computers because they could be paid less than their male counterparts. By 1943, most human computers were women. From the end of the 19th century the word began to take on its more familiar meaning, a machine that carries out computations; the Online Etymology Dictionary gives the first attested use of "computer" in the 1640s, meaning "one who calculates". The Online Etymology Dictionary states that the use of the term to mean "'calculating machine' is from 1897."

The Online Etymology Dictionary indicates that the "modern use" of the term, to mean "programmable digital electronic computer" dates from "1945 under this name. Devices have been used to aid computation for thousands of years using one-to-one correspondence with fingers; the earliest counting device was a form of tally stick. Record keeping aids throughout the Fertile Crescent included calculi which represented counts of items livestock or grains, sealed in hollow unbaked clay containers; the use of counting rods is one example. The abacus was used for arithmetic tasks; the Roman abacus was developed from devices used in Babylonia as early as 2400 BC. Since many other forms of reckoning boards or tables have been invented. In a medieval European counting house, a checkered cloth would be placed on a table, markers moved around on it according to certain rules, as an aid to calculating sums of money; the Antikythera mechanism is believed to be the earliest mechanical analog "computer", according to Derek J. de Solla Price.

It was designed to calculate astronomical positions. It was discovered in 1901 in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, has been dated to c. 100 BC. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later. Many mechanical aids to calculation and measurement were constructed for astronomical and navigation use; the planisphere was a star chart invented by Abū Rayhān al-Bīrūnī in the early 11th century. The astrolabe was invented in the Hellenistic world in either the 1st or 2nd centuries BC and is attributed to Hipparchus. A combination of the planisphere and dioptra, the astrolabe was an analog computer capable of working out several different kinds of problems in spherical astronomy. An astrolabe incorporating a mechanical calendar computer and gear-wheels was invented by Abi Bakr of Isfahan, Persia in 1235. Abū Rayhān al-Bīrūnī invented the first mechanical geared lunisolar calendar astrolabe, an early fixed-wired knowledge processing machine with a gear train and gear-wheels, c. 1000 AD.

The sector, a calculating instrument used for solving problems in proportion, trigonometry and division, for various functions, such as squares and cube roots, was developed in

Simulation

A simulation is an approximate imitation of the operation of a process or system. This model is a well-defined description of the simulated subject, represents its key characteristics, such as its behaviour and abstract or physical properties; the model represents the system itself. Simulation is used in many contexts, such as simulation of technology for performance optimization, safety engineering, training and video games. Computer experiments are used to study simulation models. Simulation is used with scientific modelling of natural systems or human systems to gain insight into their functioning, as in economics. Simulation can be used to show the eventual real effects of alternative conditions and courses of action. Simulation is used when the real system cannot be engaged, because it may not be accessible, or it may be dangerous or unacceptable to engage, or it is being designed but not yet built, or it may not exist. Key issues in simulation include the acquisition of valid source information about the relevant selection of key characteristics and behaviours, the use of simplifying approximations and assumptions within the simulation, fidelity and validity of the simulation outcomes.

Procedures and protocols for model verification and validation are an ongoing field of academic study, refinement and development in simulations technology or practice in the field of computer simulation. Simulations used in different fields developed independently, but 20th-century studies of systems theory and cybernetics combined with spreading use of computers across all those fields have led to some unification and a more systematic view of the concept. Physical simulation refers to simulation in which physical objects are substituted for the real thing; these physical objects are chosen because they are smaller or cheaper than the actual object or system. Interactive simulation is a special kind of physical simulation referred to as a human in the loop simulation, in which physical simulations include human operators, such as in a flight simulator, sailing simulator, or a driving simulator. Continuous simulation is a simulation where time evolves continuously based on numerical integration of Differential Equations.

Discrete Event Simulation is a simulation where time evolves along events that represent critical moments, while the values of the variables are not relevant between two of them or result trivial to be computed in case of necessityStochastic Simulation is a simulation where some variable or process is regulated by stochastic factors and estimated based on Monte Carlo techniques using pseudo-random numbers, so replicated runs from same boundary conditions are expected to produce different results within a specific confidence band Deterministic Simulation is a simulation where the variable is regulated by deterministic algorithms, so replicated runs from same boundary conditions produce always identical results. Hybrid Simulation corresponds to a mix between Continuous and Discrete Event Simulation and results in integrating numerically the differential equations between two sequential events to reduce the number of discontinuities Stand Alone Simulation is a Simulation running on a single workstation by itself.

Distributed Simulation is operating over distributed computers in order to guarantee access from/to different resources. Modeling & Simulation as a Service where Simulation is accessed as a Service over the web. Modeling, interoperable Simulation and Serious Games where Serious Games Approaches are integrated with Interoperable Simulation. Simulation Fidelity is used to describe the accuracy of a simulation and how it imitates the real-life counterpart. Fidelity is broadly classified as 1 of 3 categories: low and high. Specific descriptions of fidelity levels are subject to interpretation but the following generalization can be made: Low – the minimum simulation required for a system to respond to accept inputs and provide outputs Medium – responds automatically to stimuli, with limited accuracy High – nearly indistinguishable or as close as possible to the real systemHuman in the loop simulations can include a computer simulation as a so-called synthetic environment. Simulation in failure analysis refers to simulation in which we create environment/conditions to identify the cause of equipment failure.

This was the fastest method to identify the failure cause. A computer simulation is an attempt to model a real-life or hypothetical situation on a computer so that it can be studied to see how the system works. By changing variables in the simulation, predictions may be made about the behaviour of the system, it is a tool to investigate the behaviour of the system under study. Computer simulation has become a useful part of modeling many natural systems in physics and biology, human systems in economics and social science as well as in engineering to gain insight into the operation of those systems