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Quantum Annealing
Quantum annealing (QA) is an optimization process for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete (combinatorial optimization problems) with many local minima; such as finding the ground state of a spin glass or solving the traveling salesman problem. The term "quantum annealing" was first proposed in 1988 by B. Apolloni, N. Cesa Bianchi and D. De Falco as a quantum-inspired classical algorithm. It was formulated in its present form by T. Kadowaki and H. Nishimori ( ja) in 1998, though an imaginary-time variant without quantum coherence had been discussed by A. B. Finnila, M. A. Gomez, C. Sebenik and J. D. Doll in 1994. Quantum annealing starts from a quantum-mechanical superposition of all possible states (candidate states) with equal weights. Then the system evolves following the time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Minimum
In mathematical analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum, they may be defined either within a given range (the ''local'' or ''relative'' extrema) or on the entire domain (the ''global'' or ''absolute'' extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. In statistics, the corresponding concept is the sample maximum and minimum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science (journal)
''Science'' is the peer review, peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, is currently circulated weekly and has a subscriber base of around 130,000. Because institutional subscriptions and online access serve a larger audience, its estimated readership is over 400,000 people. ''Science'' is based in Washington, D.C., United States, with a second office in Cambridge, UK. Contents The major focus of the journal is publishing important original scientific research and research reviews, but ''Science'' also publishes science-related news, opinions on science policy and other matters of interest to scientists and others who are concerned with the wide implications of science and technology. Unlike most scientific journals, which focus on a specific field, ''Science'' and its rival ''Nature (journal), Nature'' cover the full range of List of academ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Computer
A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing takes advantage of this behavior using specialized hardware. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer. Theoretically a large-scale quantum computer could break some widely used encryption schemes and aid physicists in performing physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications. The basic unit of information in quantum computing, the qubit (or "quantum bit"), serves the same function as the bit in classical computing. However, unlike a classical bit, which can be in one of two states (a binary), a qubit can exist in a superposition of its two " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reviews Of Modern Physics
''Reviews of Modern Physics'' (often abbreviated RMP) is a quarterly Peer review, peer-reviewed scientific journal published by the American Physical Society. It was established in 1929 and the current editor-in-chief is Michael Thoennessen. The journal publishes review articles, usually by established researchers, on all aspects of physics and related fields. The reviews are usually accessible to non-specialists and serve as introductory material to graduate students, which survey recent work, discuss key problems to be solved and provide perspectives toward the end. The journal has published several historically significant papers on quantum foundations, as well as the development of the Standard Model of particle physics. References External links * Academic journals established in 1929 Physics review journals Quarterly journals English-language journals American Physical Society academic journals {{physics-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boltzmann Constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the molar gas constant, in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating Johnson–Nyquist noise, thermal noise in resistors. The Boltzmann constant has Dimensional analysis, dimensions of energy divided by temperature, the same as entropy and heat capacity. It is named after the Austrian scientist Ludwig Boltzmann. As part of the 2019 revision of the SI, the Boltzmann constant is one of the seven "Physical constant, defining constants" that have been defined so as to have exact finite decimal values in SI units. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly joules per kelvin, with the effect of defining the SI unit ke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Hamiltonian Quaternions
William Rowan Hamilton invented quaternions, a mathematical entity in 1843. This article describes Hamilton's original treatment of quaternions, using his notation and terms. Hamilton's treatment is more geometry, geometric than the modern approach, which emphasizes quaternions' algebraic properties. Mathematically, quaternions discussed differ from the modern definition only by the terminology which is used. Classical elements of a quaternion Hamilton defined a quaternion as the quotient of two directed lines in tridimension (vector space), dimensional space; or, more generally, as the quotient of two vectors. A quaternion can be represented as the sum of a #Scalar, ''scalar'' and a #Vector, ''vector''. It can also be represented as the product of its #Tensor, ''tensor'' and its #Versor, ''versor''. Scalar Hamilton invented the term ''scalars'' for the real numbers, because they span the "scale of progression from positive to negative infinity" or because they represent the " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Monte Carlo
Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation) of the quantum many-body problem. The diverse flavors of quantum Monte Carlo approaches all share the common use of the Monte Carlo method to handle the multi-dimensional integrals that arise in the different formulations of the many-body problem. Quantum Monte Carlo methods allow for a direct treatment and description of complex many-body effects encoded in the wave function, going beyond mean-field theory. In particular, there exist numerically exact and polynomially-scaling algorithms to exactly study static properties of boson systems without geometrical frustration. For fermions, there exist very good approximations to their static properties and numerically exact exponentially scaling quantum Monte Carlo algorithms, but none that are b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Annealing Analogy
In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum. For example, a photon is a single quantum of light of a specific frequency (or of any other form of electromagnetic radiation). Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom. Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Physics A
The ''Journal of Physics A: Mathematical and Theoretical'' is a peer-reviewed scientific journal published by IOP Publishing, the publishing branch of the Institute of Physics. It is part of the '' Journal of Physics'' series and covers theoretical physics focusing on sophisticated mathematical and computational techniques. The journal is divided into six sections covering: statistical physics; chaotic and complex systems; mathematical physics; quantum mechanics and quantum information theory; classical and quantum field theory; fluid and plasma theory. The editor in chief is Joseph A Minahan ( Uppsala Universitet, Sweden). According to the ''Journal Citation Reports'', the journal has a 2023 impact factor of 2.0. History ''Journal of Physics A'' was established in 1968 as one of the subdivisions of the earlier title, '' Proceedings of the Physical Society'', established in 1874, the flagship journal of the Physical Society of London. The Physical Society later became the In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Mathematical Physics
The ''Journal of Mathematical Physics'' is a peer-reviewed journal published monthly by the American Institute of Physics devoted to the publication of papers in mathematical physics. The journal was first published bimonthly beginning in January 1960; it became a monthly publication in 1963. The current editor is Jan Philip Solovej from University of Copenhagen The University of Copenhagen (, KU) is a public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in Scandinavia, after Uppsala University. .... Its 2018 Impact Factor is 1.355 Abstracting and indexing This journal is indexed by the following services: 2013. References External ...
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Simulated Annealing
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA can find the global optimum. It is often used when the search space is discrete (for example the traveling salesman problem, the boolean satisfiability problem, protein structure prediction, and job-shop scheduling). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to exact algorithms such as gradient descent or branch and bound. The name of the algorithm comes from annealing in metallurgy, a technique involving heating and controlled cooling of a material to alter its physical properties. Both are attributes of the material that depend on their thermodynamic free energy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-completeness
In computational complexity theory, NP-complete problems are the hardest of the problems to which ''solutions'' can be verified ''quickly''. Somewhat more precisely, a problem is NP-complete when: # It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". # When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) ''solution''. # The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # The problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. Hence, if we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
