In computability theory, the Church–Turing thesis is a hypothesis about the nature of computable functions. It states that a function on the natural numbers is computable by a human being following an algorithm, ignoring resource limitations, if and only if it is computable by a Turing machine. The thesis is named after American mathematician Alonzo Church and the British mathematician Alan Turing. Before the precise definition of computable function, mathematicians often used the informal term effectively calculable to describe functions that are computable by paper-and-pencil methods. In the 1930s, several independent attempts were made to formalize the notion of computability:
David Elieser Deutsch is a British physicist at the University of Oxford. He is a Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation (CQC) in the Clarendon Laboratory of the University of Oxford. He pioneered the field of quantum computation by formulating a description for a quantum Turing machine, as well as specifying an algorithm designed to run on a quantum computer. He is a proponent of the many-worlds interpretation of quantum mechanics.
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.
A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, given any computer algorithm, a Turing machine capable of simulating that algorithm's logic can be constructed.
In computability theory, a system of data-manipulation rules is said to be Turing complete or computationally universal if it can be used to simulate any Turing machine. This means that this system is able to recognize or decide other data-manipulation rule sets. Turing completeness is used as a way to express the power of such data-manipulation rule set. The expression power of these grammars is captured in the Chomsky hierarchy. Virtually all programming languages today are Turing Complete. The concept is named after English mathematician and computer scientist Alan Turing.
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on more mathematical topics
of computing and includes the theory of computation.
In physics and cosmology, digital physics is a collection of theoretical perspectives based on the premise that the universe is describable by information. It is a form of digital ontology about the physical reality. According to this theory, the universe can be conceived of as either the output of a deterministic or probabilistic computer program, a vast, digital computation device, or mathematically isomorphic to such a device.
Ray Solomonoff's theory of universal inductive inference is a theory of prediction based on logical observations, such as predicting the next symbol based upon a given series of symbols. The only assumption that the theory makes is that the environment follows some unknown but computable probability distribution. It is a mathematical formalization of Occam's razor and the Principle of Multiple Explanations.
In computer science and quantum physics, the Church–Turing–Deutsch principle is a stronger, physical form of the Church–Turing thesis formulated by David Deutsch in 1985.
In computational complexity theory, an alternating Turing machine (ATM) is a non-deterministic Turing machine (NTM) with a rule for accepting computations that generalizes the rules used in the definition of the complexity classes NP and co-NP. The concept of an ATM was set forth by Chandra and Stockmeyer and independently by Kozen in 1976, with a joint journal publication in 1981.
Reversible computing is a model of computing where the computational process to some extent is reversible, i.e., time-invertible. In a model of computation that uses deterministic transitions from one state of the abstract machine to another, a necessary condition for reversibility is that the relation of the mapping from (nonzero-probability) states to their successors must be one-to-one. Reversible computing is a form of unconventional computing.
In computational complexity theory, R is the class of decision problems solvable by a Turing machine, which is the set of all recursive languages.
A quantum Turing machine (QTM), also a universal quantum computer, is an abstract machine used to model the effect of a quantum computer. It provides a very simple model which captures all of the power of quantum computation. Any quantum algorithm can be expressed formally as a particular quantum Turing machine. Such Turing machines were first proposed in a 1985 article written by Oxford University physicist David Deutsch suggesting quantum gates could function in a similar fashion to traditional digital computing binary logic gates.
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 operations, called programs. These programs enable computers to perform an extremely wide range of tasks. A "complete" computer including the hardware, the operating system, and 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.
A quantum cellular automaton (QCA) is an abstract model of quantum computation, devised in analogy to conventional models of cellular automata introduced by John von Neumann. The same name may also refer to quantum dot cellular automata, which are a proposed physical implementation of "classical" cellular automata by exploiting quantum mechanical phenomena. QCA have attracted a lot of attention as a result of its extremely small feature size and its ultra-low power consumption, making it one candidate for replacing CMOS technology.
In his book A New Kind of Science, Stephen Wolfram described a universal 2-state 5-symbol Turing machine, and conjectured that a particular 2-state 3-symbol Turing machine might be universal as well.
Mobile translation refers to any electronic device or software application that provides audio translation. It includes any handheld electronic device that is specifically designed for audio translation. It also includes any machine translation service or software application for hand-held devices, including mobile telephones, Pocket PCs, and PDAs. Mobile translation provides hand-held device users with the advantage of instantaneous and non-mediated translation from one human language to another, usually against a service fee that is, nevertheless, significantly smaller than a human translator charges.
Norman H. Margolus is a Canadian-American physicist and computer scientist, known for his work on cellular automata and reversible computing. He is a research affiliate with the Computer Science and Artificial Intelligence Laboratory at the Massachusetts Institute of Technology.
Quantum machine learning is an emerging interdisciplinary research area at the intersection of quantum physics and machine learning. The most common use of the term refers to machine learning algorithms for the analysis of classical data executed on a quantum computer. While machine learning algorithms are used to compute immense quantities of data, quantum machine learning increases such capabilities intelligently, by creating opportunities to conduct analysis on quantum states and systems. This includes hybrid methods that involve both classical and quantum processing, where computationally difficult subroutines are outsourced to a quantum device. These routines can be more complex in nature and executed faster with the assistance of quantum devices. Furthermore, quantum algorithms can be used to analyze quantum states instead of classical data. Beyond quantum computing, the term "quantum machine learning" is often associated with machine learning methods applied to data generated from quantum experiments, such as learning quantum phase transitions or creating new quantum experiments. Quantum machine learning also extends to a branch of research that explores methodological and structural similarities between certain physical systems and learning systems, in particular neural networks. For example, some mathematical and numerical techniques from quantum physics are applicable to classical deep learning and vice versa. Finally, researchers investigate more abstract notions of learning theory with respect to quantum information, sometimes referred to as "quantum learning theory".
