Gregory John Chaitin is an Argentine-American mathematician and computer scientist. Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a computer-theoretic result equivalent to Gödel's incompleteness theorem. He is considered to be one of the founders of what is today known as algorithmic complexity together with Andrei Kolmogorov and Ray Solomonoff. Along with the works of e.g. Solomonoff, Kolmogorov, Martin-Löf, and Leonid Levin, algorithmic information theory became a foundational part of theoretical computer science, information theory, and mathematical logic. It is a common subject in several computer science curricula. Besides computer scientists, Chaitin's work draws attention of many philosophers and mathematicians to fundamental problems in mathematical creativity and digital philosophy.
A quantum computer is a computer that takes advantage of quantum mechanical phenomena.
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. It is Turing complete and can simulate a universal constructor or any other Turing machine.
A cellular automaton is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. Cellular automata have found application in various areas, including physics, theoretical biology and microstructure modeling.
Langton's ant is a two-dimensional universal Turing machine with a very simple set of rules but complex emergent behavior. It was invented by Chris Langton in 1986 and runs on a square lattice of black and white cells. The universality of Langton's ant was proven in 2000. The idea has been generalized in several different ways, such as turmites which add more colors and more states.
Hypercomputation or super-Turing computation is a set of models of computation that can provide outputs that are not Turing-computable. For example, a machine that could solve the halting problem would be a hypercomputer; so too would one that can correctly evaluate every statement in Peano arithmetic.
Combinatorial game theory measures game complexity in several ways:
- State-space complexity,
- Game tree size,
- Decision complexity,
- Game-tree complexity,
- Computational complexity.
The Rule 110 cellular automaton is an elementary cellular automaton with interesting behavior on the boundary between stability and chaos. In this respect, it is similar to Conway's Game of Life. Like Life, Rule 110 with a particular repeating background pattern is known to be Turing complete. This implies that, in principle, any calculation or computer program can be simulated using this automaton.
In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is usually used for those algorithms which seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement.
Quantum information science is a field that combines the principles of quantum mechanics with information theory to study the processing, analysis, and transmission of information. It covers both theoretical and experimental aspects of quantum physics, including the limits of what can be achieved with quantum information. The term quantum information theory is sometimes used, but it does not include experimental research and can be confused with a subfield of quantum information science that deals with the processing of quantum information.
A cellular automaton (CA) is Life-like if it meets the following criteria:
Seeds is a cellular automaton in the same family as the Game of Life, initially investigated by Brian Silverman and named by Mirek Wójtowicz. It consists of an infinite two-dimensional grid of cells, each of which may be in one of two states: on or off. Each cell is considered to have eight neighbors, as in Life. In each time step, a cell turns on or is "born" if it was off or "dead" but had exactly two neighbors that were on; all other cells turn off. Thus, in the notation describing the family of cellular automata containing Life, it is described by the rule B2/S.
Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory.
The following tables list the computational complexity of various algorithms for common mathematical operations.
In computational complexity theory, QMA, which stands for Quantum Merlin Arthur, is the set of languages for which, when a string is in the language, there is a polynomial-size quantum proof that convinces a polynomial time quantum verifier of this fact with high probability. Moreover, when the string is not in the language, every polynomial-size quantum state is rejected by the verifier with high probability.
Golly is a tool for the simulation of cellular automata. It is free open-source software written by Andrew Trevorrow and Tomas Rokicki; it can be scripted using Lua or Python. It includes a hashlife algorithm that can simulate the behavior of very large structured or repetitive patterns such as Paul Rendell's Life universal Turing machine, and that is fast enough to simulate some patterns for 232 or more time units. It also includes a large library of predefined patterns in Conway's Game of Life and other rules.
In quantum computing, quantum supremacy or quantum advantage is the goal of demonstrating that a programmable quantum computer can solve a problem that no classical computer can solve in any feasible amount of time, irrespective of the usefulness of the problem. The term was coined by John Preskill in 2012, but the concept dates back to Yuri Manin's 1980 and Richard Feynman's 1981 proposals of quantum computing.
Continuous-variable (CV) quantum information is the area of quantum information science that makes use of physical observables, like the strength of an electromagnetic field, whose numerical values belong to continuous intervals. One primary application is quantum computing. In a sense, continuous-variable quantum computation is "analog", while quantum computation using qubits is "digital." In more technical terms, the former makes use of Hilbert spaces that are infinite-dimensional, while the Hilbert spaces for systems comprising collections of qubits are finite-dimensional. One motivation for studying continuous-variable quantum computation is to understand what resources are necessary to make quantum computers more powerful than classical ones.
This glossary of quantum computing is a list of definitions of terms and concepts used in quantum computing, its sub-disciplines, and related fields.
