Future Computers

Alan Turing 23 June 1912 – 7 June 1954 English mathematician Logician cryptanalyst and computer scientist

Alan Turing For a time he was head of Hut 8, the section responsible for German naval cryptanalysis during World War II An Enigma machine is any of a family of related electro-mechanical rotor machines used for the encryption and decryption of secret messages, the German military model, the – Wehrmacht Enigma, is the version most commonly discussed.

Alan Turing Together with Gordon Welchman designed La Bombe that could break any Enigma-enciphered message The basic property of the Bombe was that it could break any Enigma-enciphered message, provided that the hardware of the Enigma was known and that a plain-text 'crib' of about 20 letters could be guessed accurately After the war he worked at the National Physical Laboratory, where he created one of the first designs for a stored-program computer, the ACE.

Touring Machine 1936

Execution. Initially the Turing machine starts in one distinguished state called the start state, and the tape head points to one distinguished cell called the start cell. There is at most one possible transition corresponding to each combination of state and input symbol; thus, the actions of the machine are completely determined in advance.

4turing/ p p Turing Machine

Touring Machine 1936 Read the input symbol from the active cell. Look up the transition rule associated with the current state and input symbol. Overwrite the input symbol with the new symbol. Change the current state according to the transition rule. Shift the tape head one cell to the left or right, according to the new state's designation.

Universal Turing Machine "It is possible to invent a single machine which can be used to compute any computable sequence. If this machine U is supplied with a tape on the beginning of which is written the S.D ["standard description" of an action table] of some computing machine M, then U will compute the same sequence as M."

John Von Neumann December 28, 1903 – February 8, 1957 Made major contributions to: Set theory, Functional analysis, Quantum mechanics, Ergodic theory, Continuous geometry, Economics Computer science, Numerical analysis, Hydrodynamics

John Von Neumann Von Neumann distinguished himself from his peers in childhood for having a photographic memory, being able to memorize and recite back a page out of a phone book in a few minutes. Science, history, and psychology were among his many interests; he succeeded in every academic subject in school.

John Von Neumann He published his first mathematical paper in collaboration with his tutor at the age of eighteen, and resolved to study mathematics in college.

John Von Neumann Architecture

Alonzo Church June 14, 1903 – August 11, 1995 American mathematician and logician Made major contributions to: Mathematical logic and the Foundations of theoretical computer science

Alonzo Church He is best known for the lambda calculus, – is a formal system for function definition, function application and recursion – smallest universal programming language of the World – It is equivalent to Turing machines. However, it emphasizes the use of transformation rules and does not care about the actual machine implementing them Church–Turing thesis, Frege–Church ontology, and the Church–Rosser theorem.

Church–Turing Thesis Informally it states that if an algorithm (a procedure that terminates) exists then there is an equivalent – Turing machine, – recursively-definable function, – or applicable λ-function, for that algorithm. Today the thesis has near-universal acceptance

Modern Computers Von Neumann Machine implement a universal Turing machine and have a sequential architecture Modern Computers are based on John Von Neumann architecture Modern Computers are based on 1936 architecture

Travelling salesman problem The Travelling Salesman Problem (TSP) is a problem in combinatorial optimization studied in operations research and theoretical computer science. Given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits each city exactly once. oblem oblem

Travelling salesman problem The most direct solution would be to try all permutations (ordered combinations) and see which one is cheapest (using brute force search). The running time for this approach lies within a polynomial factor of O(n!), the factorial of the number of cities, so this solution becomes impractical even for only 20 cities. permutationsbrute force searchfactorial One of the earliest applications of dynamic programming is an algorithm that solves the problem in time O(n 2 2 n )dynamic programming

New Computer Paradigm Superposition

New Computer Paradigm In 1982, the Nobel prize-winning physicist Richard Feynman thought up the idea of a 'quantum computer', a computer that uses the effects of quantum mechanics to its advantage. Quantum Computers use non classic logic operations to perform numeric calculations. The advantage of Quantum Computers derives from their capabilities to execute multiple operations simultaneously on a single computer. The Quantum Computers are inspired on Quantum Mechanics.

New Computer Paradigm “I think it is safe to say that no one understands Quantum Mechanics. … What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it.... That is because I don't understand it. Nobody does. (Richard Feynman)

David Deutsch’s Algorithm Compute in a single step:

Different Computer Paradigm Quantum algorithms will probably be used in computers within a 10 year range; there are several efficient algorithms already developed and many to come. Following we will show some interesting comparisons that would will help to illustrate the importance of these developments:

Dr. Quantum

Different Computer Paradigm

Mother Computer

IBM’s Quantum Computer