Quantum computing studies theoretical computation systems (quantum computers) that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data.[1] Quantum computers are different from binary digital electronic computers based on transistors. Whereas common digital computing requires that the data are encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation is analog and uses quantum bits, which can be in an infinite number of superpositions of states. A quantum Turing machine is a theoretical model of such a computer, and is also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers. The field of quantum computing was initiated by the work of Paul Benioff[2] and Yuri Manin in 1980,[3] Richard Feynman in 1982,[4] and David Deutsch in 1985.[5] A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in 1968.[6]

As of 2016, the development of actual quantum computers is still in its infancy, but experiments have been carried out in which quantum computational operations were executed on a very small number of quantum bits.[7] Both practical and theoretical research continues, and many national governments and military agencies are funding quantum computing research in an effort to develop quantum computers for civilian, business, trade, environmental and national security purposes, such as cryptanalysis.[8]

Large-scale quantum computers would theoretically be able to solve certain problems much more quickly than any classical computers that use even the best currently known algorithms, like integer factorization using Shor’s algorithm or the simulation of quantum many-body systems. There exist quantum algorithms, such as Simon’s algorithm, that run faster than any possible probabilistic classical algorithm.[9] Given sufficient computational resources, a classical computer could in theory simulate any quantum algorithm, as quantum computation does not violate the Church–Turing thesis.[10] On the other hand, quantum computers may be able to efficiently solve problems which are not practically feasible on classical computers.