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On the Power of Quantum Computation: Oracles

Niklas Johansson

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

Quantum computation solve some computational problems faster than the best-known alternative in classical computation. The evidence for this consists of examples where a quantum algorithm outperfor ...

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Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation and, in particular, on problems with an algebraic flavor.