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}}</ref> A classical (or non-quantum) 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,<ref>{{Cite book|title = Quantum Computer Science|url = https://books.google.com/books?id=-wkJIuw0YRsC&pg=PA23&lpg=PA23&dq=quantum%2520computer%2520equivalent%2520classical%2520computer&source=bl&ots=a4GtRJVB3c&sig=TwUadwnVELCCwY6EXkKne-2GZVw&hl=en&sa=X&ved=0ahUKEwi54efO39PJAhUG7WMKHSg6BkIQ6AEIRDAH#v=onepage&q=quantum%2520computer%2520equivalent%2520classical%2520computer&f=false|publisher = Morgan & Claypool Publishers|date = 2009-01-01|isbn = 9781598297324|first = Marco|last = Lanzagorta|first2 = Jeffrey K.|last2 = Uhlmann}}</ref> 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]].
Problems which are [[Undecidable problem|undecidable]] using classical computers remain undecidable using quantum computers{{citation needed|date=February 2018}}. What makes quantum algorithms interesting is that they might be able to solve some problems faster than classical algorithms{{why|date=February 2018}}.
The most well known algorithms are [[Shor's algorithm]] for factoring, and [[Grover's algorithm]] for searching an unstructured database or an unordered list. Shor's algorithms runs exponentially faster than the best known classical algorithm for factoring, the [[general number field sieve]]{{citation needed|date=February 2018}}. Grover's algorithm runs quadratically faster than the best possible classical algorithm for the same task{{citation needed|date=February 2018}}{{which|date=February 2018}}.
==Overview==
Quantum algorithms are usually described, in the commonly used circuit model of quantum computation, by a [[quantum circuit]] which acts on some input [[qubit]]s and terminates with a [[measurement]]. A quantum circuit consists of simple [[quantum gate]]s which act on at most a fixed number of qubits{{why|date=February 2018}}, usually two or three{{according to whom|date=February 2018}}. Quantum algorithms may also be stated in other models of quantum computation, such as the [[Hamiltonian oracle model]].<ref name=Hamiltonian_NAND_Tree>
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