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{{cite arxiv
| last = Mosca | first = M.
| date = 2008
| title = Quantum Algorithms
| class = quant-ph
| eprint = 0808.0369
}}</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, 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]].
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|last2=Hoyer |first2=P.
|last3=Tapp |first3=A.
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{{cite arxiv
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A quantum walk is the quantum analogue of a classical [[random walk]]. Similar to a classical random walk, which can be described by a [[probability distribution]] over some states, a quantum walk can be described by a [[quantum superposition]] over states. Quantum walks are known to give exponential speedups for some black-box problems.<ref>
{{cite
|last1=Childs |first1=A. M.
|last2=Cleve |first2=R.
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|year=2003
|title=Exponential algorithmic speedup by quantum walk
|pages=59–68▼
|publisher=[[Association for Computing Machinery]]
|arxiv=quant-ph/0209131▼
|bibcode=
|doi=10.1145/780542.780552
|isbn=1581136749
▲ |pages=59–68
▲ |journal=Proc. th ACM Symposium on Theory of Computing (STOC ), pp.
▲ |arxiv=quant-ph/0209131
}}</ref><ref>
{{cite
|last1=Childs |first1=A. M.
|last2=Schulman |first2=L. J.
|last3=Vazirani |first3=U. V.
|year=2007
|
|pages=395–404▼
|publisher=[[IEEE]]
|arxiv=0705.2784▼
|doi=10.1109/FOCS.2007.18
▲ |chapter=Quantum Algorithms for Hidden Nonlinear Structures
|isbn=0-7695-3010-9
▲ |pages=395–404
▲ |arxiv=0705.2784
}}</ref> They also provide polynomial speedups for many problems. A framework for the creation quantum walk algorithms exists and is quite a versatile tool.<ref name=Search_via_quantum_walk/>
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