A formal derivation of Grover's quantum search algorithm

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  2. Dr Paolo Zuliani
Author(s)Zuliani P
Publication type Conference Proceedings (inc. Abstract)
Conference Name1st Joint Symposium on Theoretical Aspects of Software Engineering (TASE)
Conference Location
Year of Conference2007
Source Publication Date6-8 June 2007
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In this paper we aim at applying established formal methods techniques to a recent software area: quantum programming. In particular, we aim at providing a stepwise derivation of Grover's quantum search algorithm. Our work shows that, in principle, traditional software engineering techniques such as specification and refinement can be applied to quantum programs. We have chosen Grover's algorithm as an example because it is one of the two main quantum algorithms. The algorithm can find with high probability an element in an unordered array of length L in just O(radicL) steps (while any classical probabilistic algorithm needs Omega(L) steps). The derivation starts from a rigorous probabilistic specification of the search problem, then we stepwise refine that specification via standard refinement laws and quantum laws, until we arrive at a quantum program. The final program will thus be correct by construction.