Parameterized query complexity in quantum computation

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Purohit, Parijat Prashun
University of Lethbridge. Faculty of Arts and Science
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Lethbridge, Alta. : Universtiy of Lethbridge, Department of Mathematics and Computer Science
Given a function promised to be constant or balanced. Deutsch's algorithm and it's extension Deutsch-Jozsa are the algorithms that can determine the property of the function in constant number of queries. The algorithm works only on the functions that are promised to be either constant or balanced. There exist functions that are neither constant nor balanced. Our proposal is to analyze the query complexity of two such functions as a function of some parameter. We apply the methodology to two different problems. We parameterize the degree of imbalance for an arbitrarily chosen function. The same parameterization is used for the functions that are not self-dual. We give global and local adiabatic algorithms for both the problems. Our adiabatic algorithms have smaller query complexity as compared to the deterministic algorithms.
adiabatic quantum computation , balanced function , constant function , Deutsch-Jozsa algorithm , function self-duality , parameterized complexity