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Computing Relations in the Quantum Query Model

Query algorithms are used to compute mathematical functions. Classical version of this model is also known as decision trees. Quantum counterpart of decision trees – quantum query model – has been actively studied in recent years. Typically, query model is used to compute Boolean functions. In this paper, we consider computing mathematical relations instead of functions. A relation is a set of ordered pairs and the difference from a function is that each element from a domain set may be mapped to multiple elements from a range set. We demonstrate that quantum query model is well suited for computing relations. We present examples of quantum query algorithms that are more efficient than the best possible classical algorithms for computing specific relations.