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We introduce a complete transformation rule set and a minimal equation set for controlled-NOT (CNOT)-based quantum circuits. Using these rules, quantum circuits that compute the same Boolean function ...are reduced to a same normal form. We can thus easily check the equivalence of circuits by comparing their normal forms. By applying the Knuth-Bendix completion algorithm to a set of modified 18 equations introduced by Iwama et al. 2002 [IKY02], we obtain a complete transformation rule set (i.e., a set of transformation rules with the properties of `termination' and `confluence'). Our transformation rule set consists of 114 rules. Moreover, we found a minimal subset of equations for the initial equation set.続きを見る
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Mendeley出力
JMI2013B-2