transformation rules for designing cnot-based quantum circuits
This paper gives a simple but nontrivial set of local transformation rules for Control-NOT(CNOT) -based combinatorial circuits. It is shown that this rule set is complete, namely, for any two equivalent circuits, S 1 and S 2 , there is a sequence of transformations, each of them in the rule set, which changes S 1 to S 2 . Our motivation is to use this rule set for developing a design theory for quantum circuits whose Boolean logic parts should be implemented by CNOT based circuits. As a preliminary example, we give a design procedure based on our transformation rules which reduces the cost of CNOT-based circuits.
quantum circuit local transformation rules cnot gate