Modified Karnaugh map for quantum Boolean circuits construction

Karnaugh map is an efficient method of minimization for conventional logic design. Unfortunately, it is usually used for 3 or 4 variables, at most 6 variables. In this paper, we modify the Karnaugh map and propose a set of reduction rules for quantum Boolean circuit optimization. By applying these rules, we can efficiently simplify a quantum Boolean circuit that has an arbitrary number of input variables. In terms of the space consumption, we use only one auxiliary qubit as the output qubit, and keep all the input qubits unchanged.