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The construction of quantum computers is based on the synthesis of low-cost quantum circuits. The quantum circuit of any Boolean function expressed in a Positive Polarity Reed-Muller PPRM expansion can be synthesized using Multiple-Control Toffoli (MCT) gates. This paper proposes two algorithms to construct a quantum circuit for any Boolean function expressed in a Positive Polarity Reed-Muller PPRM expansion. The Boolean function can be expressed with various algebraic forms, so there are different quantum circuits can be synthesized for the Boolean function based on its algebraic form. The proposed algorithms aim to map the MCT gates into the NCV gates for any quantum circuit by generating a simple algebraic form for the Boolean function. The first algorithm generates a special algebraic form for any Boolean function by rearrangement of terms of the Boolean function according to a predefined degree of term dₓ₄ₑ₌, then synthesizes the corresponding quantum circuit. The second algorithm applies the decomposition methods to decompose MCT circuit into its elementary gates followed by applying a set of simplification rules to simplify and optimize the synthesized quantum circuit. The proposed algorithms achieve a reduction in the quantum cost of synthesized quantum circuits when compared with relevant work in literature. The proposed algorithms synthesize quantum circuits that can applied on IBM quantum computer.
Ahmed et al. (Fri,) studied this question.