Multi-strategy Based Quantum Cost Reduction of Quantum Boolean Circuits

TL;DR

This paper introduces two algorithms for constructing and optimizing quantum circuits for Boolean functions expressed in PPRM form, reducing quantum cost and enabling implementation on IBM quantum computers.

Contribution

The paper presents novel algorithms that synthesize and optimize quantum circuits from PPRM Boolean functions, reducing quantum cost and facilitating implementation on IBM quantum hardware.

Findings

Achieved significant quantum cost reduction compared to existing methods.

Generated quantum circuits compatible with IBM quantum computers.

Applied algebraic rearrangement and decomposition techniques for optimization.

Abstract

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 $d_{term}$, 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.