A Novel Hypercube-Based Heuristic for Quantum Boolean Circuit Synthesis

Quantum computation has extraordinary capabilities for solving complicated problems. As quantum computations are reversible by nature, reversible circuits are important for the development of quantum computation techniques. Designing an effective and efficient method for synthesizing reversible circuits to reduce costs and stabilize circuit efficiency is crucial. The traditional synthesis methods of solving reversible circuits focus on the conversion efficiency rather than discussing the properties of the reversible function. Thus, this paper aims to propose a novel synthesis method that directly and efficiently optimizes reversible circuit synthesis with the properties of the reversible circuit. The proposed method converts the reversible function into a hypercube, allowing visual observations of the overall circuit. Two new indicators, the adjacent Hamming distance (AHD) and total cycle distance (TCD), aid in effective decision-making, generating shorter circuits. Furthermore, we use the generalized Toffoli gate set, which without requiring any additional ancilla bits and has applications in error correction and fault tolerance. The experimental results show that our method can find better solutions than traditional methods, significantly reducing the gate count, while the hypercube assists in synthesizing the reversible circuit.