Quantum circuit optimization of an integer divider

Efficient arithmetic operations in quantum circuits play a vital role in the implementation of quantum algorithms. Quantum circuits constructed exclusively using gates of the Clifford+T group are compatible with error detection and correction codes available in the quantum literature. However, the T gate, a member of this group, has a higher cost compared to other gates, making it crucial to minimize its usage to reduce circuit expenses. While the T gate cannot be entirely avoided since the Clifford group is not a universal set of gates, circuit optimization can effectively reduce the number of T gates required for implementation. In this work, we present a novel divider circuit for quantum computing that focuses on reducing the number of T gates while maintaining a reasonable number of qubits for this type of operation. To achieve this, we introduce variants of minor circuits, including a comparator and two types of subtractors. These circuits are based on published literature but undergo modifications to optimize their resource utilization for performing the division operation. The obtained results demonstrate that the proposed divider circuit outperforms other currently published divider circuits in terms of T gate usage, highlighting its efficiency and potential practicality in quantum algorithms.