Quantum Circuit Design of Integer Division Optimizing Ancillary Qubits and T-Count

Abstract

In this paper, we present Clifford+T gates based quantum circuit design of integer division having $n$ ancillary qubits. The proposed quantum circuit is based on restoring division algorithm. The proposed quantum circuit of integer division consists of (i) quantum circuitry of conditional addition operation, (ii) quantum circuitry of integer subtraction. To design ancillary and T-count optimized design of quantum integer division, the optimized quantum circuit design of integer conditional addition operation and integer subtraction are presented. The proposed quantum integer division circuitry has 50\% improvement in terms of ancillary qubits, and 90\% improvement in terms of T-count compared to the existing design of integer quantum division based on quantum fourier transform.