A novel fault-tolerant quantum divider and its simulation

Efficient quantum circuits of algebraic operations are vital for quantum algorithms. In this paper, we propose a novel fault-tolerant quantum divider based on long division algorithm using Clifford+ T gates. Firstly, two efficient quantum subtractors are designed which we call them equal-bit subtractor and unequal-bit subtractor. The advantage of these quantum subtractors is that the number of the constant inputs is 2, which will dramatically reduce the qubit cost. Then, based on the quantum comparator and the quantum subtractors, we propose a novel fault-tolerant quantum divider. Compared with existing work, the proposed quantum divider has better performances in quantum cost, T -depth, T -count, qubit cost, constant inputs and garbage outputs. Finally, we simulate these algorithms on IBM Quantum Experience (IBM Q Experience) platform, and the probability histograms show that these algorithms are feasible and efficient.