An improved circuit for Shor’s factoring algorithm using \(2n+2\) qubits

Abstract

Due to the existence of decoherence, researchers are limited in controlling large-scale qubits, which also prevents the application of Shor’s factoring algorithm in the case of large-scale qubits for the time being. To reduce the number of qubits required when using Shor’s factoring algorithm, by using borrowed ancilla qubits and reducing the number of gates in the constant addition circuit, a new quantum circuit for Shor’s factoring algorithm is proposed. The designed circuit works on \(2n+2\) qubits, in practice is about 35% and 40% less than the best circuit of Takahashi et al. (Quantum Inf Comput 5(6):440–448, 2005) and Haner et al. (Quantum Inf Comput 17(7 &8):673–684, 2017) in terms of depth and size, respectively. Also, the designed circuit is completely general, and it does not depend on any property of the composite number to be factorized. Finally, we use Python with Qiskit to implement and simulate our circuit.