Using Shor's algorithm on near term Quantum computers: a reduced version

Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm, this peculiar problem can be solved in polynomial time. However, both the number of qubits and applied gates detrimentally affect the ability to run a particular quantum circuit on the near term Quantum hardware. In this work, we help addressing both these problems by introducing a reduced version of Shor's algorithm that proposes a step forward in increasing the range of numbers that can be factorized on noisy Quantum devices. More specifically, the structure of the Shor's circuit has been modified to reduce the number of gates in the modular arithmetic and the Quantum Fourier Transform. The implementation presented in this work is general and does not use any assumptions on the number to factor. In particular, we have found noteworthy results in most cases, often being able to factor the given number with only one iteration of the proposed algorithm. Finally, comparing the original quantum algorithm with our version on simulator, the outcomes are identical for some of the numbers considered.