Implementation of a noise-robust quantum algorithm for multivariate polynomial factorization

Abstract

We implement in an IBM quantum computer a quantum algorithm for multivariate polynomial factoring and propose a noise-avoiding protocol to distill the experimental results in the presence of noise. This algorithm uses single-qubit quantum state tomography (QST) processes to factor a specific type of multivariate polynomials. In one-to-one correspondence, it encodes each multivariate polynomial to one quantum state. While the validity of the algorithm is experimentally verified, the quality of the final results is subjected to the decoherence levels of the preparation of the quantum states. In this paper we propose a protocol to ensure the validity of factors found by our algorithm in the presence of such decoherence and noise. This method might be, in fact, part of a larger class of methods based on that same premise and useful outside the implementation of this specific algorithm. In combination with the noise robustness of the single-qubit QST, our factorization algorithm performs perfectly, even reversing the effects of weak noise, for the second- to fifth-order polynomial cases for which it has been implemented.