Factorization of large tetra and penta prime numbers on IBM quantum processor

Abstract

The factorization of large digit integers in polynomial time is a challenging computational task to decipher. The development of Shor’s algorithm sparked a new resolution for solving the factorization problem. However, putting Shor’s algorithm into use in real-world situations presents major difficulties. The algorithm largely depends on the availability of large-scale, fault-tolerant quantum computers, which are not available at present. The need for qubit coherence and error correction makes the algorithm susceptible to noise and decoherence, hindering its practical realization. Therefore, exploring alternative quantum factorization algorithms and investing in quantum computing hardware advancements are vital steps toward overcoming these drawbacks and harnessing the full potential of quantum computing for factorization tasks. This article explores an alternative method of converting the factorization problem into an optimization problem using appropriate analytic algebra. The generalized Grover’s protocol is used to increase the amplitude of the necessary states and, in turn, help in the execution of the quantum factorization of tetra and penta primes as a proof of concept for different integers, including 875, 1 269 636 549 803, and 4375, using three and four qubits of IBMQ Perth (a seven-qubit processor). The fidelity of the quantum factorization protocol with the IBMQ Perth qubits was near unity. A generalization of the method is provided at the end for implementing factorization problems in various cases.