Exact search algorithm to factorize large biprimes and a triprime on IBM quantum computer
Avinash Dash, Deepankar Sarmah, Bikash K. Behera, Prasanta K., Panigrahi

TL;DR
This paper demonstrates the factorization of large biprimes and a triprime using IBM quantum processors by applying a generalized Grover's algorithm, marking a significant advancement in quantum integer factorization capabilities.
Contribution
The work introduces an optimized implementation of a generalized Grover's algorithm for quantum factorization and reports the largest numbers factored on quantum hardware to date.
Findings
Successfully factorized biprimes 4088459 and 966887 on 5- and 16-qubit IBM processors.
First quantum factorization of a triprime (175) on a 5-qubit device.
High fidelity results with good agreement between experimental and theoretical outcomes.
Abstract
Factoring large integers using a quantum computer is an outstanding research problem that can illustrate true quantum advantage over classical computers. Exponential time order is required in order to find the prime factors of an integer by means of classical computation. However, the order can be drastically reduced by converting the factorization problem to an optimization one and solving it using a quantum computer. Recent works involving both theoretical and experimental approaches use Shor's algorithm, adiabatic quantum computation and quantum annealing principles to factorize integers. However, our work makes use of the generalized Grover's algorithm as proposed by Liu, with an optimal version of classical algorithm/analytic algebra. We utilize the phase-matching property of the above algorithm for only amplitude amplification purposes to avoid an inherent phase factor that…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Quantum Mechanics and Applications
