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arXiv · 2601.16116

Experimental prime factorization via the feedback quantum control

K. B. Hari Krishnan·Vishal Varma·T. S. Mahesh
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Abstract

Prime factorization on quantum processors is typically implemented either via circuit-based approaches such as Shor's algorithm or through Hamiltonian optimization methods based on adiabatic, annealing, or variational techniques. While Shor's algorithm demands high-fidelity quantum gates, Hamiltonian optimization schemes, with prime factors encoded as degenerate ground states of a problem Hamiltonian, generally require substantial classical post-processing to determine control parameters. We propose an all-quantum, measurement-based feedback approach that iteratively steers a quantum system toward the target ground state, eliminating the need for classical computation of drive parameters once the problem Hamiltonian is determined and realized. As a proof of principle, we experimentally factor the biprime 551 using a three-qubit NMR quantum register and numerically analyze the robustness of the method against control field-errors. We further demonstrate scalability by numerically implementing the FALQON factorization of larger biprimes, 9,167 and 2,106,287, using 5 and 9 qubits, respectively.

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K. B. Hari Krishnan, Vishal Varma, T. S. Mahesh. 2026-01-22. Experimental prime factorization via the feedback quantum control. https://arxiv.org/abs/2601.16116

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