Experimental prime factorization via the feedback quantum control

TL;DR

This paper introduces a measurement-based feedback quantum control method for prime factorization, demonstrated experimentally on a small system and numerically scaled to larger biprimes, offering an alternative to traditional quantum algorithms.

Contribution

It presents a novel all-quantum feedback approach for prime factorization that reduces classical post-processing and demonstrates scalability with larger biprimes.

Findings

Successfully factored 551 with a three-qubit NMR system.

Analyzed robustness against control errors.

Numerically scaled to larger biprimes with 5 and 9 qubits.

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.