Factorization by quantum annealing using superconducting flux qubits implementing a multiplier Hamiltonian

• Published in: Scientific reports Vol. 12; no. 1; p. 13669
• Main Authors: Saida, Daisuke, Hidaka, Mutsuo, Imafuku, Kentaro, Yamanashi, Yuki
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 11.08.2022; Nature Publishing Group; Nature Portfolio
• Subjects: 639/166/987; 639/766/1130; 639/766/483; Algorithms; Annealing; Bias; Energy; Humanities and Social Sciences; multidisciplinary; Quantum computing; Science; Science (multidisciplinary)
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-022-17867-9

Prime factorization ( P  =  M  ×  N ) is a promising application for quantum computing. Shor’s algorithm is a key concept for breaking the limit for analyzing P , which cannot be effectively solved by classical computation; however, the algorithm requires error-correctable logical qubits. Here, we describe a quantum annealing method for solving prime factorization. A superconducting quantum circuit with native implementation of the multiplier Hamiltonian provides combinations of M and N as a solution for number P after annealing. This circuit is robust and can be expanded easily to scale up the analysis. We present an experimental and theoretical exploration of the multiplier unit. We demonstrate the 2-bit factorization in a circuit simulation and experimentally at 10 mK. We also explain how the current conditions can be used to obtain high success probability and all candidate factorized elements.