Period finding and prime factorization using classical wave superposition

• Main Authors: Balinskiy, M. (Author), Khitun, A. (Author)
• Format: Article
• Language: English
• Published: American Institute of Physics Inc. 2022
• Subjects: Classical waves; Digital computers; Factorization; Key parts; Numerical models; Polynomial approximation; Polynomial-time; Prime factorization; Prime factors; Quanta computers; Quantum entanglement; Quantum superpositions; Spin waves; Super-polynomials; Superposition of state; Wave superposition
• Online Access: View Fulltext in Publisher

 Prime factorization is a procedure of determining the prime factors of a given number N that requires super-polynomial time for conventional digital computers. Peter Shor developed a polynomial-time algorithm for quantum computers. Period finding is the key part of the algorithm, which is accomplished with the help of quantum superposition of states and quantum entanglement. The period finding can be also accomplished using classical wave superposition. In this study, we present experimental data obtained on a multi-port spin wave interferometer made of Y3Fe2(FeO4)3. Number 817 was factorized by a sequence of phase measurements. We also present the results of numerical modeling on the prime factorization of larger numbers 334 597, 1 172 693, 3 377 663, and 9 363 239. The results of numerical modeling reveal significant shortcomings of the period-based approach. The major problems are associated with an inability to predict the period of the modular function, significant overhead over classical digital computers in some cases, and phase accuracy requirements. We argue that the same problems are inherent in classical analog and quantum computers. © 2022 Author(s).