Realizing Shor's algorithm with topological acoustic phase bits.

Quantum algorithms motivate alternative approaches to computation, and classical physical systems that generate correlations can enable parallelism. Here we present a framework for quantum-inspired computing based on phase bits (phibits), which represent logical units through the phases of nonlinear topological acoustic waves. We define two theoretical tools: the phase cache, which dynamically tracks the evolution of geometric phases, and the operator spectra shift, which enables consistent mapping between physical manipulations and computational operations. Using this framework, we implement the period finding core of Shor's algorithm and demonstrate the factorization of composite integers 15 and 35. The experimental probability distributions for the measured outcomes show good agreement with theoretical predictions, validating the accuracy of the phibit implementation and the robustness of the nonlinear acoustic platform. These results show the potential of phibits as an approach to performing complex computational tasks.