Elastic bits in granular metamaterials: A quantum-inspired framework for robust topological computing

This study introduces the concept of elastic bits in a driven granular metamaterial. These elastic bits function similarly to quantum bits (qubits), but they can maintain more stable superpositions by forming topological braiding structures with robust information stored in their phase. We have recently developed models using classical nonlinear granular metamaterials to simulate quantum-inspired computing. Using a two-coupled granular system, we analyze nonlinear vibrations and eigenstates through molecular dynamics simulations and Fourier analysis to map displacement fields into Hilbert spaces. These models demonstrate states resembling a multipartite two-level quantum system, where each subsystem represents an elastic bit analogous to time-dependent coherent superpositions of elastic bits. The study demonstrates the creation of two and three elastic bits, represented as tensor products of eigenstates in higher-dimensional Hilbert spaces. By manipulating these elastic bits—similar to quantum braiding operations—we can adjust the phase of the wave function. This allows for various types of braiding that enable robust quantum-inspired computations. Notably, “time” serves as the direction of braiding in this setup. [Funding: NSF Grants 2204382 and 2242925.]