This grant will support research that will be a leap forward in advancing sound as a classical analogue of quantum information science (QIS), promoting the progress of science, and ensuring US leadership in QIS, which is a national priority. The development of robust, classically entangled acoustic waves analogous to quantum bits, or qubits, can make impactful contributions as core components of practical quantum-like technologies without suffering from quantum fragility. By exploiting recently discovered analogies between acoustics, quantum mechanics, and condensed matter physics, this research will create the foundations for a path to promising and validating modes of storing, processing, and retrieving information in acoustic waves that complement conventional quantum technologies. This grant will support the development of educational resources that bridge the educational gap between classical mechanics and quantum mechanics for future QIS learners. It will help broaden the participation of underrepresented groups in gaining a working understanding of acoustic quantum analogies and related complex quantum concepts. At the core of QIS, quantum entanglement has the property of non-separability. While non-separability creates the possibility of operating in parallel on the coherent superpositions of states for multipartite quantum systems, the quantum coherent superpositions of wave functions (probability amplitude) collapse upon measurement or thermal fluctuations. Costly solutions are cryogenics and error corrections, both use significant hardware and software resources. However, quantum computing is essentially phase computing; it exploits the possibility of achieving and rotating the coherent superpositions of states of correlated multipartite systems with complex amplitudes that are represented as vectors in large, exponentially complex Hilbert spaces. The notion of ?classical entanglement? for sound waves possesses the non-separability and complexity essential to reach the promise of parallelism in quantum computing, yet without the fragility of decoherence even at room temperature. The research team will investigate metamaterials comprising arrays of externally driven, linearly and nonlinearly coupled, acoustic waveguides, known for supporting acoustic waves analogous to qubits, namely phase-bits or phi-bits. The team will experimentally, computationally, and theoretically investigate the exponentially complex and scalable Hilbert spaces of states of multiple phi-bits and the non-separability of their coherent superpositions. They will analyze the scalability and controllability of Hilbert space with billions of dimensions and their QIS applicability, and demonstrate systematic and predictable proof-of-concept operations within these Hilbert spaces to establish foundations for acoustic quantum-like gates and algorithms for future quantum-like information processing. This project is jointly funded by Dynamics, Control and Systems Diagnostics (DCSD) Program and Mechanics of Materials & Structures (MOMS) Program. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.