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The analogy between acoustic modes in nonlinear metamaterials and quantum computing platforms constituted of correlated two-level systems opens new frontiers in information science. We use an inductive procedure to demonstrate scalable initialization of and scalable unitary transformations on superpositions of states of multiple correlated logical phi-bits, classical nonlinear acoustic analog of qubits. A multiple phi-bit state representation as a complex vector in a high-dimensional, exponentially scaling Hilbert space is shown to correspond with the state of logical phi-bits represented in a low-dimensional linearly scaling physical space of an externally driven acoustic metamaterial. Manipulation of the phi-bits in the physical space enables the implementation of a non-trivial multiple phi-bit unitary transformation that scales exponentially. This scalable transformation operates in parallel on the components of the multiple phi-bit complex state vector, requiring only a single physical action on the metamaterial. This work demonstrates that acoustic metamaterials offer a viable path toward achieving massively parallel information processing capabilities that can challenge current quantum computing paradigms.