We present a sensing modality using the geometric phase of acoustic waves propagating in an underwater environment. We experimentally investigate the effect of scattering by a small subwavelength perturbation on a flat submerged surface. We represent the state of an acoustic field in the unperturbed and perturbed cases as multidimensional vectors. The change in geometric phase is obtained by calculating the angle between those vectors. This angle represents a rotation of the state vector of the wave due to scattering by the perturbation. We perform statistical analysis to define a signal-to-noise ratio to quantify the sensitivity of the geometric phase measurement and compare it to magnitude based measurements. This geometric phase sensing modality is shown to have higher sensitivity than the magnitude based sensing approach.

We introduce a method, topological acoustic sensing, which exploits changes in the geometric phase of nonseparable coherent superpositions of acoustic waves to sense mass defects in arrays of coupled acoustic waveguides. Theoretical models and experimental results shed light on the origin of the behavior and sensitivity of the geometric phase due to the presence of mass defects. The choice of the coherent superposition of waves used to probe the defects as well as the mathematical representation determining the topological characteristics of its space of states are shown to be critical in maximizing the sensitivity of the topological acoustic sensing method.

The creation of multilevel quantum states, qudits, has revolutionized concepts for quantum computing. Classical systems that capture behavior analogous to quantum systems have been demonstrated. In this spirit, we consider a three-level classical analogue of the qudit composed of coupled acoustic waveguides. Here, we demonstrate both the experimental realization of a three-level classical analogue of the qudit and the creation and tuning of nonseparable superpositions of two of these analogues, which are classically “entangled.” Measurements of velocities and transmission inform our assignment of these nonseparable states.

Logical phi-bits are nonlinear acoustic modes analogous to qubits and supported by an externally driven acoustic metastructure. A correspondence is established between the state of three correlated logical phi-bits represented in a low-dimensional linearly scaling physical space and their state representation as a complex vector in a high-dimensional exponentially scaling Hilbert space. We show the experimental implementation of a nontrivial three phi-bit unitary operation analogous to a quantum circuit. This three phi-bit gate operates in parallel on the components of the three phi-bit complex state vector. While this operation would be challenging to perform in one step on a quantum computer, by comparison, ours requires only a single physical action on the metastructure.

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.