Cryptography is crucial in protecting sensitive information and ensuring secure transactions in a time when data security and privacy are major concerns. Traditional cryptography techniques, which depend on mathematical algorithms and secret keys, have historically protected against data breaches and illegal access. With the advent of quantum computers, traditional cryptography techniques are at risk. In this work, we present a cryptography idea using logical phibits, which are classical analogues of quantum bits (qubits) and are supported by driven acoustic metamaterials. The state of phibits displays superpositions similar to quantum bits, with complex amplitudes and phases. We present a representation of the state vector of single and multiphibit systems. The state vector of multiple phibits system lies in a complex exponentially scaling Hilbert space and is used to encode information or messages. By changing the driving conditions of the metamaterial, the information can be encrypted with exceptional security and efficiency. We illustrate experimentally the practicality and effectiveness of encoding and encryption of a message using a 5 phibits system and emphasize the scalability of this approach to an
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Abstract N phibits system with the same processing time. 
Phibits, akin to the quantum concept of qubits but in a classical mechanical framework, play a critical role in the development of quantumanalogue computing, and hence, understanding the nonlinear dynamics governing their control and interactions is crucial. These phibits, represented by acoustic waves within nonlinearly coupled arrays of waveguides, can exist in coherent superpositions of states. Adjusting external drivers' frequency, amplitude, and phase allows precise control over the phibit states. We have devised a discrete element model to analyze and predict the nonlinear response of phibits to external drivers, considering various types, strengths, and orders of nonlinearity stemming from intrinsic medium coupling among waveguides and external factors like signal generators, transducers, and ultrasonic couplant assemblies. Notable findings include the influence of nonlinearity type, strength, and order on the complex amplitudes within the coherent superposition of phibit states. This investigation serves as a groundwork for controlling design parameters in phibit creation, facilitating the preparation and manipulation of state superpositions crucial for developing phibitbased quantum analogue information processing platforms.more » « lessFree, publiclyaccessible full text available April 13, 2025

Understanding the control of phibits, akin to qubits, is crucial for developing quantuminspired computing. Phibits, or two states of an acoustic wave in coupled waveguides, can be in a superposition of states. Our experiments showed that external drivers' frequency, amplitude, and phase influence phibit states. We developed a discrete element model to predict phibit responses under varying nonlinear conditions, influenced by the intrinsic medium coupling the waveguides and external factors like signal generators and transducers. The study reveals that nonlinearity and damping significantly affect the amplitude and phase of phibit states, with a notable impact on their predictability and stability, particularly at high damping levels. These findings are crucial to manipulating phibits for quantuminspired information processing, highlighting the importance of optimizing nonlinearity and damping to control phibit states.more » « lessFree, publiclyaccessible full text available April 12, 2025

Phibits are classical mechanical analogues of qubits. Comprehending the nonlinear phenomena that underlie the control and relationships between phibits is of utmost importance for advancing phibitbased quantumanalogue computing systems. Phibits are acoustic waves in externally driven nonlinearly coupled arrays of waveguides, that can exist in a coherent superposition of two states. Tuning the frequency, amplitude, and phase of external drivers is a means of controlling the phibit states. We have developed a discrete element model to analyze and predict the nonlinear phibit response to external drivers that may result from different types, strengths, and orders of nonlinearity due to the presence of (i) intrinsic medium (epoxy) coupling the waveguides and (ii) external factors such as signal generators/transducers/ultrasonic couplant assembly. Key findings include the impact of nonlinearity type, strength, and order as well as damping on the modulus and phases of the complex amplitudes of the phibit coherent superposition of states. This research serves as an exploration for control of design parameters in the creation of phibits, which will enable the preparation and manipulation of superpositions of states essential for developing phibitbased quantum analogue information processing platforms.more » « lessFree, publiclyaccessible full text available March 6, 2025

Quantum computing utilizes superposition and entanglement to surpass classical computer capabilities. Central to this are qubits and their use to realize parallel quantum algorithms through circuits of simple one or two qubit gates. Controlling and measuring quantum systems is challenging. Here, we introduce a paradigm utilizing logical phibits, classical analogues of qubits using nonlinear acoustic waves, supported by an externally driven acoustic metastructure. These phibits bridge a lowdimensional linearly scaling physical space to a highdimensional exponentially scaling Hilbert space in which parallel processing of information can be realized in the form of unitary operations. Here, we show the implementation of a nontrivial threephibit unitary operation analogous to a quantum circuit but achieved via a single action on the metastructure, whereby the qubitbased equivalent requires sequences of qubit gates. A phibitbased approach might offer advantages over quantum systems, especially in tasks requiring large complex unitary operations. This breakthrough hints at a fascinating intersection of classical and quantum worlds, potentially redefining computational paradigms by harnessing nonlinear classical mechanical systems in quantumanalogous manners, blending the best of both domains.more » « lessFree, publiclyaccessible full text available March 4, 2025

The analogy between acoustic modes in nonlinear metamaterials and quantum computing platforms constituted of correlated twolevel 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 phibits, classical nonlinear acoustic analog of qubits. A multiple phibit state representation as a complex vector in a highdimensional, exponentially scaling Hilbert space is shown to correspond with the state of logical phibits represented in a lowdimensional linearly scaling physical space of an externally driven acoustic metamaterial. Manipulation of the phibits in the physical space enables the implementation of a nontrivial multiple phibit unitary transformation that scales exponentially. This scalable transformation operates in parallel on the components of the multiple phibit 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.more » « lessFree, publiclyaccessible full text available February 5, 2025

It is shown that multiple logical phibit largescale unitary operations analogous to quantum circuits can be realized by design. Logical phibits are nonlinear acoustic analogues of qubits which arise when elastic waveguides are coupled and driven at multiple frequencies in the presence of nonlinearities. The contribution presents an approach that maps both the state of multiple phibits in their supporting nonlinear acoustic metastructure and their representations as complex state vectors in exponentially scaling Hilbert spaces. Upon physically actuating π changes in phibit phases and by engineering appropriate multiple phibits representations, one can realize a scalable phibitbased quantum Fourier transform.more » « lessFree, publiclyaccessible full text available December 24, 2024

Abstract Using experiments and theory, we investigate the behavior of nonlinear acoustic modes in a physical system composed of an array of three coupled acoustic waveguides, two of which are externally driven with two different frequencies. Nonlinear modes with frequency given by linear combinations of the driving frequencies are realizations of socalled logical phibits. A phibit is a twostate degree of freedom of an acoustic wave, which can be in a coherent superposition of states with complex amplitude coefficients, i.e., a qubit analogue. We demonstrate experimentally that phibit modes are supported in the array of waveguides. Using perturbation theory, we show that phibits may result from the intrinsic nonlinearity of the material used to couple the waveguides. We have also isolated possible effects on phibit states associated with the systems’ electronics, transducers and ultrasonic coupling agents used to probe the array and that may introduce extrinsic nonlinearities. These extrinsic effects are shown to be easily separable from the intrinsic behavior. The intrinsic behavior includes sharp jumps in phibit phases occurring over very narrow ranges of driving frequency. These jumps may also exhibit hysteretic behavior dependent on the direction of driving frequency tuning. The intrinsic states of phibits and multiple nonlinearly correlated phibits may serve as foundation for robust and practical quantumanalogue information technologies.more » « lessFree, publiclyaccessible full text available December 1, 2024

We experimentally navigate the Hilbert space of two logical phibits supported by an externally driven nonlinear array of coupled acoustic waveguides by parametrically changing the relative phase of the drivers. We observe sharp phase jumps of approximately 180° in the individual phibit states as a result of the phase tuning of the drivers. The occurrence of these sharp phase jumps varies from phibit to phibit. All phibit phases also possess a common background dependency on the drivers’ phase. Within the context of multiple time scale perturbation theory, we develop a simple model of the nonlinear array of externally driven coupled acoustic waveguides to shed light on the possible mechanisms for the experimentally observed behavior of the logical phibit phase. Finally, we illustrate the ability to experimentally initialize the state of single and multiple phibit systems by exploiting the drivers’ phase as a tuning parameter. We also show that the nonlinear correlation between phibits enables parallelism in the manipulation of two and multiphibit superpositions of states.more » « less

Logical phibits 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 phibits represented in a lowdimensional linearly scaling physical space and their state representation as a complex vector in a highdimensional exponentially scaling Hilbert space. We show the experimental implementation of a nontrivial three phibit unitary operation analogous to a quantum circuit. This three phibit gate operates in parallel on the components of the three phibit 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.more » « less