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1. Acoustic metamaterials for realizing a scalable multiple phi-bit unitary transformation

   https://doi.org/10.1063/5.0188462  

   Runge, K.; Deymier, P_A; Hasan, M_A; Lata, T_D; Levine, J_A (February 2024, AIP Advances)

   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. 

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2. Realizing permutation gates with phi-bits: Acoustic quantum analogue computing

   https://doi.org/10.1063/5.0241680  

   Cavalluzzi, David; Ige, Akinsanmi_S; Runge, Keith; Deymier, Pierre_A (March 2025, Journal of Applied Physics)

   We present both the theoretical framework and experimental implementation of permutation gates using logical phi-bits, classical acoustic analogs of qubits. Logical phi-bits are nonlinear acoustic modes supported by externally driven acoustic metamaterials. Using a tensor product of modified Bloch sphere representations, we realize all possible two logical phi-bit permutations including SWAP and C-NOT. We also illustrate the scalability of a permutation for any number of logical phi-bits. Experimental demonstrations of these permutations require a single physical action on the driving conditions of the acoustic metamaterial. All logical phi-bits exist in the same physical system. We compare the phi-bit system with its quantum counterpart using Qiskit simulations, which illustrate the complexity of realizing these permutations in a quantum context. 

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3. Information encoding and encryption in acoustic analogues of qubits

   https://doi.org/10.1038/s41598-024-65800-z  

   Ige, Akinsanmi_S; Cavalluzzi, David; Djordjevic, Ivan_B; Runge, Keith; Deymier, Pierre_A (June 2024, Scientific Reports)

   Abstract 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 phi-bits, which are classical analogues of quantum bits (qubits) and are supported by driven acoustic metamaterials. The state of phi-bits displays superpositions similar to quantum bits, with complex amplitudes and phases. We present a representation of the state vector of single and multi-phi-bit systems. The state vector of multiple phi-bits 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 phi-bits system and emphasize the scalability of this approach to anNphi-bits system with the same processing time. 

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4. Unlocking the Future of Phi-bits: Advancing Quantum-Inspired Computing

   Faiaz, Abrar Nur_E; Ige, Akinsanmi S; Mahmood, Kazi T; Balla, Jake; Hasan, M Afridi; Hasan, M Arif; Deymier, Pierre; Runge, Keith; Levine, Josh (April 2024, The American Institute of Physics, publisher, Bulletin of the American Physical Society)

   Understanding the control of phi-bits, akin to qubits, is crucial for developing quantum-inspired computing. Phi-bits, 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 phi-bit states. We developed a discrete element model to predict phi-bit 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 phi-bit states, with a notable impact on their predictability and stability, particularly at high damping levels. These findings are crucial to manipulating phi-bits for quantum-inspired information processing, highlighting the importance of optimizing nonlinearity and damping to control phi-bit states. 

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5. Setting the stage for materials simulation using acoustic metamaterials digital quantum analogue computing platforms

   https://doi.org/10.1088/1361-651X/ac991e  

   Deymier, P A; Runge, K; Hasan, M A; Levine, J A; Cutillas, P (October 2022, Modelling and Simulation in Materials Science and Engineering)

   Abstract We present a model of an externally driven acoustic metamaterial constituted of a nonlinear parallel array of coupled acoustic waveguides that supports logical phi-bits, classical analogues of quantum bits (qubit). Descriptions of correlated multiple phi-bit systems emphasize the importance of representations of phi-bit and multiple phi-bit vector states within the context of their corresponding Hilbert space. Experimental data are used to demonstrate the realization of the single phi-bit Hadamard gate and the phase shift gate. A three phi-bit system is also used to illustrate the development of multiple phi-bit gates as well as a simple quantum-like algorithm. These demonstrations set the stage for the implementation of a digital quantum analogue computing platform based on acoustic metamaterial that can implement quantum-like gates and may offer promise as an efficient platform for the simulation of materials. 

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