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1. Potential of Nonlinear Phi-Bit Modes in Elastic Systems to Revolutionize Quantum-Analogue 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)

   Phi-bits, akin to the quantum concept of qubits but in a classical mechanical framework, play a critical role in the development of quantum-analogue computing, and hence, understanding the nonlinear dynamics governing their control and interactions is crucial. These phi-bits, 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 phi-bit states. We have devised a discrete element model to analyze and predict the nonlinear response of phi-bits 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 phi-bit states. This investigation serves as a groundwork for controlling design parameters in phi-bit creation, facilitating the preparation and manipulation of state superpositions crucial for developing phi-bit-based quantum analogue information processing platforms. 

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2. 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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3. Realizing acoustic qubit analogues with nonlinearly tunable phi-bits in externally driven coupled acoustic waveguides

   https://doi.org/10.1038/s41598-023-27427-4  

   Deymier, P. A.; Runge, K.; Hasan, M. A.; Lata, T. D.; Levine, J. A.; Cutillas, P. (December 2023, Scientific Reports)

   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 so-called logical phi-bits. A phi-bit is a two-state 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 phi-bit modes are supported in the array of waveguides. Using perturbation theory, we show that phi-bits may result from the intrinsic nonlinearity of the material used to couple the waveguides. We have also isolated possible effects on phi-bit 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 phi-bit 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 phi-bits and multiple nonlinearly correlated phi-bits may serve as foundation for robust and practical quantum-analogue information technologies. 

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4. 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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5. Tuning Logical Phi-Bit State Vectors in an Externally Driven Nonlinear Array of Acoustic Waveguides via Drivers’ Phase

   https://doi.org/10.3390/quantum5020022  

   Deymier, Pierre A.; Runge, Keith; Hasan, M. Arif; Lata, Trevor D.; Levine, Josh A. (June 2023, Quantum Reports)

   We experimentally navigate the Hilbert space of two logical phi-bits 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 phi-bit states as a result of the phase tuning of the drivers. The occurrence of these sharp phase jumps varies from phi-bit to phi-bit. All phi-bit 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 phi-bit phase. Finally, we illustrate the ability to experimentally initialize the state of single- and multiple- phi-bit systems by exploiting the drivers’ phase as a tuning parameter. We also show that the nonlinear correlation between phi-bits enables parallelism in the manipulation of two- and multi-phi-bit superpositions of states. 

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