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The Berry phase, a concept of significant interest in quantum and classical mechanics, illuminates the dynamics of physical systems. Our current study explores this phenomenon within a classical granular network, employing an "elastic bit" that serves as a classical counterpart to the quantum bit. This approach establishes a connection between classical and quantum mechanics. By adjusting external forces, we generate an elastic bit within the granular network and map its behavior onto a Bloch sphere, akin to operating quantum logic gates. Varied manipulations of these external drivers yield a spectrum of Berry phases, from trivial (0) to nontrivial (π), unveiling the topological nature of the elastic bit. Crucially, this topological behavior is governed by external manipulations rather than the material or geometric properties of the medium. The nontrivial Berry phases, in particular, highlight energy localization within the granule vibrations, marking a significant insight into system dynamics. This research bridges the gap between the quantum and classical realms and paves the way for designing novel materials with unique properties.more » « lessFree, publiclyaccessible full text available April 13, 2025

In quantum computing and information technology, the coherent superposition of states is an essential topic for realizing the physical state of data processing and storage. The fundamentals of current technology, a quantum bit, have limitations due to the collapse and decoherence of wave function, which hinders the superposition of states. We eliminate the limitations by introducing the elastic bit generated through the Hertztype nonlinearity of granular beads. This study shows the experimental formation of the elastic bit in a coupled granular network manipulated by external harmonic excitation. The excitation generates a phasedependent dynamic movement, and mapping onto the energy states of the linear vibration modes forms the coherent superposition of states. This state vector component comes from the amplitude of the coherent states, which is projected into the Hilbert space through time dependency. The coherent states represent an actual amplitude, which makes the elastic bit susceptible to decoherence. The elastic bit also demonstrates quantum operation, showcasing the Hadamard gate, which maps one superposed state to another. These characteristics of the elastic bit pave the way for sustainable quantum computation and data storage.more » « lessFree, publiclyaccessible full text available April 12, 2025

This study investigates the Berry phase, a key concept in classical and quantum physics, and its manifestation in a classical system. We achieve controlled accumulation of the Berry phase by manipulating the elastic bit (a classical analogue to a quantum bit) in an externally driven, homogeneous, spherical, nonlinear granular network. This is achieved through the classical counterpart of quantum coherent superposition of states. The elastic bit's state vectors are navigated on the Bloch sphere using external drivers' amplitude, phase, and frequency, yielding specific Berry phases. These phases distinguish between trivial and nontrivial topologies of the elastic bit, with the zero Berry phase indicating pure states of the linearized granular system and the nontrivial π phase representing equal superposed states. Other superposed states acquire different Berry phases. Crucially, these phases correlate with the structure's eigenmode vibrations: trivial phases align with distinct, inphase, or outofphase eigenmodes, while nontrivial phases correspond to coupled vibrations where energy is shared among granules, alternating between oscillation and rest. Additionally, we explore Berry's phase generalizations for noncyclic evolutions. This research paves the way for advanced quantuminspired sensing and computation applications by utilizing and controlling the Berry phase.
Free, publiclyaccessible full text available March 1, 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

We review the notion of “phase bit” or “phibit” in externally driven nonlinear acoustic metamaterials. Phibits are classical analogues of quantum bits, which open pathways to promising and validated modes of initializing, operating, and measuring information. Acoustic metamaterials offer ways to compute information using phase that should compare favorably with stateoftheart quantum systems without suffering from quantum fragility.
Free, publiclyaccessible full text available March 1, 2025 
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

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

Demonstration of a twobit controlledNOT quantumlike gate using classical acoustic qubitanaloguesAbstract The ControlledNOT (CNOT) gate is the key to unlock the power of quantum computing as it is a fundamental component of a universal set of gates. We demonstrate the operation of a twobit CNOT quantumlike gate using classical qubit acoustic analogues, called herein logical phibits. The logical phibits are supported by an externally driven nonlinear acoustic metamaterial composed of a parallel array of three elastically coupled waveguides. A logical phibit has a twostate degree of freedom associated with the two independent relative phases of the acoustic wave in the three waveguides. A simple physical manipulation involving the detuning of the frequency of one of the external drivers is shown to operate on the complex vectors in the Hilbert space of pairs of logical phibits. This operation achieves a systematic and predictable CNOT gate with unambiguously measurable input and output. The possibility of scaling the approach to more phibits is promising.more » « less