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Applied Physics Letters

Scalable exponentially complex representations of logical phi-bit states and experimental demonstration of an operable three phi-bit gate using an acoustic metastructure

Pierre Alix Deymier, Keith Runge, P. Cutillas, M. Arif Hasan, Trevor D. Lata, Joshua A. Levine

Published Apr 3, 2023• 11 citations
Publisher

Abstract

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.

DOI
10.1063/5.0136733

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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.
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The Controlled-NOT (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 two-bit C-NOT quantum-like gate using classical qubit acoustic analogues, called herein logical phi-bits. The logical phi-bits are supported by an externally driven nonlinear acoustic metamaterial composed of a parallel array of three elastically coupled waveguides. A logical phi-bit has a two-state 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 phi-bits. This operation achieves a systematic and predictable C-NOT gate with unambiguously measurable input and output. The possibility of scaling the approach to more phi-bits is promising.
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.
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 an N phi-bits system with the same processing time.
This study introduces a framework using acoustic phase bits (phibits) as classical analogs to quantum bits for realizing quantum-like gates. These phibits are realized on a metastructure composed of aluminum rods glued with epoxy. First, we realize a single phibit gate in a general form for a Bloch sphere representation, providing a foundation for implementing arbitrary gate operations on a single phibit. Second, within a single mathematical representation, we achieve either the Hadamard or NOT gate by applying the corresponding distinct physical actions for each. Third, we demonstrate the implementation of a sequence of two quantum-like gates, Hadamard followed by CNOT, using a single physical action. This illustrates the effectiveness of the phibit framework, which has the potential to simplify the implementation of a whole series of sequential gates into a single unified physical operation. Finally, we realize a universal set of gates, including the Hadamard, CNOT, and T gates, within a single mathematical representation with three distinctive actions. This approach addresses prior limitations of phibit-based gates, such as Hadamard and CNOT, which were implemented in separate mathematical representations, by introducing a unified framework that eliminates the need for distinct formulations maintaining computational efficiency.
Abstract Vibration responses from nonlinear mechanical systems exhibit rich dynamical structure that can be utilized for information encoding and processing. We demonstrate that such structures can be used to encode and manipulate information in a manner analogous to multi-qubit systems. By using a coupled mass and conical spring oscillator, we reveal that distinct harmonic segments of the nonlinear response can be projected onto modal eigenstates to form two-level elastic-bit subsystems, which are analogous to qubits. These bits arise from measurable amplitudes and phase relationships across the Fourier spectrum and evolve deterministically under steady-state excitation. By combining multiple spectral segments within a single oscillator, we achieve two-bit and three-bit states that occupy four- and eight-dimensional Hilbert spaces, respectively. The time dependence of the complex modal coefficients yields intrinsic transformations that act as phase and rotation type gates. The temporal evolution of the complex modal coefficients results in phase accumulation and a rotation-like evolution within this state space. To characterize how the system moves between experimentally observed logical states at different times, we derive a Householder reflection that yields the exact Hermitian and unitary operator connecting these states. This unitary transformation is subsequently decomposed into sequences of analogous quantum gates, providing a representation of the observed modal evolution in terms of familiar multi-qubit logic primitives. This spectral-encoding approach enables scalable state construction within a single mechanical platform, establishing a pathway toward room-temperature mechanical computation based on deterministic nonlinear dynamics.