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The Journal of the Acoustical Society of America

Quantum logic gate analogies in nonlinear acoustics

Ilia Kuk, Ivan B. Djordjević, Ildar R. Gabitov, Keith Runge, Akinsanmi S. Ige, Pierre Alix Deymier

Published Jun 1, 2025• 2 citations
Publisher

Abstract

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.

DOI
10.1121/10.0036901

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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.
This work considers a recent framework for realizing quantum-like gates using acoustic analogues to quantum bits, known as phase bits or phibits. Phibits, and gate operations upon them, are produced by utilizing an experimental metastructure of three aluminum waveguides bonded with epoxy and observing nonlinear vibrations when the system is driven at controllable frequencies. While this framework specifies the conditions for the system to produce gates, it leaves a gap in how to identify ideal driving frequencies that match the specification. We show how to use data-driven visualization methods to address the characterization and calibration of this system. Specifically, by characterization, we mean identifying and comparing conditions under which target operations are feasible. By calibration, we mean selecting concrete channel triplets and driver frequencies that realize those operations reproducibly. We develop a visualization platform that enhances the framework with reproducible characterization and calibration tools. Our method encodes target operations as explicit phase change tests between an initial and a final driver setting, presented in two, linked, parallel coordinate plots. We demonstrate the utility of this approach on multiple experimental runs, showing the potential to further streamline utilizing acoustic systems in computational settings.
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.
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.
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.
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.
Quantum algorithms motivate alternative approaches to computation, and classical physical systems that generate correlations can enable parallelism. Here we present a framework for quantum-inspired computing based on phase bits (phibits), which represent logical units through the phases of nonlinear topological acoustic waves. We define two theoretical tools: the phase cache, which dynamically tracks the evolution of geometric phases, and the operator spectra shift, which enables consistent mapping between physical manipulations and computational operations. Using this framework, we implement the period finding core of Shor’s algorithm and demonstrate the factorization of composite integers 15 and 35. The experimental probability distributions for the measured outcomes show good agreement with theoretical predictions, validating the accuracy of the phibit implementation and the robustness of the nonlinear acoustic platform. These results show the potential of phibits as an approach to performing complex computational tasks. Ilia Kuk and colleagues report a phase-bit computing that encodes information in phases of nonlinear topological acoustic waves. They implement Shor’s algorithm to factor 15 and 35 at room temperature, obtaining results consistent with the theory.