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Scientific Reports

A visualization tool for controlling acoustic qubit analogues

M. Afridi Hasan, Akinsanmi S. Ige, Joshua A. Levine, M. Arif Hasan, Keith Runge, Pierre Alix Deymier

Published Sep 16, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-026-71287-7

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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.
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 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.
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.
Computers have transformed the way we live, work, and innovate. While Quantum computers based on quantum bits (qubits) exploit principles such as superposition and entanglement to offer unprecedented computational power compared to conventional computers. However, their scalability and practical realization are limited by challenges associated with wavefunction decoherence, the need for cryogenic temperatures, and extreme sensitivity to noise and environmental disturbances. The analogy between topological acoustic waves and quantum mechanics offers a path toward the design and operation of an acoustic quantum-analogue computer which does not suffer from the fragility of qubits. In this work, we present the demonstration and characterization of such a scalable, cost-effective, room-temperature acoustic analogue quantum computing platform. This platform harnesses the intrinsic nonlinearity of physical systems to generate wave superposition. We demonstrate several scalable quantum operations, including the realization of quantum permutation gates and quantum-inspired cryptography, using experimental results from this system. In addition, we discuss the underlying concepts and characterization of the platform, along with the ongoing efforts both through analytical simulation in ANSYS mechanical and experimental validation to develop a model of the acoustic quantum analogue computer. Finally, the dissertation concludes with an assessment of the platform’s reliability and robustness, highlighting its promise as a practical alternative for quantum-inspired computation.