Multi-Bit Quantum-Inspired Dynamics in Nonlinear Mechanical Oscillators.
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| Title: | Multi-Bit Quantum-Inspired Dynamics in Nonlinear Mechanical Oscillators. |
|---|---|
| Authors: | Mahmood, Kazi T.1 kazi.mahmood@wayne.edu, Hasan, M. Afridi2 afridi@arizona.edu, Faiaz, Abrar N.-E.1 abrar.faiaz@wayne.edu, Hasan, M. Arif1 hasan.arif@wayne.edu, Deymier, Pierre A.3 deymier@arizona.edu, Runge, Keith3 krunge@arizona.edu, Levine, Joshua A.2 josh@cs.arizona.edu |
| Source: | Journal of Applied Mechanics. Jun2026, Vol. 93 Issue 6, p1-13. 13p. |
| Subjects: | Nonlinear oscillators, Unitary transformations, Mechanical vibration research, Frequency spectra, Quantum theory, Computational mechanics, Encoding |
| 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Applied Mechanics is the property of American Society of Mechanical Engineers and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194718080 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Multi-Bit Quantum-Inspired Dynamics in Nonlinear Mechanical Oscillators. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Mahmood%2C+Kazi+T%2E%22">Mahmood, Kazi T.</searchLink><relatesTo>1</relatesTo><i> kazi.mahmood@wayne.edu</i><br /><searchLink fieldCode="AR" term="%22Hasan%2C+M%2E+Afridi%22">Hasan, M. Afridi</searchLink><relatesTo>2</relatesTo><i> afridi@arizona.edu</i><br /><searchLink fieldCode="AR" term="%22Faiaz%2C+Abrar+N%2E-E%2E%22">Faiaz, Abrar N.-E.</searchLink><relatesTo>1</relatesTo><i> abrar.faiaz@wayne.edu</i><br /><searchLink fieldCode="AR" term="%22Hasan%2C+M%2E+Arif%22">Hasan, M. Arif</searchLink><relatesTo>1</relatesTo><i> hasan.arif@wayne.edu</i><br /><searchLink fieldCode="AR" term="%22Deymier%2C+Pierre+A%2E%22">Deymier, Pierre A.</searchLink><relatesTo>3</relatesTo><i> deymier@arizona.edu</i><br /><searchLink fieldCode="AR" term="%22Runge%2C+Keith%22">Runge, Keith</searchLink><relatesTo>3</relatesTo><i> krunge@arizona.edu</i><br /><searchLink fieldCode="AR" term="%22Levine%2C+Joshua+A%2E%22">Levine, Joshua A.</searchLink><relatesTo>2</relatesTo><i> josh@cs.arizona.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mechanics%22">Journal of Applied Mechanics</searchLink>. Jun2026, Vol. 93 Issue 6, p1-13. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Nonlinear+oscillators%22">Nonlinear oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Unitary+transformations%22">Unitary transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+vibration+research%22">Mechanical vibration research</searchLink><br /><searchLink fieldCode="DE" term="%22Frequency+spectra%22">Frequency spectra</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+theory%22">Quantum theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+mechanics%22">Computational mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Encoding%22">Encoding</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Applied Mechanics is the property of American Society of Mechanical Engineers and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1115/1.4071523 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 1 Subjects: – SubjectFull: Nonlinear oscillators Type: general – SubjectFull: Unitary transformations Type: general – SubjectFull: Mechanical vibration research Type: general – SubjectFull: Frequency spectra Type: general – SubjectFull: Quantum theory Type: general – SubjectFull: Computational mechanics Type: general – SubjectFull: Encoding Type: general Titles: – TitleFull: Multi-Bit Quantum-Inspired Dynamics in Nonlinear Mechanical Oscillators. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Mahmood, Kazi T. – PersonEntity: Name: NameFull: Hasan, M. Afridi – PersonEntity: Name: NameFull: Faiaz, Abrar N.-E. – PersonEntity: Name: NameFull: Hasan, M. Arif – PersonEntity: Name: NameFull: Deymier, Pierre A. – PersonEntity: Name: NameFull: Runge, Keith – PersonEntity: Name: NameFull: Levine, Joshua A. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00218936 Numbering: – Type: volume Value: 93 – Type: issue Value: 6 Titles: – TitleFull: Journal of Applied Mechanics Type: main |
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