Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm framework proposed by Babbush et al. (2023), we present and im...
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2025-01-01
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| author | Natt Luangsirapornchai Peeranat Sanglaor Apimuk Sornsaeng Stephane Bressan Thiparat Chotibut Kamonluk Suksen Prabhas Chongstitvatana |
| author_facet | Natt Luangsirapornchai Peeranat Sanglaor Apimuk Sornsaeng Stephane Bressan Thiparat Chotibut Kamonluk Suksen Prabhas Chongstitvatana |
| author_sort | Natt Luangsirapornchai |
| collection | DOAJ |
| description | Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm framework proposed by Babbush et al. (2023), we present and implement a detailed quantum circuit construction for simulating one-dimensional spring–mass systems. Our approach incorporates key quantum subroutines, including block encoding, quantum singular value transformation (QSVT), and amplitude amplification, to realize the unitary time-evolution operator associated with simulating classical oscillators dynamics. In the uniform mass–spring setting, our circuit construction requires a gate complexity of <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}\bigl (\log _{2}^{2} N\,\log _{2}(1/\varepsilon )\bigr )$ </tex-math></inline-formula>, where N is the number of oscillators and <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> is the target accuracy of the approximation. For more general, heterogeneous mass–spring systems, the total gate complexity is <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}\bigl (N\log _{2} N\,\log _{2}(1/\varepsilon )\bigr )$ </tex-math></inline-formula>. Both settings require <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(\log _{2} N)$ </tex-math></inline-formula> qubits. Numerical simulations agree with classical solvers across all tested configurations, indicating that this circuit-based Hamiltonian simulation approach can substantially reduce computational costs and potentially enable larger-scale many-body studies on future quantum hardware. |
| format | Article |
| id | doaj-art-558f6c73f4b64993a1fe9601f841c70a |
| institution | DOAJ |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-558f6c73f4b64993a1fe9601f841c70a2025-08-20T03:05:31ZengIEEEIEEE Access2169-35362025-01-0113527385275710.1109/ACCESS.2025.355130810926901Practical Quantum Circuit Implementation for Simulating Coupled Classical OscillatorsNatt Luangsirapornchai0https://orcid.org/0009-0005-4555-9435Peeranat Sanglaor1https://orcid.org/0009-0004-0371-7485Apimuk Sornsaeng2https://orcid.org/0000-0003-3698-8412Stephane Bressan3https://orcid.org/0000-0001-5536-3296Thiparat Chotibut4https://orcid.org/0000-0002-8936-1413Kamonluk Suksen5https://orcid.org/0009-0006-1452-6400Prabhas Chongstitvatana6https://orcid.org/0000-0003-0744-7801Department of Computer Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, ThailandDepartment of Physics, Chula Intelligent and Complex Systems Laboratory, Faculty of Science, Chulalongkorn University, Bangkok, ThailandDepartment of Physics, Chula Intelligent and Complex Systems Laboratory, Faculty of Science, Chulalongkorn University, Bangkok, ThailandSchool of Computing, National University of Singapore, Queenstown, SingaporeDepartment of Physics, Chula Intelligent and Complex Systems Laboratory, Faculty of Science, Chulalongkorn University, Bangkok, ThailandDepartment of Computer Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, ThailandDepartment of Computer Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok, ThailandSimulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm framework proposed by Babbush et al. (2023), we present and implement a detailed quantum circuit construction for simulating one-dimensional spring–mass systems. Our approach incorporates key quantum subroutines, including block encoding, quantum singular value transformation (QSVT), and amplitude amplification, to realize the unitary time-evolution operator associated with simulating classical oscillators dynamics. In the uniform mass–spring setting, our circuit construction requires a gate complexity of <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}\bigl (\log _{2}^{2} N\,\log _{2}(1/\varepsilon )\bigr )$ </tex-math></inline-formula>, where N is the number of oscillators and <inline-formula> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> is the target accuracy of the approximation. For more general, heterogeneous mass–spring systems, the total gate complexity is <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}\bigl (N\log _{2} N\,\log _{2}(1/\varepsilon )\bigr )$ </tex-math></inline-formula>. Both settings require <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(\log _{2} N)$ </tex-math></inline-formula> qubits. Numerical simulations agree with classical solvers across all tested configurations, indicating that this circuit-based Hamiltonian simulation approach can substantially reduce computational costs and potentially enable larger-scale many-body studies on future quantum hardware.https://ieeexplore.ieee.org/document/10926901/Many-body simulationcoupled classical oscillatorsquantum algorithmquantum circuitblock encodingquantum singular value transformation |
| spellingShingle | Natt Luangsirapornchai Peeranat Sanglaor Apimuk Sornsaeng Stephane Bressan Thiparat Chotibut Kamonluk Suksen Prabhas Chongstitvatana Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators IEEE Access Many-body simulation coupled classical oscillators quantum algorithm quantum circuit block encoding quantum singular value transformation |
| title | Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators |
| title_full | Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators |
| title_fullStr | Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators |
| title_full_unstemmed | Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators |
| title_short | Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators |
| title_sort | practical quantum circuit implementation for simulating coupled classical oscillators |
| topic | Many-body simulation coupled classical oscillators quantum algorithm quantum circuit block encoding quantum singular value transformation |
| url | https://ieeexplore.ieee.org/document/10926901/ |
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