Abstract
It is shown that multiple logical phi-bit large-scale unitary operations analogous to quantum circuits can be realized by design. Logical phi-bits are nonlinear acoustic analogues of qubits which arise when elastic waveguides are coupled and driven at multiple frequencies in the presence of non-linearities. The contribution presents an approach that maps both the state of multiple phi-bits in their supporting nonlinear acoustic metastructure and their representations as complex state vectors in exponentially scaling Hilbert spaces. Upon physically actuating \(\pi \) changes in phi-bit phases and by engineering appropriate multiple phi-bits representations, one can realize a scalable phi-bit-based quantum Fourier transform.
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The data that support the findings of the present study are available from the corresponding author upon reasonable request.
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Acknowledgements
The development of the acoustic metastructure and experimental setup was supported in part by a grant from the W.M. Keck foundation. P.A.D and J.A.L acknowledge partial support from NSF Grant # 2204400. M.A.H. acknowledges partial support from NSF Grant # 2204382 and thanks Wayne State University startup funds for additional support. This work was also partially supported by the Science and Technology Center New Frontiers of Sound (NewFoS) through NSF grant # 2242925.
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PAD wrote the main manuscript text with contributions from all authors. PAD developed the theoretical models. MAH and TDL conducted the experiments and acquired the data. PAD, KR, MAH, TDL, and JAL contributed equally to the analysis and interpretation of the data.
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Deymier, P.A., Runge, K., Hasan, M.A. et al. Practical implementation of a scalable discrete Fourier transform using logical phi-bits: nonlinear acoustic qubit analogues. Quantum Stud.: Math. Found. 11, 217–229 (2024). https://doi.org/10.1007/s40509-023-00312-5
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DOI: https://doi.org/10.1007/s40509-023-00312-5