Let Quantum Neural Networks Choose Their Own Frequencies
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914763420729344 |
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| author | Jaderberg, Ben Gentile, Antonio A. Berrada, Youssef Achari Shishenina, Elvira Elfving, Vincent E. |
| author_facet | Jaderberg, Ben Gentile, Antonio A. Berrada, Youssef Achari Shishenina, Elvira Elfving, Vincent E. |
| contents | Parameterized quantum circuits as machine learning models are typically well described by their representation as a partial Fourier series of the input features, with frequencies uniquely determined by the feature map's generator Hamiltonians. Ordinarily, these data-encoding generators are chosen in advance, fixing the space of functions that can be represented. In this work we consider a generalization of quantum models to include a set of trainable parameters in the generator, leading to a trainable frequency (TF) quantum model. We numerically demonstrate how TF models can learn generators with desirable properties for solving the task at hand, including non-regularly spaced frequencies in their spectra and flexible spectral richness. Finally, we showcase the real-world effectiveness of our approach, demonstrating an improved accuracy in solving the Navier-Stokes equations using a TF model with only a single parameter added to each encoding operation. Since TF models encompass conventional fixed frequency models, they may offer a sensible default choice for variational quantum machine learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03279 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Let Quantum Neural Networks Choose Their Own Frequencies Jaderberg, Ben Gentile, Antonio A. Berrada, Youssef Achari Shishenina, Elvira Elfving, Vincent E. Quantum Physics Machine Learning Parameterized quantum circuits as machine learning models are typically well described by their representation as a partial Fourier series of the input features, with frequencies uniquely determined by the feature map's generator Hamiltonians. Ordinarily, these data-encoding generators are chosen in advance, fixing the space of functions that can be represented. In this work we consider a generalization of quantum models to include a set of trainable parameters in the generator, leading to a trainable frequency (TF) quantum model. We numerically demonstrate how TF models can learn generators with desirable properties for solving the task at hand, including non-regularly spaced frequencies in their spectra and flexible spectral richness. Finally, we showcase the real-world effectiveness of our approach, demonstrating an improved accuracy in solving the Navier-Stokes equations using a TF model with only a single parameter added to each encoding operation. Since TF models encompass conventional fixed frequency models, they may offer a sensible default choice for variational quantum machine learning. |
| title | Let Quantum Neural Networks Choose Their Own Frequencies |
| topic | Quantum Physics Machine Learning |
| url | https://arxiv.org/abs/2309.03279 |