Effect of data encoding on the expressive power of variational quantum-machine-learning models
By Maria Schuld, Ryan Sweke, Johannes Jakob Meyer. Physical Review A, 2020
850 citations recorded by the source corpus.
Quantum computers can be used for supervised learning by treating parametrised quantum circuits as models that map data inputs to predictions. While a lot of work has been done to investigate practical implications of this approach, many important theoretical properties of these models remain unknown. Here we investigate how the strategy with which data is encoded into the model influences the expressive power of parametrised quantum circuits as function approximators. We show that one can naturally write a quantum model as a partial Fourier series in the data, where the accessible frequencies are determined by the nature of the data encoding gates in the circuit. By repeating simple data encoding gates multiple times, quantum models can access increasingly rich frequency spectra. We show that there exist quantum models which can realise all possible sets of Fourier coefficients, and therefore, if the accessible frequency spectrum is asymptotically rich enough, such models are universal function approximators.
Subfields: Artificial Intelligence
View Paper: https://www.semanticscholar.org/paper/ab2e4ca081ef195a7bd3a95f1771b73e2880d913
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In Artificial Intelligence
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- Hsin-Yuan Huang
- Guillaume Verdon
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Citations in the corpus
- Challenges and opportunities in quantum machine learning (2022, background): “[23] Maria Schuld, Ryan Sweke, and Johannes Jakob Meyer, “Effect of data encoding on the expressive power of variational quantum-machine-learning models,” Physical Review A 103, 032430 (2021).”
- Quantum machine learning models are kernel methods (2021, background): “type of quantum model in [25] suggests that some quantum kernels of the form (1) are universal in the asymptotic limit of exponentially large circuits.”