2020/08/31 by Maria Schuld, Ryan Sweke, Johannes Jakob Meyer · 5 citations
Physics and Astronomy · Mathematics · #quant-ph #stat.ML
paper · pdf · doi:10.1103/physreva.103.032430
published as Phys. Rev. A 103, 032430 (2021) · Minor corrections, including credits to a closely related paper. Source code available at https://github.com/XanaduAI/expressive_power_of_quantum_models
arxiv created 2021/03/09 · arxiv updated 2021/03/31
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.