The effect of data encoding on the expressive power of variational
quantum machine learning models
M. Schuld, R. Sweke, and J. Meyer. (2020)cite arxiv:2008.08605Comment: 16 pages, 6 figures; source code available at https://github.com/XanaduAI/expressive_power_of_quantum_models.
Abstract
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.
Description
The effect of data encoding on the expressive power of variational quantum machine learning models
%0 Generic
%1 schuld2020effect
%A Schuld, Maria
%A Sweke, Ryan
%A Meyer, Johannes Jakob
%D 2020
%K Quantum
%T The effect of data encoding on the expressive power of variational
quantum machine learning models
%U http://arxiv.org/abs/2008.08605
%X 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.
@misc{schuld2020effect,
abstract = {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.},
added-at = {2020-08-21T18:40:51.000+0200},
author = {Schuld, Maria and Sweke, Ryan and Meyer, Johannes Jakob},
biburl = {https://www.bibsonomy.org/bibtex/20f17b4487b40bd45f536aad5a2b51385/butch0416},
description = {The effect of data encoding on the expressive power of variational quantum machine learning models},
interhash = {ca6ad3e3c2eada07600c4102f7d4f009},
intrahash = {0f17b4487b40bd45f536aad5a2b51385},
keywords = {Quantum},
note = {cite arxiv:2008.08605Comment: 16 pages, 6 figures; source code available at https://github.com/XanaduAI/expressive_power_of_quantum_models},
timestamp = {2020-08-21T18:40:51.000+0200},
title = {The effect of data encoding on the expressive power of variational
quantum machine learning models},
url = {http://arxiv.org/abs/2008.08605},
year = 2020
}