  Quantum machine learning (QML) offers a powerful, flexible paradigm for
programming near-term quantum computers, with applications in chemistry,
metrology, materials science, data science, and mathematics. Here, one trains
an ansatz, in the form of a parameterized quantum circuit, to accomplish a task
of interest. However, challenges have recently emerged suggesting that deep
ansatzes are difficult to train, due to flat training landscapes caused by
randomness or by hardware noise. This motivates our work, where we present a
variable structure approach to build ansatzes for QML. Our approach, called
VAns (Variable Ansatz), applies a set of rules to both grow and (crucially)
remove quantum gates in an informed manner during the optimization.
Consequently, VAns is ideally suited to mitigate trainability and noise-related
issues by keeping the ansatz shallow. We employ VAns in the variational quantum
eigensolver for condensed matter and quantum chemistry applications and also in
the quantum autoencoder for data compression, showing successful results in all
cases.
