  Quantum machine learning -- and specifically Variational Quantum Algorithms
(VQAs) -- 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 VQAs. 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, in the quantum autoencoder for data
compression and in unitary compilation problems showing successful results in
all cases.
