  The current generation of quantum computing technologies call for quantum
algorithms that require a limited number of qubits and quantum gates, and which
are robust against errors. A suitable design approach are variational circuits
where the parameters of gates are learnt, an approach that is particularly
fruitful for applications in machine learning. In this paper, we propose a
low-depth variational quantum algorithm for supervised learning. The input
feature vectors are encoded into the amplitudes of a quantum system, and a
quantum circuit of parametrised single and two-qubit gates together with a
single-qubit measurement is used to classify the inputs. This circuit
architecture ensures that the number of learnable parameters is
poly-logarithmic in the input dimension. We propose a quantum-classical
training scheme where the analytical gradients of the model can be estimated by
running several slightly adapted versions of the variational circuit. We show
with simulations that the circuit-centric quantum classifier performs well on
standard classical benchmark datasets while requiring dramatically fewer
parameters than other methods. We also evaluate sensitivity of the
classification to state preparation and parameter noise, introduce a quantum
version of dropout regularisation and provide a graphical representation of
quantum gates as highly symmetric linear layers of a neural network.
