  The building blocks of quantum algorithms and software are quantum gates,
with the appropriate combination of quantum gates leading to a desired quantum
circuit. Deep expert knowledge is necessary to discover effective combinations
of quantum gates to achieve a desired quantum algorithm for solving a specific
task. This is especially challenging for quantum machine learning and signal
processing. For example, it is not trivial to design a quantum Fourier
transform from scratch. This work proposes a quantum architecture search
algorithm which is based on a Monte Carlo graph search and measures of
importance sampling. It is applicable to the optimization of gate order, both
for discrete gates, as well as gates containing continuous variables. Several
numerical experiments demonstrate the applicability of the proposed method for
the automatic discovery of quantum circuits.
