  The task of testing whether two uncharacterized quantum devices behave in the
same way is crucial for benchmarking near-term quantum computers and quantum
simulators, but has so far remained open for continuous-variable quantum
systems. In this Letter, we develop a machine learning algorithm for comparing
unknown continuous variable states using limited and noisy data. The algorithm
works on non-Gaussian quantum states for which similarity testing could not be
achieved with previous techniques. Our approach is based on a convolutional
neural network that assesses the similarity of quantum states based on a
lower-dimensional state representation built from measurement data. The network
can be trained offline with classically simulated data from a fiducial set of
states sharing structural similarities with the states to be tested, or with
experimental data generated by measurements on the fiducial states, or with a
combination of simulated and experimental data. We test the performance of the
model on noisy cat states and states generated by arbitrary selective
number-dependent phase gates. Our network can also be applied to the problem of
comparing continuous variable states across different experimental platforms,
with different sets of achievable measurements, and to the problem of
experimentally testing whether two states are equivalent up to Gaussian unitary
transformations.

Quantum Physics;Machine Learning