Supervised learning of random quantum circuits via scalable neural
  networks
Predicting the output of quantum circuits is a hard computational task that
plays a pivotal role in the development of universal quantum computers. Here we
investigate the supervised learning of output expectation values of random
quantum circuits. Deep convolutional neural networks (CNNs) are trained to
predict single-qubit and two-qubit expectation values using databases of
classically simulated circuits. These circuits are represented via an
appropriately designed one-hot encoding of the constituent gates. The
prediction accuracy for previously unseen circuits is analyzed, also making
comparisons with small-scale quantum computers available from the free IBM
Quantum program. The CNNs often outperform the quantum devices, depending on
the circuit depth, on the network depth, and on the training set size. Notably,
our CNNs are designed to be scalable. This allows us exploiting transfer
learning and performing extrapolations to circuits larger than those included
in the training set. These CNNs also demonstrate remarkable resilience against
noise, namely, they remain accurate even when trained on (simulated)
expectation values averaged over very few measurements.
S. Cantori D. Vitali S. Pilati