  Deep learning and quantum computing have achieved dramatic progresses in
recent years. The interplay between these two fast-growing fields gives rise to
a new research frontier of quantum machine learning. In this work, we report
the first experimental demonstration of training deep quantum neural networks
via the backpropagation algorithm with a six-qubit programmable superconducting
processor. In particular, we show that three-layer deep quantum neural networks
can be trained efficiently to learn two-qubit quantum channels with a mean
fidelity up to 96.0% and the ground state energy of molecular hydrogen with an
accuracy up to 93.3% compared to the theoretical value. In addition, six-layer
deep quantum neural networks can be trained in a similar fashion to achieve a
mean fidelity up to 94.8% for learning single-qubit quantum channels. Our
experimental results explicitly showcase the advantages of deep quantum neural
networks, including quantum analogue of the backpropagation algorithm and less
stringent coherence-time requirement for their constituting physical qubits,
thus providing a valuable guide for quantum machine learning applications with
both near-term and future quantum devices.
