  Currently available quantum hardware allows for small scale implementations
of quantum machine learning algorithms. Such experiments aid the search for
applications of quantum computers by benchmarking the near-term feasibility of
candidate algorithms. Here we demonstrate the quantum learning of a two-qubit
unitary by a sequence of three parameterized quantum circuits containing a
total of 21 variational parameters. Moreover, we variationally diagonalize the
unitary to learn its spectral decomposition, i.e., its eigenvalues and
eigenvectors. We illustrate how this can be used as a subroutine to compress
the depth of dynamical quantum simulations. One can view our implementation as
a demonstration of entanglement-enhanced machine learning, as only a single
(entangled) training data pair is required to learn a 4x4 unitary matrix.
