  We perform quantum simulation on classical and quantum computers and set up a
machine learning framework in which we can map out phase diagrams of known and
unknown quantum many-body systems in an unsupervised fashion. The classical
simulations are done with state-of-the-art tensor network methods in one and
two spatial dimensions. For one dimensional systems, we utilize matrix product
states (MPS) that have many practical advantages and can be optimized using the
efficient density matrix renormalization group (DMRG) algorithm. The data for
two dimensional systems is obtained from entangled projected pair states (PEPS)
optimized via imaginary time evolution. Data in form of observables,
entanglement spectra, or parts of the state vectors from these simulations, is
then fed into a deep learning (DL) pipeline where we perform anomaly detection
to map out the phase diagram. We extend this notion to quantum computers and
introduce quantum variational anomaly detection. Here, we first simulate the
ground state and then process it in a quantum machine learning (QML) manner.
Both simulation and QML routines are performed on the same device, which we
demonstrate both in classical simulation and on a physical quantum computer
hosted by IBM.
