Machine Learning Matrix Product State Ansatz for strongly correlated systems

Machine learning (ML) has been used to optimize the matrix product state (MPS) ansatz for wavefunction of strongly correlated systems. The ML optimization of MPS has been tested for Heisenberg Hamiltonian on one-dimensional and ladder lattices which correspond to conjugated molecular systems. The input descriptors and output for the supervised ML are lattice configurations and configuration interaction coefficients, respectively. Efficient learning can be achieved from data over the full Hilbert space via exact diagonalization or full configuration interaction (FCI), as well as over a much smaller sub-space via Monte Carlo Configuration Interaction (MCCI). We show that this circumvents the need to calculate energy and operator expectation values, and is therefore, a computationally efficient alternative to variational optimization.