/deepQuantum

Groundstate finding using neural nets

Primary LanguagePython

deepQuantum

TensorFlow implementation of the algorithm from this paper Finds groundstate solutions for arbitrary spin Hamiltonians.

Current state

  • Metropolis sampling accurately samples arbitrary distribution
  • Minimising H_avg (expectation of H) and feeding the whole configuration space works--Overlap asymptotically approaches 1, variation in Re(E_loc) approaches 0
  • Minimising E_var for a MC sample doesn't seem to work
  • Time taken even for simple problems is very large, slightly ominous
    • Inefficient implemntation? Profile using cPython and Tensorflow the timeline module
    • Metropolis takes a long time, TensorFlow rewrite might be useful

To-Do

Neural Net Wavefunction

Refactor Hamiltonian

  • Make hamiltonian template that accepts a function which defines the operations used to compute the variational energy

Overlap

  • Overlap between DQ wavefunction and exact wavefunction is almost zero; problem either in Hamiltonian or overlap computation Working
    • Check overlap computation Done

Function support

  • Workaround lack of complex support with simpler operations Done
  • Build CPU/GPU kernels for functions not supporting complex data types

Metropolis sampler

  • Implement single-site update Done

    • Flip one spin site randomly, decide whether to accept Done
    • Repeat for some number of steps (until the state is statistically uncorrelated with the last step) Done
    • Accept new state as new member of Metropolis sample Done
    • Rewritten as pure TensorFlow

  • Rewrite as RNN in tensorflow

    • Rewrite tests for RNN Metropolis

Diagnostics

  • Set up tensorBoard
  • Write wrappers for timeline

Exact solver

  • Generalise to solve (simple) arbitrary spin Hamiltonians
  • Write solver for simple 2D Hamiltonians

MPS Solver

  • Use ALPS

Roadmap

  1. Reproduce 1D TFI, AFH groundstate solutions from paper
  2. Repeat 1D TFI, AFH groundstate solutions using deep nets
  3. Reproduce 2D TFI, AFH groundstate solutions from paper
  4. Repeat 2D TFI, AFH groundstate solutions using deep nets
  5. Explore performance of DQ in non-integrable systems