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Summary of the TDVP algorithm

EMU-MPS uses a second order 2-site TDVP to compute the time-evolution of the system (see here for details). Briefly, the algorithm repeatedly computes the time-evolution for 2 neighbouring qubits while truncating the resulting MPS to keep the state small. It does this by

  • evolving qubit 1 and 2 forwards in time by \(dt/2\)
  • evolving qubit 2 backwards by \(dt/2\)
  • evolving qubit 2 and 3 forwards in time by \(dt/2\)

...

  • evolving qubit \(n-1\) and \(n\) forward in time by \(dt\)
  • evolving qubit \(n-1\) backwards in time by \(dt/2\)
  • evolving qubit \(n-2\) and \(n-1\) forward in time by \(dt/2\)

...

  • evolving qubit 1 and 2 forwards in time by \(dt/2\)

The fact that we sweep left-right and the right-left with timesteps of \(dt/2\) makes this a second-order TDVP.