Dataset for Benchmarking Variational Fast Forward Pipielines based on Hydrogen Molecule Simulation

[RishiNandha]

Summary

Benchmarking dataset for variational fast-forwarding (VFF) pipelines using the time evolution of quantum states from hydrogen-based molecules. The dataset is structured to support learning-based extrapolation of quantum dynamics: short-term, potentially noisy training states are provided alongside long-term, exact reference evolutions.

The data generator gives us the following:

• ⎢ѱHK〉: The Hartree Fock State of the system
• X_train: [Δt, 2Δtm …NΔt] which are uniform timestamps at which short-term evolutions are recorded
• Y_train: U(Δt)⎢ѱHK〉...U(NΔt)⎢ѱHK〉 which are the short-term evolutions but with noise
• X_test: [PΔt…QΔt] which are the long-term timestamps
• Y_test: U(PΔt)⎢ѱHK〉…U(QΔt)⎢ѱHK〉 which are the long-term noiseless evolutions

Details and comments

• This PR adds qiskit_aer and qiskit_ibm_runtime as user dependencies too and not just dev dependencies
• Generating the Hamiltonians from scratch needs PySCF, but to keep it simple I've saved the hamiltonians and included the generation code as an optional dev-only module. PySCF has not been included as a dev-requirement
• Unittests are taking about half a minute to run. I can try any suggestions on how I can make them faster
• Usage of Noise Models from a runtime has been included as an optional feature
• When running unittests I'm getting deprecation warnings saying the transpiler I'm using to take a hamiltonians to realistic ciruits will not be in 2.0.0 anymore. Any suggestions on keeping the generator 2.0.0-friendly would be helpful too

Literature that uses a similar training procedure for VFFs: https://quantum-journal.org/papers/q-2024-03-13-1278/pdf/