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Added simple VQE sample #2073

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Added simple VQE sample #2073

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@DmitryVasilevsky DmitryVasilevsky commented Dec 19, 2024

This PR adds simple self-contained example of a Variational Quantum Eigensolver (VQE).

This example includes:

  1. Simple classical optimization to find minimum of a multi-variable function in order to find the approximation to the minimum eigenvalue of a Hamiltonian.
  2. Finding Hamiltonian expectation value as a weighted sum of terms.
  3. Finding one term expectation value by performing multiple shots of preparing ansatz state and measuring it.
  4. Ansatz state preparation similar to the circuit in the published paper "Ground-state energy estimation of the water molecule on a trapped ion quantum computer" (https://arxiv.org/abs/1902.10171)

To keep this sample simple and self-contained Hamiltonian is artificial (doesn't correspond to any actual chemistry problem). Also, this sample doesn't include any application of VQE, for example, finding a geometry of a molecule.

@DmitryVasilevsky DmitryVasilevsky changed the title Added simple VQE sample - quantum step of VQE Added simple VQE sample Jan 9, 2025
@DmitryVasilevsky DmitryVasilevsky marked this pull request as ready for review January 9, 2025 10:25
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