[ebenlassoued]

• Please check if the PR fulfills these requirements

• The commit message follows our guidelines
• Tests for the changes have been added (for bug fixes / features)
• Docs have been added / updated (for bug fixes / features)

Docs: no documentation pages changed; this PR adds an example notebook.
Tests: not applicable, since this PR only adds an example notebook and changes no code. The notebook runs top to bottom, and ruff check / ruff format pass.

• What kind of change does this PR introduce? (Bug fix, feature, docs update, ...)

Examples update: a new example notebook emulating the two-spin Heisenberg model with the analog emulator.

• What is the current behavior? (You can also link to an open issue here)

There is no example covering the two-spin dynamics of the Heisenberg model.

• What is the new behavior (if this is a feature change)?

Not a feature change. The notebook contains three experiments:

1. Aligned spins: emulating the time dynamics of an eigenstate of the Heisenberg Hamiltonian.
2. Anti-aligned spins: emulating the time dynamics of the anti-aligned state and its von Neumann entanglement entropy.
3. Singlet and triplet state preparation: using the emulator's analog pulses to prepare two eigenstates of the Heisenberg Hamiltonian.

Each Pauli string is measured as a separate Expectation metric, as a workaround for OpenQuantumDesign/oqd-analog-emulator#18.

• Does this PR introduce a breaking change? (What changes might users need to make in their application due to this PR?)

No.

@benjimaclellan