Observables (Pauli-string expectation values)
Exact expectation values of Pauli strings, computed directly from a statevector in O(dim) via bit manipulation -- the 2^n_qubits Hamiltonian matrix is never built.
::: dense_evolution.physics.observables
See also: circuit_to_energy_fn for the differentiable, h_matrix @ statevector
approach to expectation values (needed for jax.grad-based VQE, at the cost of an explicit
dense Hamiltonian matrix) -- use pauli_expectation/pauli_sum_expectation instead whenever a
dense Hamiltonian isn't otherwise needed, or the system is too large for one to be practical.