| # 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`](autodiff.md) 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. | |