linear-combination

Use LinCombEstimatorGradient from qiskit_algorithms.gradients with an Estimator primitive such as StatevectorEstimator. Pass your circuit, observable, and parameter values to its run method, and it returns exact gradients without finite-difference error.

LCU gradients use ancilla-augmented circuits with controlled derivative operators and support a broader gate set including ccx, swap, and iswap. Parameter-shift uses shifted evaluations of the original circuit and supports a narrower gate set.

The supported gates are rx, ry, rz, rzx, rzz, ryy, rxx, cx, cy, cz, ccx, swap, iswap, h, t, s, sdg, x, y, and z. Circuits containing other gates fail during preprocessing unless they can be decomposed into this set.

Use LinCombQGT with an Estimator primitive and call run with your circuit and parameter values. Keep phase_fix set to True, the default, to obtain the standard QGT used by quantum natural gradient algorithms.

When derivative_type is set to COMPLEX, each augmented circuit is evaluated twice, once for the real and once for the imaginary observable part. This doubles the PUB count from n to 2n for n parameters.

LCU requires one extra ancilla qubit per augmented circuit, which can exceed hardware qubit capacity. It also only works with gates from its supported set, and cached circuits can become stale if the circuit is modified between runs.