parameter-shift

Use ParamShiftEstimatorGradient from qiskit_algorithms.gradients with an Estimator primitive, then call .run() with your circuit, observable, and parameter values. The result's gradients field contains one array per circuit with exact analytic derivatives.

Parameter shift computes exact analytic gradients by evaluating the circuit at theta plus and minus pi/2, introducing no approximation error. Finite difference approximates derivatives with small step sizes and carries truncation error that depends on the chosen epsilon.

Supported gates are x, y, z, h, rx, ry, rz, p, cx, cy, cz, ryy, rxx, rzz, and rzx. Circuits containing other gates are automatically decomposed during preprocessing, but gates that cannot be decomposed will raise an error.

Yes, pass a parameters argument to .run() listing the specific Parameter objects to differentiate. The output gradient array then contains one entry per requested parameter, in the same order as your list.

The error occurs when a circuit contains gates outside the supported set that cannot be decomposed during preprocessing. Check your circuit's operations against the supported gate list and manually decompose exotic gates before running the gradient.

Avoid it when gates have generators with eigenvalues other than plus or minus one half, since the fixed pi/2 shift no longer yields exact gradients. In those cases use linear combination of unitaries or finite difference methods instead.