What problem does it solve? Computing gradients of parameterized quantum circuits with many parameters is expensive when each parameter requires separate circuit evaluations. This Skill explains and demonstrates the SPSA (Simultaneous Perturbation Stochastic Approximation) method, which estimates full gradients using only 2 times batch_size circuit evaluations regardless of parameter count. ## Core Features & Use Cases - Estimator Gradients: Use Qiskit's SPSAEstimatorGradient to differentiate expectation values of observables with configurable epsilon, batch_size, and seed. - Sampler Gradients: Apply SPSASamplerGradient to compute gradients of output probability distributions per bitstring. - Manual Reference Implementation: A NumPy-based spsa_gradient function and solver class show the core perturbation logic for validation and reimplementation. - Use Case: When training a variational quantum algorithm with 50 parameters, use SPSA to estimate the full gradient vector with a fixed small number of circuit evaluations instead of 100+ parameter-shift evaluations. ## Quick Start Ask the assistant to explain or run the SPSA gradient estimation example on a two-qubit RY-CX circuit with the ZZ observable using Qiskit.
