Qiskit SPSA Optimizer

This tool enables SPSA-based optimization for parameterized quantum circuits within the Qiskit framework. It accepts a problem definition, a cost function, and SPSA hyperparameters to perform stochastic gradient-like updates using two objective evaluations per iteration. The workflow is designed for researchers and developers who need robust optimization under noise, without relying on explicit gradient calculations. The core concept is to perturb the parameter vector in random ±1 directions, estimate the gradient from the difference in objective values, and update parameters with a scaled step. Through multiple iterations, users obtain a trajectory of costs and parameter vectors, enabling analysis of convergence behavior and robustness to noise. The tool supports setting bounds, adaptive update rules, and optional logging to assist benchmarking across problem sizes. Beneficiaries include quantum algorithm developers, educators demonstrating variational optimization, and researchers comparing SPSA to alternative optimizers. Unique value lies in tight integration with Qiskit-style workflows, reproducible hyperparameter configurations, and a clear separation between core SPSA logic and problem-specific objective definitions. Core features include a configurable problem dimension, initial parameters, two-evaluation-per-iteration gradient estimation, and a history log for post-analysis. Use cases span hyperparameter sweeps, comparative studies of stochastic optimizers, and educational demonstrations of SPSA on noisy simulators or real devices. The tool emphasizes domain-relevant control over optimization dynamics, with explicit handling for invalid evaluations, convergence thresholds, and parameter bounding to keep experiments well-behaved. Examples include tuning a variational circuit for a toy Hamiltonian, benchmarking SPSA against Adam in a noisy emulator, or teaching the impact of hyperparameters on convergence speed and stability.