Abstract Hybrid quantum-classical adaptive Variational Quantum Eigensolvers (VQE) hold the potential to outperform classical computing for simulating many-body quantum systems. However, practical implementations on current quantum processing units (QPUs) are challenging due to the noisy evaluation of a polynomially scaling number of observables, undertaken for operator selection and high-dimensional cost function optimization. We introduce an adaptive algorithm using analytic, gradient-free optimization, called Greedy Gradient-free Adaptive VQE (GGA-VQE). In addition to demonstrating the algorithm’s improved resilience to statistical sampling noise in the computation of simple molecular ground states, we execute GGA-VQE on a 25-qubit error-mitigated QPU by computing the ground state of a 25-body Ising model. Although hardware noise on the QPU produces inaccurate energies, our implementation outputs a parameterized quantum circuit yielding a favorable ground-state approximation. We demonstrate this by retrieving the parameterized operators calculated on the QPU and evaluating the resulting ansatz wave-function via noiseless emulation (i.e., hybrid observable measurement).