Optimization Strategies for Variational Quantum Algorithms in Noisy Landscapes

Variational Quantum Algorithms (VQAs) are a promising tool in the NISQ era, leveraging quantum computing across diverse fields. However, their performance is hindered by optimization challenges like local minima, barren plateaus, and noise from current quantum hardware. Variational Quantum Eigensolver (VQE), a key subset of VQAs, approximates molecular ground-state energies by minimizing a Hamiltonian, enabling quantum chemistry applications. Beyond this, VQE contributes to condensed matter physics by exploring quantum phase transitions and exotic states, and to quantum machine learning by optimizing parameterized circuits for classifiers and generative models. This study systematically evaluates over 50 meta-heuristic optimization algorithms including evolution-based, swarm-based, and music-inspired methods-on their ability to navigate VQE's multimodal and noisy landscapes. Using a multi-phase sieve-like approach, we identify the most capable optimizers and compare their performance on a 1D Ising model (3-9 qubits). Further testing on the Hubbard model (up to 192 parameters) reveals insights into convergence rates, effectiveness, and resilience under noise, offering valuable guidance for advancing optimization in noisy quantum environments.