Particle swarm optimization for a variational quantum eigensolver

In the field of finding ground and excited states, where quantum computation holds significant promise, using a variational quantum eigensolver (VQE) is a typical approach. However, the success of this approach is vulnerable to two factors: classical optimization for the ansätz parameters and noise from quantum devices. To address these challenges, we adopted particle swarm optimization (PSO) based on swarm intelligence for VQE and presented its performance. Furthermore, a modified PSO, gradient-based adaptive quantum-behaved particle swarm optimization (GAQPSO), is proposed. This algorithm adaptively upgrades parameters based on gradients or shared information within the swarm, enhancing optimization capability and noise resistance. We tested this algorithm using VQE simulations on several molecular systems with different geometries and found that, when using random initial values, GAQPSO achieves accurate results even in the presence of noise, whereas traditional PSO, QPSO, COBYLA, and gradient-based algorithms (GD and L-BFGS-B) fail. The GAQPSO algorithm presents a novel approach to optimizing VQE, demonstrating superior performance in parameter optimization and noise resilience compared to traditional optimization algorithms. This effectively advances the process of achieving a quantum advantage for quantum computing in quantum chemistry problems.