Comparative studies of optimizer performance in a variational quantum eigensolver.

Area of Science:

• Quantum Computing
• Computational Chemistry
• Quantum Algorithms

Background:

• Variational Quantum Eigensolver (VQE) is a leading quantum algorithm for complex problems.
• Classical optimizers are essential for VQE's expectation value estimation.
• Optimizer performance in quantum circuits remains under-explored.

Purpose of the Study:

• To evaluate and compare the performance of 12 classical optimizers within the VQE framework.
• To understand how optimizer choice impacts VQE convergence for various system sizes and circuit depths.
• To identify optimizers that can effectively address challenges like the barren plateau problem.

Main Methods:

• Systematic benchmarking of 12 distinct classical optimizers.
• VQE calculations were performed with varied numbers of qubits and circuit depths.
• Convergence was analyzed across different initial guesses and measurement counts.

Main Results:

• Gradient-based optimizers generally showed superior convergence compared to derivative-free methods.
• Optimizers employing stochastic processes frequently failed to find the global minimum.
• Optimizer step length significantly influences convergence, and the Powell method demonstrated potential for barren plateau mitigation.

Conclusions:

• Optimizer selection is critical for efficient VQE performance.
• Gradient-based methods are recommended for VQE, with careful tuning of step length.
• The Powell method emerges as a promising candidate for enhancing VQE scalability and overcoming barren plateaus.