Statistical Benchmarking of Optimization Methods for Variational Quantum Eigensolver under Quantum Noise

TL;DR

This work addresses how numerical optimizers perform when applied to the state-averaged orbital-optimized VQE (SA-OO-VQE) for quantum chemistry on noisy, near-term quantum devices. It systematically benchmarks six optimizers—BFGS, SLSQP, Nelder-Mead, Powell, COBYLA, and iSOMA—across ideal conditions and multiple quantum-noise models (phase damping, depolarizing, and thermal relaxation) for the H2 molecule, including sampling noise via different measurement counts. The results show that BFGS delivers the most accurate energies with minimal evaluations and robust behavior under moderate decoherence; gradient-free methods cluster near optimal values but require more evaluations, while SLSQP becomes unstable with noise and iSOMA, though globally oriented, is computationally expensive. Depolarizing noise generally degrades performance more than dephasing, and in severe thermal-relaxation regimes the hardware noise floor dominates, making optimizer choice less impactful. The study provides practical guidance for selecting noise-aware optimizers in variational quantum simulations and outlines future directions for scaling to larger systems and integrating error mitigation.

Abstract

This work investigates the performance of numerical optimization algorithms applied to the State-Averaged Orbital-Optimized Variational Quantum Eigensolver for the H2 molecule under various quantum noise conditions. The goal is to assess the stability, accuracy, and computational efficiency of commonly used gradient-based, gradient-free, and global optimization strategies within the Noisy Intermediate-Scale Quantum regime. We systematically compare six representative optimizers, BFGS, SLSQP, Nelder-Mead, Powell, COBYLA, and iSOMA,under ideal, stochastic, and decoherence noise models, including phase damping, depolarizing, and thermal relaxation channels. Each optimizer was tested over multiple noise intensities and measurement settings to characterize convergence behavior and sensitivity to noise-induced landscape distortions. The results show that BFGS consistently achieves the most accurate energies with minimal evaluations, maintaining robustness even under moderate decoherence. COBYLA performs well for low-cost approximations, while SLSQP exhibits instability in noisy regimes. Global approaches such as iSOMA show potential but are computationally expensive. These findings provide practical guidance for selecting suitable optimizers in variational quantum simulations, highlighting the importance of noise-aware optimization strategies for reliable and efficient quantum chemistry computations on current hardware.

Figures (29)

• Figure 1: Scatter plot of ground state energy (x-axis) and excited state energy (y-axis) for optimization method. Dashed lines mark the ideal value. All noise models are shown.
• Figure 2: Scatter plot of ground state energy (x-axis) and excited state energy (y-axis) for optimization method. Dashed lines mark the ideal value. All noise models are shown.
• Figure 3: Scatter plot of ground state energy (x-axis) and excited state energy (y-axis) for optimization method. Dashed lines mark the ideal value. All noise models are shown.
• Figure 4: Scatter plot of ground state energy (x-axis) and excited state energy (y-axis) for optimization method. Dashed lines mark the ideal value. All noise models are shown.
• Figure 5: Scatter plot of ground state energy (x-axis) and excited state energy (y-axis) for optimization method. Dashed lines mark the ideal value. All noise models are shown.