Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Velocity Verlet-based optimization for variational quantum eigensolvers

Rinka Miura

TL;DR

This work proposes using the velocity Verlet algorithm, inspired by classical molecular dynamics, to address the VQE challenge by introducing an inertial “velocity” term, and compares its performance against standard optimizers on H2 and LiH molecules.

Abstract

The Variational Quantum Eigensolver (VQE) is a key algorithm for near-term quantum computers, yet its performance is often limited by the classical optimization of circuit parameters. We propose using the velocity Verlet algorithm, inspired by classical molecular dynamics, to address this challenge. By introducing an inertial "velocity" term, our method efficiently explores complex energy landscapes. We compare its performance against standard optimizers on H$_2$ and LiH molecules. For H$_2$, our method achieves chemical accuracy with fewer quantum circuit evaluations than L-BFGS-B. For LiH, it attains the lowest final energy, demonstrating its potential for high-accuracy VQE simulations.

Velocity Verlet-based optimization for variational quantum eigensolvers

TL;DR

This work proposes using the velocity Verlet algorithm, inspired by classical molecular dynamics, to address the VQE challenge by introducing an inertial “velocity” term, and compares its performance against standard optimizers on H2 and LiH molecules.

Abstract

The Variational Quantum Eigensolver (VQE) is a key algorithm for near-term quantum computers, yet its performance is often limited by the classical optimization of circuit parameters. We propose using the velocity Verlet algorithm, inspired by classical molecular dynamics, to address this challenge. By introducing an inertial "velocity" term, our method efficiently explores complex energy landscapes. We compare its performance against standard optimizers on H and LiH molecules. For H, our method achieves chemical accuracy with fewer quantum circuit evaluations than L-BFGS-B. For LiH, it attains the lowest final energy, demonstrating its potential for high-accuracy VQE simulations.
Paper Structure (17 sections, 2 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 17 sections, 2 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Theory and Methods
  3. Variational Quantum Eigensolver
  4. Velocity Verlet optimization with damping
  5. Molecular systems, mappings, and exact references
  6. Ansatz and initialization
  7. Gradient Estimation and Evaluation-Count Accounting
  8. Optimizers, hyperparameters, and stopping conditions
  9. Results
  10. Hydrogen molecule (H$_2$, 4 qubits)
  11. Lithium hydride (LiH, 12 qubits)
  12. Discussion
  13. Relation to the Variational Principle
  14. Comparison with Other Optimization Methods and Interpretation of Results
  15. Hyperparameter Sensitivity and Tuning Strategies
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Energy convergence as a function of optimization iteration for the H$_2$ molecule. The plot displays the energy expectation value for the velocity Verlet, COBYLA, L-BFGS-B, and SLSQP optimizers. The dashed line represents the exact FCI energy.
  • Figure 2: Absolute error versus the number of energy evaluations for the H$_2$ molecule. The vertical axis is on a logarithmic scale. The velocity Verlet method achieves chemical accuracy (red dotted line) with a lower number of quantum circuit evaluations than L-BFGS-B.
  • Figure 3: Energy convergence as a function of iteration for the LiH molecule. In this more complex landscape, the velocity Verlet method finds a substantially lower energy solution compared to the other optimizers.
  • Figure 4: Absolute error versus the number of energy evaluations for the LiH molecule. Although no method reaches chemical accuracy, the velocity Verlet method consistently maintains the lowest error throughout the optimization.