Second-Order FALQON Parameter Transfer for the Max-Cut Problem on 3-Regular Graphs

TL;DR

This paper shows that transferring second-order FALQON parameters from small to larger graphs significantly improves Max-Cut approximation ratios, reducing computational costs and enabling near-term quantum hardware application.

Contribution

It demonstrates the effectiveness of parameter transferability in FALQON, enabling better performance on larger graphs by leveraging small-instance optimizations.

Findings

Transferred parameters outperform native optimization on larger graphs.

Larger time steps can be safely adopted when using transferred parameters.

Transfer strategy reduces computational overhead and improves approximation ratios.

Abstract

The Feedback-based Algorithm for Quantum Optimization (FALQON) offers a deterministic alternative to variational quantum algorithms by bypassing classical optimization loops. However, maintaining convergence on large problem instances often requires restricting the time step, necessitating quantum circuit depths that exceed Noisy Intermediate-Scale Quantum (NISQ) hardware capabilities. This paper investigates the parameter transferability of second-order FALQON applied to the Max-Cut problem on 3-regular graphs. Through numerical experiments evaluating quantum circuits up to 16 layers on graphs up to 24 nodes, we demonstrate a highly advantageous scaling behavior: transferring feedback parameters optimized on small instances to larger target graphs yields significantly higher approximation ratios than natively optimizing the parameters directly on the larger graphs. This performance advantage arises because parameters trained on smaller instances can safely adopt aggressively larger time steps. By offloading the expensive parameter discovery phase to small-scale instances, this transfer strategy simultaneously reduces computational overhead and enhances the approximation ratio, thereby bringing FALQON closer to practical viability on near-term quantum architectures.