Investigating layer-selective transfer learning of QAOA parameters for Max-Cut problem

TL;DR

This work tackles reducing the optimization burden of QAOA after transferring parameters between Max-Cut problem instances. It introduces a layer-selective fine-tuning regime where, after a donor-to-acceptor parameter transfer, only a subset of layers is re-optimized, balancing the approximation ratio $r$ against the optimization time $ au$. Numerical results show that, across 12–18 node graphs, optimizing the second QAOA layer typically yields the best $r/ au$ trade-off, while full-layer optimization remains superior mainly for weighted graphs. The findings provide practical guidance for efficient QAOA deployment on larger problems and contribute to understanding the relative importance of individual circuit layers.

Abstract

Quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful for solving combinatorial optimization problems (COPs). It has been observed that the optimal variational parameters obtained from one instance of a COP can be transferred to another instance, producing sufficiently satisfactory solutions for the latter. In this context, a suitable method for further improving the solution is to fine-tune a subset of the transferred parameters. We numerically explore the role of optimizing individual QAOA layers in improving the approximate solution of the Max-Cut problem after parameter transfer. We also investigate the trade-off between a good approximation and the required optimization time when optimizing transferred QAOA parameters. These studies show that optimizing a subset of layers can be more effective at a lower time-cost compared to optimizing all layers.

Figures (6)

• Figure 1: A schematic diagram of the layer-selective transfer learning scheme of QAOA for Max-Cut problem.
• Figure 2: Approximation ratio $r$ obtained from full parameter transfer, as well as from optimizing each of the layers individually for (a) 12 node instances and (b) 18 node instances. The horizontal axis shows the seed values using which 20 random graphs were generated.
• Figure 3: Approximation ratio $r$ obtained from full parameter transfer, as well as from optimizing each of the layers individually for 12-node instances and $p=7$.
• Figure 4: A comparison between approximation ratios obtained from full parameter transfer, as well as from optimizing the second layer alone, the first two layers, first three layers, and from optimizing all layers for (a) 12-node graph instance and (b) 16-node graph instance.
• Figure 5: (a) Average of approximation ratio $r$, (b) average of optimization time, and (c) average of $\delta r / \tau$ for some of the optimization schemes presented in Fig. \ref{['multiple_layer_comparison']} and for a range of number of nodes.