Multi-Angle QAOA Does Not Always Need All Its Angles

TL;DR

This paper demonstrates that leveraging problem symmetries in multi-angle QAOA can significantly reduce the number of parameters needed without sacrificing solution quality, thereby improving efficiency in quantum optimization.

Contribution

It establishes a numerical connection between problem symmetries and parameter redundancy in ma-QAOA, enabling parameter reduction without loss of performance.

Findings

Symmetry-based parameter reduction is effective in 67.4% of tested graphs.

Average parameter reduction achieved is 28.1%.

Using the largest symmetry reduces parameters by 37.1% with minimal impact on objective.

Abstract

Introducing additional tunable parameters to quantum circuits is a powerful way of improving performance without increasing hardware requirements. A recently introduced multiangle extension of the quantum approximate optimization algorithm (ma-QAOA) significantly improves the solution quality compared with QAOA by allowing the parameters for each term in the Hamiltonian to vary independently. Prior results suggest, however, considerable redundancy in parameters, the removal of which would reduce the cost of parameter optimization. In this work we show numerically the connection between the problem symmetries and the parameter redundancy by demonstrating that symmetries can be used to reduce the number of parameters used by ma-QAOA without decreasing the solution quality. We study Max-Cut on all 7,565 connected, non-isomorphic 8-node graphs with a nontrivial symmetry group and show numerically that in 67.4% of these graphs, symmetry can be used to reduce the number of parameters with no decrease in the objective, with the average ratio of parameters reduced by 28.1%. Moreover, we show that in 35.9% of the graphs this reduction can be achieved by simply using the largest symmetry. For the graphs where reducing the number of parameters leads to a decrease in the objective, the largest symmetry can be used to reduce the parameter count by 37.1% at the cost of only a 6.1% decrease in the objective. We demonstrate the central role of symmetries by showing that a random parameter reduction strategy leads to much worse performance.