Structured Parameterization and Non-Stabilizerness in Hypergraph QAOA

TL;DR

This paper introduces the $k$-interaction-angle QAOA ($k$A-QAOA), a new parameterization scheme for hypergraph problems that balances expressiveness and resource efficiency, outperforming some existing methods.

Contribution

The authors propose $k$A-QAOA, a novel parameterization for hypergraph QAOA that groups terms by interaction order, offering a middle ground between existing approaches.

Findings

$k$A-QAOA achieves approximation ratios comparable to MA-QAOA.

$k$A-QAOA requires fewer function evaluations than MA-QAOA.

$k$A-QAOA reduces quantum resource consumption while maintaining solution quality.

Abstract

The quantum approximate optimization algorithm (QAOA) has emerged as a promising candidate for demonstrating quantum advantage on noisy intermediate-scale quantum (NISQ) devices. While various QAOA parameterization schemes exist, ranging from the original single-angle approach to the more expressive multi-angle quantum approximate optimization algorithm (MA-QAOA) and automorphic-angle quantum approximate optimization algorithm (AA-QAOA), each presents distinct trade-offs between expressiveness and classical optimization complexity. In this work, we introduce the $k$-interaction-angle quantum approximate optimization algorithm ($k$A-QAOA), a parameterization scheme that groups cost function terms by their $k$-body interaction order, providing a natural middle ground between parameter efficiency and solution quality. This approach is particularly well-suited for combinatorial optimization problems defined on hypergraphs, where multi-body interactions naturally arise in applications such as Boolean satisfiability and resource allocation with multi-party constraints. We benchmark $k$A-QAOA against standard single-angle quantum approximate optimization algorithm (SA-QAOA), MA-QAOA, and AA-QAOA on two problem classes: 3-uniform cyclic sign-alternating hypergraphs and random coefficient hypergraphs. Our results demonstrate that $k$A-QAOA achieves approximation ratios comparable to MA-QAOA while requiring significantly fewer function evaluations, thereby reducing quantum resource consumption.