Structured Parameterization and Non-Stabilizerness in Hypergraph QAOA

• URL: http://arxiv.org/abs/2605.01620v1
• Date: Sat, 02 May 2026 22:12:18 GMT
• Title: Structured Parameterization and Non-Stabilizerness in Hypergraph QAOA
• Abstract summary: We introduce the $k$-interaction-angle quantum approximate optimization algorithm ($k$A-QAOA)<n>We show that $k$A-QAOA achieves approximation ratios comparable to the more expressive multi-angle quantum approximate optimization algorithm (MA-QAOA)<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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