Detrimental Agnostic Entanglement: The Case Against Hardware-Efficient Ans\"atze for Combinatorial Optimization

TL;DR

This paper investigates the role of entanglement in variational quantum algorithms for combinatorial optimization, showing that less entanglement often leads to better performance for diagonal Hamiltonians.

Contribution

It introduces control mechanisms to modulate entanglement in hardware-efficient ans"atze and demonstrates that reduced entanglement improves optimization outcomes.

Findings

Fully separable ansatz outperforms entangled configurations.

Less problem-agnostic entanglement yields better results.

QAOA maintains high entanglement but still achieves competitive solutions.

Abstract

Variational quantum algorithms (VQAs) for combinatorial optimization routinely employ entangling gates as a default design choice, yet the role of entanglement, in its amount and structure, remains poorly understood. This gap is particularly consequential for problems governed by diagonal Hamiltonians, whose ground states are classical product states and therefore require no entanglement in principle, raising the fundamental question of whether and how entangling gates help or hinder the variational search. We investigate this question for MaxCut by introducing two complementary control mechanisms that provide smooth, monotonic control over hardware-efficient ansatz (HEA) entanglement as quantified by the Meyer-Wallach measure $Q$, and by benchmarking against QAOA as a problem-structured reference. Tracking the entanglement trajectory $Q(t)$ throughout VQA training reveals that when the ansatz grants the optimizer indirect control over entanglement through its parameters, it consistently drives entanglement down. In line with this tendency, a fully separable ansatz outperforms all entangled hardware-efficient configurations, establishing a monotonic relationship: less problem-agnostic entanglement yields better performance. In contrast, QAOA, whose entanglement is structurally derived from the problem Hamiltonian, maintains high entanglement yet achieves competitive solution quality, demonstrating that entanglement structure, not merely quantity, determines its utility. These findings suggest that HEAs for diagonal Hamiltonians are inappropriate and that variational approaches to combinatorial optimization should prioritize problem-structured circuit designs.