[J4] From Problem-Structured QAOA to Problem-Agnostic Variational MaxCut Solvers: Representation, Redundancy, and Optimization Landscapes

We investigate how circuit architecture, parameterization, and optimization landscapes influence the performance of variational quantum algorithms. Focusing on the Maximum Cut (MaxCut) problem, we progressively remove the problem-specific structure of the Quantum Approximate Optimization Algorithm (QAOA) to examine the role of representational capacity, entanglement, and trainability. On the theoretical side, we show that simple product-state circuits preserve the exact MaxCut optimum, establish equivalences between different parameterizations, and characterize the relationship between local optima of the resulting continuous landscape and classical single-vertex-flip solutions.

We complement these analytical results with a numerical comparison involving 95 graph instances, several variational architectures, and QAOA circuits of different depths under a common optimization budget. Interestingly, simple separable circuits achieve competitive, and often better, approximation ratios than the more structured QAOA circuits considered, while requiring substantially fewer objective evaluations. Introducing additional parameters or generic entangling gates does not consistently improve solution quality and can make optimization more expensive. Although these findings are limited to small, noiseless simulations and do not imply a quantum advantage, they highlight an important consideration in variational quantum algorithm design: increasing circuit complexity does not necessarily improve practical performance, and the geometry of the optimization landscape can be just as important as the expressive power of the circuit itself.

The article is available here. Code available here and related blog post here.