Analysis of CV-QAOA beyond one layer for broader nonconvex functions

Extend the theoretical analysis of Continuous-Variable Quantum Approximate Optimization Algorithm (CV-QAOA) beyond depth p=1 to broader classes of nonconvex functions, including functions with multiple interacting minima or highly anisotropic landscapes.

Background

The paper rigorously analyzes one-step CV-QAOA for broad real-analytic functions whose global minimizer is aligned with the gradient at the origin, and it analyzes higher-depth or delocalized regimes primarily through specific quadratic, rotated double-well, and rotated square-well constructions. These results do not provide a general theory for shallow CV-QAOA on arbitrary nonconvex landscapes.

The authors explicitly identify extending the analysis beyond depth p=1, particularly for landscapes with multiple interacting minima or strong anisotropy, as an unresolved theoretical problem.

References

From a theoretical perspective, extending the analysis of CV-QAOA beyond depth $p=1$ to broader classes of nonconvex functions, including those with multiple interacting minima or highly anisotropic landscapes, remains an open problem.

— CV-QAOA: Efficient Low-Depth Quantum Optimization of Continuous Variables  (2610.06815 - Bharadwaj et al., 5 Oct 2026) in Section 7, Discussion and Outlook