Erratum: Progress toward favorable landscapes in quantum combinatorial optimization [Phys. Rev. A 104 , 032401 (2021)]
Juneseo Lee, Alicia B Magann, HERSCHEL A. RABITZ, Christian Arenz · Physical Review A · 2024
Recently, Leontica and Amaro found a counterexample [1] to our claim in Lemma 1 of our paper that the optimization landscape for the MaxCut problem with an X-Ansatz is free of local optima.We describe and investigate this counterexample.We confirm that the central Theorem (2) of our paper, i.e., that establishes the equivalence between the solution sets of the X-Ansatz and a purely classical algorithm, remains valid.In Appendix A 2 b of our paper, we distinguished between different cases (a)-(c) when the critical points condition in Eq. ( A27) can be satisfied, yielding different types of critical points.We have found that the conclusion presented in case (a) is false, as Eq. ( A28) only holds at a critical point.For example, consider the vector θ + x 2 v k for some real scalar x, and v k being the unit vector with a 1 in the kth position and 0 everywhere else.Using the critical point condition in Eq. ( A27), we obtain