Reply to comment on 'control landscapes are almost always trap free: A geometric assessment'

This paper is a rebuttal of the comment by Zhdanov (2018 J. Phys. A: Math. Theor.) with regard to our paper (Russell et al 2017 J. Phys. A: Math. Theor. 50 205302). Parts of the comment either misrepresent the original claims in Russell et al (2017 J. Phys. A: Math. Theor. 50 205302) or consider issues that go beyond the scope of Russell et al (2017 J. Phys. A: Math. Theor. 50 205302). We address all of these points in the rebuttal. A remaining item about the prospect of an accumulation of null sets was already considered in a prior work (Russell et al 2018 J. Phys. A: Math. Theor. 51 335103). Importantly, the comment fails to consider the vast and continually growing set of successful quantum control tests under well-defined conditions, which serves as foundational evidence for the results in Russell et al (2017 J. Phys. A: Math. Theor. 50 205302). In summary, the remarks in the comment either misconstrue the claims of Russell et al (2017 J. Phys. A: Math. Theor. 50 205302) or raise points that are irrelevant to the goal of the original work. Thus, we conclude that the primary claim of the original paper stands: almost all closed finite dimensional quantum systems are trap free given adequate control resources.