Reply to comment on “Control landscapes are almost always trap free: a geometric assessment”. (English) Zbl 1411.81105
Summary: This paper is a rebuttal of the comment by D. V. Zhdanov [ibid. 61, No. 50, Article ID 508001, 8 p. (2018; Zbl 1411.81106)] with regard to our paper [B. Russell et al., ibid. 50, No. 20, Article ID 205302, 19 p. (2017; Zbl 1367.81074)]. Parts of the comment either misrepresent the original claims in [Russell et al., loc. cit. (2017)] or consider issues that go beyond the scope of [Russell et al., loc. cit. (2017)]. 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 [B. Russell et al., ibid. 51, No. 33, Article ID 335103, 20 p. (2018; Zbl 1401.93111)]. 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., loc. cit.(2017)]. In summary, the remarks in the comment either misconstrue the claims of [Russell et al., loc. cit.(2017)] 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.
MSC:
| 81Q93 | Quantum control |
| 81P68 | Quantum computation |
| 93C70 | Time-scale analysis and singular perturbations in control/observation systems |
References:
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