Comment on "Control landscapes are almost always trap free: a geometric assessment"

Abstract

We analyze a recent claim that almost all closed, finite dimensional quantum systems have trap-free (i.e., free from local optima) landscapes (B. Russell et.al. J. Phys. A: Math. Theor. 50, 205302 (2017)). We point out several errors in the proof which compromise the authors' conclusion. Interested readers are highly encouraged to take a look at the "rebuttal" (see Ref. [1]) of this comment published by the authors of the criticized work. This "rebuttal" is a showcase of the way the erroneous and misleading statements under discussion will be wrapped up and injected in their future works, such as R. L. Kosut et.al, arXiv:1810.04362 [quant-ph] (2018).

arXiv comment6 pages, 1 figure

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• Constraint optimization and $\mathcal{S}\mathcal{U}(N)$ quantum control landscapes
• Quantum mechanics and speed limit of ultrafast local control in spin chains
• On optimization of coherent and incoherent controls for two-level quantum systems
• Control landscapes for high-fidelity generation of C-NOT and C-PHASE gates with coherent and environmental driving
• On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation