Quantum optimal control is an important technology that enables fast state preparation and gate design. In the absence of analytic solution, most quantum methods rely on iterative scheme to update solution estimate. At present, convergence rate existing solvers is, at most, superlinear. This paper develops a general-purpose solver for based projection operator Newton method trajectory optimizat...

The normalizer of an element of a group is defined as the subgroup of all elements commuting with it; this subgroup is often also called the centralizer of the given element. In the second version [F-GM] the authors switched to the latter terminology, and we will also use the term “centralizer”. The conjecture was supported by a new algorithm for finding generators of a centralizer, suggested i...

We show that many graphs naturally associated to a connected, compact, orientable surface are hierarchically hyperbolic spaces in the sense of Behrstock, Hagen and Sisto. They also automatically have coarse median property defined by Bowditch. Consequences for such include distance formula analogous Masur Minsky's mapping class group, an upper bound on maximal dimension quasiflats, existence qu...

In this short note we study a dynamical system generated by two-parametric quadratic operator mapping 3-dimensional simplex to itself. This is an evolution of the frequencies gametes in two-locus system. We find set all (a continuum of) fixed points and show that each point nonhyperbolic. completely describe limit Namely, for any initial (taken from simplex) invariant containing unique operator...

Given a finitely generated free group $ {\mathbb {F} }$ of $\mathsf {rank}( } )\geq 3$ , we show that the mapping torus $\phi$ is (strongly) relatively hyperbolic if exponentially growing. As corollary our work, give new proof Brinkmann's theorem which proves an atoroidal outer automorphism hyperbolic. We also Bridson–Groves satisfies quadratic isoperimetric inequality. Our work solves problem ...

According to the new condition of pump peak power, we report a developed approach achieve time-frequency mapping (TFM) in spectral Fraunhofer regime by single all-optical time lens using parabolic cross-phase modulation (XPM). The is obtained combining far-field with ability pulses induce pure quadratic phase modulation. derived allows tunability different strategies when probe durations are ta...

It is shown that for non-hyperbolic real quadratic polynomials topological and qua-sisymmetric conjugacy classes are the same. By quasiconformal rigidity, each class has only one representative in the quadratic family, which proves that hyperbolic maps are dense. Statement of the results. Dense Hyperbolicity Theorem In the real quadratic family f a (x) = ax(1 − x) , 0 < a ≤ 4 the mapping f a ha...