10,121 research outputs found
Arbitrary phase rotation of the marked state can not be used for Grover's quantum search algorithm
A misunderstanding that an arbitrary phase rotation of the marked state
together with the inversion about average operation in Grover's search
algorithm can be used to construct a (less efficient) quantum search algorithm
is cleared. The rotation of the phase of the marked state is not only the
choice for efficiency, but also vital in Grover's quantum search algorithm. The
results also show that Grover's quantum search algorithm is robust.Comment: 5 pages, 5 figure
Hankel determinants, Pad\'e approximations, and irrationality exponents
The irrationality exponent of an irrational number , which measures the
approximation rate of by rationals, is in general extremely difficult to
compute explicitly, unless we know the continued fraction expansion of .
Results obtained so far are rather fragmentary, and often treated case by case.
In this work, we shall unify all the known results on the subject by showing
that the irrationality exponents of large classes of automatic numbers and
Mahler numbers (which are transcendental) are exactly equal to . Our classes
contain the Thue--Morse--Mahler numbers, the sum of the reciprocals of the
Fermat numbers, the regular paperfolding numbers, which have been previously
considered respectively by Bugeaud, Coons, and Guo, Wu and Wen, but also new
classes such as the Stern numbers and so on. Among other ingredients, our
proofs use results on Hankel determinants obtained recently by Han.Comment: International Mathematics Research Notices 201
Decentralised delay-dependent static output feedback variable structure control
In this paper, an output feedback stabilisation problem is considered for a class of large scale interconnected time delay systems with uncertainties. The uncertainties appear in both isolated subsystems and interconnections. The bounds on the uncertainties are nonlinear and time delayed. It is not required that either the known interconnections or the uncertain interconnections are matched. Then, a decentralised delay-dependant static output feedback variable structure control is synthesised to stabilise the system globally uniformly asymptotically using the Lyapunov Razumikhin approach. A case study relating to a river pollution control problem is presented to illustrate the proposed approach
Two-Dimensional Inversion Asymmetric Topological Insulators in Functionalized III-Bi Bilayers
The search for inversion asymmetric topological insulators (IATIs) persists
as an effect for realizing new topological phenomena. However, so for only a
few IATIs have been discovered and there is no IATI exhibiting a large band gap
exceeding 0.6 eV. Using first-principles calculations, we predict a series of
new IATIs in saturated Group III-Bi bilayers. We show that all these IATIs
preserve extraordinary large bulk band gaps which are well above
room-temperature, allowing for viable applications in room-temperature
spintronic devices. More importantly, most of these systems display large bulk
band gaps that far exceed 0.6 eV and, part of them even are up to ~1 eV, which
are larger than any IATIs ever reported. The nontrivial topological situation
in these systems is confirmed by the identified band inversion of the band
structures and an explicit demonstration of the topological edge states.
Interestingly, the nontrivial band order characteristics are intrinsic to most
of these materials and are not subject to spin-orbit coupling. Owning to their
asymmetric structures, remarkable Rashba spin splitting is produced in both the
valence and conduction bands of these systems. These predictions strongly
revive these new systems as excellent candidates for IATI-based novel
applications.Comment: 17 pages,5figure
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