44 research outputs found
On the relationship between continuous- and discrete-time quantum walk
Quantum walk is one of the main tools for quantum algorithms. Defined by
analogy to classical random walk, a quantum walk is a time-homogeneous quantum
process on a graph. Both random and quantum walks can be defined either in
continuous or discrete time. But whereas a continuous-time random walk can be
obtained as the limit of a sequence of discrete-time random walks, the two
types of quantum walk appear fundamentally different, owing to the need for
extra degrees of freedom in the discrete-time case.
In this article, I describe a precise correspondence between continuous- and
discrete-time quantum walks on arbitrary graphs. Using this correspondence, I
show that continuous-time quantum walk can be obtained as an appropriate limit
of discrete-time quantum walks. The correspondence also leads to a new
technique for simulating Hamiltonian dynamics, giving efficient simulations
even in cases where the Hamiltonian is not sparse. The complexity of the
simulation is linear in the total evolution time, an improvement over
simulations based on high-order approximations of the Lie product formula. As
applications, I describe a continuous-time quantum walk algorithm for element
distinctness and show how to optimally simulate continuous-time query
algorithms of a certain form in the conventional quantum query model. Finally,
I discuss limitations of the method for simulating Hamiltonians with negative
matrix elements, and present two problems that motivate attempting to
circumvent these limitations.Comment: 22 pages. v2: improved presentation, new section on Hamiltonian
oracles; v3: published version, with improved analysis of phase estimatio
Quantum algorithms for algebraic problems
Quantum computers can execute algorithms that dramatically outperform
classical computation. As the best-known example, Shor discovered an efficient
quantum algorithm for factoring integers, whereas factoring appears to be
difficult for classical computers. Understanding what other computational
problems can be solved significantly faster using quantum algorithms is one of
the major challenges in the theory of quantum computation, and such algorithms
motivate the formidable task of building a large-scale quantum computer. This
article reviews the current state of quantum algorithms, focusing on algorithms
with superpolynomial speedup over classical computation, and in particular, on
problems with an algebraic flavor.Comment: 52 pages, 3 figures, to appear in Reviews of Modern Physic
PASSIVE THERMAL CONTROL SYSTEMS FOR SPACE INSTRUMENTS MAKING – SCIENTIFIC BACKGROUND, QUALIFICATION, EXPLOITATION IN SPACE
Passive thermal control systems (TCS) are one of obligatory system of any space
mission, used as on large spacecraft and microsatellites Supporting of required temperature
range for space instruments is supported by rational design of TCS with optimal choice of
main thermal control components such as multilayer insulation, optical coatings, heat
conductive elements, heat insulation supports, thermal conductive gaskets, radiating surfaces
and other elements. New ideology in TCS design has come after appearance of new element
– heat pipe(s) which is a super heat conductive thermal conductor with constant or variable
thermal properties