We derive a generic bound on the rate of decrease transverse field for quantum annealing to converge ground state Ising model when is formulated as an infinite-time process. Our theorem based rigorous upper excitation probability in limit and mathematically counterpart previously known result derived only from leading-order term asymptotic expansion adiabatic condition. Since our gives sufficie...

Motivation Nonlinear dynamics shape the world around us, from the harmonious movements of celestial bodies, via the swirling motions in fluid flows, to the complicated biochemistry in the living cell. Mathematically these beautiful phenomena are modeled by nonlinear dynamical systems, mainly in the form of ordinary differential equations (ODEs), partial differential equations (PDEs) and delay d...

This paper sketches a rigorous correctness proof of a compiler executable. We will emphasize the central r^ ole of partial program correctness and its preservation, which captures the intuitive correct-ness requirements for transformational programs and in particular for compilers on real machines. Although often left out of sight, implementation veriication is deenitely necessary, not only but...