Some recent quantum structures

L. A. Lugiato, A. Gatti, K.I. Petsas

Katsuhiro Endo, Kazuaki Z. Takahashi

Nonlinear structural analysis, which can account for geometrical or material nonlinearities beyond the scope of linear methods, typically incurs high computational costs. Recent advances have shown that quantum computers can accelerate various numerical simulations. Although quantum acceleration of linear structural analysis via the Quantum Linear System Algorithm (QLSA) has been studied, its application to nonlinear structural analysis remains unexplored. Here, we introduce our proposed quantum algorithm for accelerating nonlinear structural analysis, summarizing its key features and performance results from our recent study.

L.A. Lugiato, A. Gatti, K.I. Petsas

Gian‐Luca Oppo, Luigi A. Lugiato

Homogeneous, periodic, quasiperiodic, irregular and disordered spatial structures have been at the heart of scientific interest and research for a long time and in many disciplines as diverse as chemistry, physics, biology and morphology. Some recent, spectacular achievements in experimental quantum optics have, however, made it possible to study quantum effects in a variety of spatial structures. The main aim of this Focus Issue is to present some of the most recent theoretical, numerical and experimental progresses in the area of Quantum Structures, i.e. spatial structures that display quantum features. A short background overview of Quantum Structures is provided at the beginning of this Focus Issue, in which individual authors' works are specifically commented. In brief, we can say that the articles can be catalogued into two main areas of research interest in Quantum Structures: quantum effects in spatial structures in nonlinear optics, and in atomic physics.

Anatolij Dvurečenskij

Josef Tkadlec

Compatibilty play an important role in the axiomatics of quantum structures and has been studied extensively. We present some recent results concerning compatibility in quantum structures, their consequences to the axiomatics and their relationship to previous achievements. We show, e.g., that a residuated orthomodular lattice is a Boolean algebra.