Efficient Simulation of Loop Quantum Gravity: A Scalable Linear-Optical Approach.

The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is loop quantum gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spin-foam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the bounded-error quantum polynomial time class, which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers, which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer that can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory.

Light-Controlled Interconversion between a Self-Assembled Triangle and a Rhombicuboctahedral Sphere.

Stimuli-responsive structural reorganizations play an important role in biological processes, often in combination with kinetic control scenarios. In supramolecular mimics of such systems, light has been established as the perfect external trigger. Here, we report on the light-driven structural rearrangement of a small, self-assembled Pd3L6 ring based on photochromic dithienylethene (DTE) ligands into a rhombicuboctahedral Pd24L48 sphere measuring about 6.4 nm across. When the wavelength is changed, this interconversion can be fully reversed, as confirmed by NMR and UV/Vis spectroscopy as well as mass spectrometry. The sphere was visualized by AFM, TEM, and GISAXS measurements. Due to dissimilarities in the photoswitch conformations, the interconversion rates between the two assemblies are drastically different in the two directions.

Rational design of a face-centred square-cuboid coordination cage.

The simple synthetic conversion of a 90°-angled bis-pyridyl ligand into a tripodal tris-pyridyl ligand leads to the formal transformation of a cubic (a=b=c) into a square-cuboid (a=b≠c) coordination cage. Mathematical considerations associated with the ligand design, together with X-ray structure results, NMR spectroscopic and mass spectrometric characterization and molecular modeling of both coordination cages are presented and discussed.

Self-assembled coordination cages based on banana-shaped ligands.

The combination of pyridyl ligands and square-planar Pd(ii) or Pt(ii) cations has proven to be a very reliable recipe for the realization of supramolecular self-assemblies. This tutorial review deals with the design, synthesis and host-guest chemistry of discrete coordination cages built according to this strategy. The focus is set on structures obeying the formula [PdnL2n] (n = 2-4). The most discussed ligands are bent, bis-monodentate bridges having their two donor sites pointing in the same direction. The structures of the resulting cages range from simple globules over intertwined knots to interpenetrated dimers featuring three small pockets instead of one large cavity. The cages have large openings that allow small guest molecules to enter and leave the cavities. Most structures are cationic and thus favour the uptake of anionic guests. Some examples of host-guest complexes are discussed with emphasis on coencapsulation and allosteric binding phenomena. Aside from cages in which the ligands have only a structural role, some examples of functional ligands based on photo- and redox-active backbones are presented.

An inclusion complex of hexamolybdate inside a supramolecular cage and its structural conversion.

A self-assembled cage compound consisting of four concave ligands and two square-planar-coordinated Pd(II) ions was found to quantitatively encapsulate a hexamolybdate dianion [Mo(6)O(19)](2-) in solution. The addition of 1 equiv more of [Mo(6)O(19)](2-) to the inclusion complex resulted in the formation of a precipitate from which single crystals were grown. X-ray analysis showed that a structural conversion had taken place upon crystallization: one hexamolybdate anion was found to be wrapped in a chiral, cyclic arrangement of three ligands in the absence of any Pd(II) ions to give a compound of the formula {[Mo(6)O(19)](2-)@(ligand)(3)+2H(+)}. We postulate the stabilization of this arrangement by attractive C-H···O and CF(3)-pyridine interactions.