The Casimir interaction between two parallel metal plates in close proximity is usually thought of as an attractive interaction. By coating one object with a low–refractive index thin film, we show that the Casimir interaction between two objects of the same material can be reversed at short distances and preserved at long distances so that two objects can remain without contact at a specific distance. With such a stable Casimir equilibrium, we experimentally demonstrate passive Casimir trapping of an object in the vicinity of another at the nanometer scale, without requiring any external energy input. This stable Casimir equilibrium and quantum trapping can be used as a platform for a variety of applications such as contact-free nanomachines, ultrasensitive force sensors, and nanoscale manipulations.

Classical simulations of quantum circuits are limited in both space and time when the qubit count is above 50, the realm where quantum supremacy reigns. However, recently, for the low depth circuit with more than 50 qubits, there are several methods of simulation proposed by teams at Google and IBM. Here, we present a scheme of simulation which can extract a large amount of measurement outcomes within a short time, achieving a 64-qubit simulation of a universal random circuit of depth 22 using a 128-node cluster, and 56-and 42-qubit circuits on a single PC. We also estimate that a 72-qubit circuit of depth 23 can be simulated in about 16 h on a supercomputer identical to that used by the IBM team. Moreover, the simulation processes are exceedingly separable, hence parallelizable, involving just a few inter-process communications. Our work enables simulating more qubits with less hardware burden and provides a new perspective for classical simulations.

The single crystalline submicrotubes of a small organic functional molecule, 2,4,5-triphenylimidazole (TPI), were successfully prepared with a facile method. A series of characterizations indicated that the tubes were obtained from the rolling followed by seaming of a preorganized two-dimensional sheet-like structure, whose formation was due to the efficient cooperation of several molecular recognition elements. The length and diameter of the TPI tubes can be readily controlled by adjusting the experimental conditions. The as-prepared submicrotubes have intensive luminescence and size-dependent optical properties, which allows them to find potential applications in novel optical and optoelectronic devices together with their single crystalline structure and good stability. The strategy described here should give a useful enlightenment for the design and fabrication of tubular structures from small organic molecules.