Kinetic Energy-Based Normal Mode Analysis of Electronic Processes in C60

A kinetic energy-based normal-mode analysis is applied to photoinduced electronic processes in C60. Due to the fact that the total kinetic energy is always a quadratic function of velocity, the expansion in normal modes is exact, in contrast to the potential-based normal-mode analysis where the total potential energy can not be exactly expanded in terms of the normal mode potentials since higher-order terms appear. This is especially true in many anharmonic relaxation processes. The calculation presented here demonstrates the appealing properties of this new scheme. In particular, the two most dominant Hg modes are identified which play an es-sential role in the dynamical properties of C60, which is consistent with the experimental results. This clarifies the previous theoretical ambiguity which showed that the electron-phonon coupling constant is basically the same for different modes

Can Variational Quantum Algorithms Demonstrate Quantum Advantages? Time Really Matters

Applying low-depth quantum neural networks (QNNs), variational quantum algorithms (VQAs) are both promising and challenging in the noisy intermediate-scale quantum (NISQ) era: Despite its remarkable progress, criticisms on the efficiency and feasibility issues never stopped. However, whether VQAs can demonstrate quantum advantages is still undetermined till now, which will be investigated in this paper. First, we will prove that there exists a dependency between the parameter number and the gradient-evaluation cost when training QNNs. Noticing there is no such direct dependency when training classical neural networks with the backpropagation algorithm, we argue that such a dependency limits the scalability of VQAs. Second, we estimate the time for running VQAs in ideal cases, i.e., without considering realistic limitations like noise and reachability. We will show that the ideal time cost easily reaches the order of a 1-year wall time. Third, by comparing with the time cost using classical simulation of quantum circuits, we will show that VQAs can only outperform the classical simulation case when the time cost reaches the scaling of $10^0$-$10^2$ years. Finally, based on the above results, we argue that it would be difficult for VQAs to outperform classical cases in view of time scaling, and therefore, demonstrate quantum advantages, with the current workflow. Since VQAs as well as quantum computing are developing rapidly, this work does not aim to deny the potential of VQAs. The analysis in this paper provides directions for optimizing VQAs, and in the long run, seeking more natural hybrid quantum-classical algorithms would be meaningful.Comment: 18 pages, 7 figure

Soft Roof Failure Mechanism and Supporting Method for Gob-Side Entry Retaining

To study the soft roof failure mechanism and the supporting method for a gateway in a gently inclined coal seam with a dip angle of 16° kept for gob-side entry retaining, and through the methodology of field investigation and numerical and analytical modeling, this paper analyzed the stress evolution law of roof strata at the working face end and determined that the sharp horizontal stress unloading phenomenon along the coal wall side did not appear after the working face advanced. Conversely, the horizontal stress along the gob side instantly decreased and the tensile stress produced, and the vertical stress in the central part of the roof had a higher reduction magnitude as well. An in-depth study indicates that the soft roof of the working face end subsided and seriously separated due to the effect of the front abutment pressure and the roof hanging length above the gob line, as well as certain other factors, including the rapid unloading of the lateral stress, tension and shear on the lower roof rock layer and dynamic disturbance. Those influencing factors also led to rapid crack propagation on a large scale and serious fracturing in the soft roof of the working face end. However, in the gob stress stabilized zone, the soft roof in the gob-side entry retaining has a shearing failure along the filling wall inside affected by the overburden pressure, rock bulking pressure, and roof gravity. To maintain the roof integrity, decrease the roof deformation, and enable the control of the working face end soft roof and the stabilization of the gob-side entry retaining roof, this study suggests that the preferred bolt installation angle for the soft roof situation is 70° based on the rock bolt extrusion strengthening theory