Ising Hamiltonians for Constrained Combinatorial Optimization Problems and the Metropolis-Hastings Warm-Starting Algorithm

Quantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis-Hastings warm-starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis-Hastings warm-starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1-depth QAOA

TEMPERATURE ANALYSIS OF HIGH LATITUDES AND LOW ALTITUDE ISLAND PERMAFROST DURING THE CONSTRUCTION OF CFG PILE

Cement fly ash gravel (CFG) pile composite foundation is an effective and economic foundation treatment approach, which is significant to building a foundation, subgrade construction, and so forth. The present paper aims to investigate the temperature behaviours of high latitudes and low altitude island permafrost when the CFG pile was constructed, in which FEM and field temperature monitoring of permafrost was utilized. The proposed findings demonstrate that the temperature disturbance of permafrost is obvious when the CFG pile was constructed, and the temperature variation of CFG pile and permafrost in FEM has a good agreement with the results of field temperature monitoring. Additionally, the influence of different height subgrade on the temperature field of CFG pile composite foundation was analyzed by FEM. The proposed findings demonstrate that the height of subgrade affects the maximum temperature increase of permafrost and the re-frozen time of permafrost after the construction of CFG pile composite foundation

Nonlinear Improvement of Qubit-qudit Entanglement Witnesses

The entanglement witness is an important and experimentally applicable tool for entanglement detection. In this paper, we provide a nonlinear improvement of any entanglement witness for $2\otimes d$ quantum systems. Compared with any existing entanglement witness, the improved separability criterion only needs two more measurements on local observables. Detailed examples are employed to illustrate the efficiency of the nonlinear improvement for general, optimal and non-decomposable entanglement witnesses.Comment: 11 pages, 0 figure

InAs/GaAs quantum dot laser epitaxially grown on on-axis (001) GaAsOI substrate

Quantum dot (QD) laser as a light source for silicon optical integration has attracted great research attention because of the strategic vision of optical interconnection. In this paper, the communication band InAs QD ridge waveguide lasers were fabricated on GaAs-on-insulator (GaAsOI) substrate by combining ion-slicing technique and molecular beam epitaxy (MBE) growth. On the foundation of optimizing surface treatment processes, the InAs/In0.13Ga0.87As/GaAs dot-in-well (DWELL) lasers monolithically grown on a GaAsOI substrate were realized under pulsed operation at 20 \ub0C. The static device measurements reveal comparable performance in terms of threshold current density, slope efficiency and output power between the QD lasers on GaAsOI and GaAs substrates. This work shows great potential to fabricate highly integrated light source on Si for photonic integrated circuits

Radial Angular Momentum Transfer and Magnetic Barrier for Short-Type Gamma-Ray Burst Central Engine Activity

Soft extended emission (EE) following initial hard spikes up to 100 seconds was observed with {\em Swift}/BAT for about half of short-type gamma-ray bursts (SGRBs). This challenges the conversional central engine models of SGRBs, i.e., compact star merger models. In the framework of the black hole-neutron star merger models, we study the roles of the radial angular momentum transfer in the disk and the magnetic barrier around the black hole for the activity of SGRB central engines. We show that the radial angular momentum transfer may significantly prolong the lifetime of the accretion process and multiple episodes may be switched by the magnetic barrier. Our numerical calculations based on the models of the neutrino-dominated accretion flows suggest that the disk mass is critical for producing the observed EE. In case of the mass being $\sim 0.8M_{\odot}$, our model can reproduce the observed timescale and luminosity of both the main and EE episodes in a reasonable parameter set. The predicted luminosity of the EE component is lower than the observed EE with about one order of magnitude and the timescale is shorter than 20 seconds if the disk mass being $\sim 0.2M_{\odot}$. {\em Swift}/BAT-like instruments may be not sensitive enough to detect the EE component in this case. We argue that the EE component would be a probe for merger process and disk formation for compact star mergers.Comment: 9 pages, 3 figures, accepted for publication in Ap