Quantum speed-up in solving the maximal clique problem

The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry, bioinformatics to social networks. Here we develop a quantum algorithm to solve the maximal clique problem for any graph $G$ with $n$ vertices with quadratic speed-up over its classical counterparts, where the time and spatial complexities are reduced to, respectively, $O(\sqrt{2^{n}})$ and $O(n^{2})$. With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm to be optimal. To justify the feasibility of the proposed quantum algorithm, we have successfully solved an exemplified clique problem for a graph $G$ with two vertices and one edge by carrying out a nuclear magnetic resonance experiment involving four qubits.Comment: 5 figure

Experimental test of Heisenberg's measurement uncertainty relation based on statistical distances

Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch, Lahti, and Werner proposed inaccuracy trade-off relations based on statistical distances between probability distributions of measurement outcomes [Phys. Rev. Lett. 111, 160405 (2013); Phys. Rev. A 89, 012129 (2014)]. Here we reform their theoretical framework, derive an improved relation for qubit measurement, and perform an experimental test on a spin system. The relation reveals that the worst-case inaccuracy is tightly bounded from below by the incompatibility of target observables, and is verified by the experiment employing joint measurement in which two compatible but typically non-commutative observables on one qubit are measured simultaneously

Design Comparison of Outer- and Inner-Rotor Permanent Magnet Motors for Hydrofoil Boat

This paper presents the design criteria of a permanent magnet motor for hydrofoil boat applications. Based on the dynamic analysis of hydrofoil boat, the constraints of propulsion motor are derived and therefore the surface-mounted permanent magnet motor is chosen as the competitive candidate. In order to have large power density in the permanent magnet motor, the outer- and inner-rotor motors are investigated and compared to demonstrate their advantages at different design constraints, which will provide the theoretical basis to improve the propulsion system in the hydrofoil boat from the perspective of motor design

Nonlinear Analytical Analysis of External Rotor Permanent Magnet Synchronous Motor

This article proposed a nonlinear analytical model (NAM) for external rotor permanent magnet synchronous motor (ER-PMSM) considering both rotor and stator saturation. The improved magnetic equivalent circuit (IMEC) is introduced to accurately describe the saturation effect of rotor and stator. The air gap reluctance is replaced by magnetic flux source, and, therefore, the size of IMEC can be reduced while keeping high accuracy. For the air gap field calculation, the analytical solution will be obtained based on the modified boundary condition from the IMEC. The complex permeance function is extended to represent the slotting effect of ER-PMSM. Hence, the NAM will be numerically solved from the combination of IMEC and analytical air gap solution. Both finite-element analysis (FEA) and experiment demonstrate that the proposed model has high accuracy and requires little time

Analytical Calculation of Eccentric Surface-Mounted Permanent-Magnet Motor Accounting for Iron Saturation

This article presents an analytical model to predict the performance of eccentric surface-mounted permanent-magnet (ESPM) motor based on the nonlinear conformal mapping and reluctance network hybrid model (NCRHM). The proposed model can reveal the mutual influence of rotor eccentricity on the stator slotting and iron saturation accounting for the distortion of the equivalent current positions and air-gap path among the conformal mappings. The transformation between magnetic voltage drop of iron and equivalent current in the air region (including air-gap and slot region) is employed to consider the increased iron saturation due to the reduced air-gap length. Based on the proposed model, the electromagnetic performance including flux linkage, back electromotive force (EMF), torque, and unbalanced magnetic force (UMF) can be accurately predicted for any kind of rotor eccentricity. In addition, the NCRHM is compared with the complex permeance model (CPM) neglecting both iron saturation and the field distortion in conformal mappings, which exhibits the great advantage of NCRHM for ESPM motor. The excellent accuracy and great efficiency of the proposed model are validated by both finite-element analysis and test results

Nonlinear Analytical Modelling for Surface-Mounted Permanent Magnet Motors with Magnet Defect Fault

This paper analyzes magnet defect fault signature in the surface-mounted permanent magnet motor (SPMM) using nonlinear analytical model considering the influence of magnet shape and magnetization direction. Based on the surface current method and conformal mapping technique, the magnet defect equivalent current and equivalent nonlinearity current are proposed to represent the magnet defect. Accordingly, the performance of SPMM can be obtained. The proposed model has great potential to investigate SPMM with non-uniform magnet defect and gives theoretical basis for fault diagnosis. The extra sensing coil is added to measure the voltage waveforms, which can also be predicted using the nonlinear analytical model and shows the influence of magnet defect fault. Finally, the finite element analysis and experimental results verify the high accuracy of nonlinear analytical model