Quantum algorithm for neighborhood preserving embedding

Neighborhood preserving embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point, constructing the weight matrix, and obtaining the transformation matrix. Liang et al. proposed a variational quantum algorithm (VQA) for NPE [Phys. Rev. A 101 032323 (2020)]. The algorithm consists of three quantum sub-algorithms, corresponding to the three steps of NPE, and was expected to have an exponential speedup on the dimensionality n. However, the algorithm has two disadvantages: (i) It is not known how to efficiently obtain the input of the third sub-algorithm from the output of the second one. (ii) Its complexity cannot be rigorously analyzed because the third sub-algorithm in it is a VQA. In this paper, we propose a complete quantum algorithm for NPE, in which we redesign the three sub-algorithms and give a rigorous complexity analysis. It is shown that our algorithm can achieve a polynomial speedup on the number of data points m and an exponential speedup on the dimensionality n under certain conditions over the classical NPE algorithm, and achieve a significant speedup compared to Liang et al.'s algorithm even without considering the complexity of the VQA.     

Influence of relative humidity and loading frequency on the PA6.6 thermomechanical cyclic behavior: Part II. Energy aspects

In this study, we investigated the influence of relative humidity (RH) and loading rate on the energy response of PA6.6 matrix specimens. The latter were subjected to oligocyclic tensile-tensile tests at 3 different RH and 2 loading rates. Infrared thermography was used to obtain a direct estimate of heat sources using the heat diffusion equation. Using the mechanical and thermal responses discussed in the first part of this work, complete energy rate balances were drawn up. In particular, the time courses of deformation, and dissipated and stored energy rates are discussed. The strong influence of the loading frequency and RH on the energy storage mechanisms is also highlighted.     

Fault tolerant deterministic secure quantum communication using logical Bell states against collective noise

This study proposes two novel fault tolerant deterministic secure quantum communication(DSQC) schemes resistant to collective noise using logical Bell states. Either DSQC scheme is constructed based on a new coding function, which is designed by exploiting the property of the corresponding logical Bell states immune to collective-dephasing noise and collective-rotation noise, respectively. The secret message can be encoded by two simple unitary operations and decoded by merely performing Bell measurements, which can make the proposed scheme more convenient in practical applications.Moreover, the strategy of one-step quanta transmission, together with the technique of decoy logical qubits checking not only reduces the influence of other noise existing in a quantum channel, but also guarantees the security of the communication between two legitimate users. The final analysis shows that the proposed schemes are feasible and robust against various well-known attacks over the collective noise channel.     

Chaotic ant swarm optimization with passive congregation

Chaotic ant swarm optimization (CASO) is a powerful chaos search algorithm for optimization problems, but it is often easy to be premature convergence. To overcome the weakness, this paper presents a CASO with passive congregation (CASOPC). Passive congregation is one type of biological information sharing mechanisms that allow animals to aggregate into groups and help to enhance the exploitation of animals. By introducing passive congregation strategy into the CASO, a modified evolution equation based on the CASO is proposed in the CASOPC. The modified evolution equation cannot only employ the parallel search of all ants and the well exploration ability of the CASO, but also stress and control the exploitation by passive congregation coefficient c in the stage of evolution. Due to linearly increasing c in the CASOPC, the exploration and exploitation ability of ants are well balanced so that premature convergence can be avoided and good performance can be achieved. In order to estimate the capability of the CASOPC, it is tested with a set of 5 benchmark functions with 30 dimensions and compared to the CASO. Experimental results indicate that the CASOPC improves the search performance on the benchmark functions significantly.     

Universal Three-Party Quantum Secret Sharing Against Collective Noise

we present a robust and universal quantum secret sharing protocol with four-qubit decoherence-free (DF) states against collective noise. The transmission's safety is ensured by the nonorthogonality of the noiseless states traveling on the quantum channel. Although this scheme uses entangled states for encoding, only single-particle product measurements are required.     

An Economical Scheme for Cloning an Unknown M-Qudit Equatorial-Like State with Assistance

We propose a scheme to realize quantum cloning of an unknown M-qudit equatorial-like entangled state. The first stage of the protocol requires teleportation. After the teleportation is accomplished, the receiver can reestablish the original state. In the second stage of the protocol, with the assistance （through a single-particle projective measurement） of the preparer, the perfect copy of an original state can be produced at the site of the sender. Our scheme requires a single maximally entangled qudit pair as the quantum channel and three dits classical communication. The scheme is feasible at the expense of consuming local resources which include M - 1 ancillary qudits introduced by the receiver and additional bi-qudit operations. Moreover, we construct a sort of unitary transformations which ensure ancillary qudits are not necessarily introduced by the sender. Comparing to the previous protocols, the proposed protocol is economical due to that the cost of both quantum nonlocal resources and classical communication is lowest.