Constructive quantum scaling of unitary matrices

In this work, we present a method of decomposition of arbitrary unitary matrix \(U\in \mathbf {U}(2^k)\) into a product of single-qubit negator and controlled-\(\sqrt{\text{ NOT }}\) gates. Since the product results with negator matrix, which can be treated as complex analogue of bistochastic matrix, our method can be seen as complex analogue of Sinkhorn–Knopp algorithm, where diagonal matrices are replaced by adding and removing an one-qubit ancilla. The decomposition can be found constructively, and resulting circuit consists of \(O(4^k)\) entangling gates, which is proved to be optimal. An example of such transformation is presented.     

Study on the security of the authentication scheme with key recycling in QKD

In quantum key distribution (QKD), the information theoretically secure authentication is necessary to guarantee the integrity and authenticity of the exchanged information over the classical channel. In order to reduce the key consumption, the authentication scheme with key recycling (KR), in which a secret but fixed hash function is used for multiple messages while each tag is encrypted with a one-time pad (OTP), is preferred in QKD. Based on the assumption that the OTP key is perfect, the security of the authentication scheme has be proved. However, the OTP key of authentication in a practical QKD system is not perfect. How the imperfect OTP affects the security of authentication scheme with KR is analyzed thoroughly in this paper. In a practical QKD, the information of the OTP key resulting from QKD is partially leaked to the adversary. Although the information leakage is usually so little to be neglected, it will lead to the increasing degraded security of the authentication scheme as the system runs continuously. Both our theoretical analysis and simulation results demonstrate that the security level of authentication scheme with KR, mainly indicated by its substitution probability, degrades exponentially in the number of rounds and gradually diminishes to zero.     

Quantum state transfer between an optomechanical cavity and a diamond nuclear spin ensemble

We explore an efficient scheme for transferring quantum state between an optomechanical cavity and nuclear spins of nitrogen-vacancy centers in diamond, where quantum information can be efficiently stored (retrieved) into (from) the nuclear spin ensemble assisted by a mechanical resonator in a dispersive regime. Our scheme works for a broad range of cavity frequencies and might have potential applications in employing the nuclear spin ensemble as a memory in quantum information processing. The feasibility of our protocol is analyzed using currently available parameters.     

Unitary equivalent classes of one-dimensional quantum walks

This study investigates unitary equivalent classes of one-dimensional quantum walks. We prove that one-dimensional quantum walks are unitary equivalent to quantum walks of Ambainis type and that translation-invariant one-dimensional quantum walks are Szegedy walks. We also present a necessary and sufficient condition for a one-dimensional quantum walk to be a Szegedy walk.     

A modular designed bolt tightening shaft based on adaptive fuzzy backstepping control

This paper presents a modular designed autonomous bolt tightening shaft system with an adaptive fuzzy backstepping control approach developed for it. The bolt tightening shaft is designed for the autonomous bolt tightening operation, which has huge potential for industry application. Due to the inherent nonlinear and uncertain properties, the bolt tightening shaft and the bolt tightening process are mathematically modeled as an uncertain strict feedback system. With the adaptive backstepping and approximation property of fuzzy logic system, the controller is recursively designed. Based on the Lyapunov stability theorem, all signals in the closed-loop system are proved to be uniformly ultimately bounded and the torque tracking error exponentially converges to a small residue. And the effectiveness and performance of the proposed autonomous system are verified by the simulation and experiment results on the bolt tightening shaft system.     

(<Emphasis Type="Italic">m</Emphasis>,<Emphasis Type="Italic">N</Emphasis>)-delay-partitioning approach to stability analysis for T-S fuzzy systems with interval time-varying delay

This paper is concerned with improved stability criteria for uncertain T-S fuzzy systems with interval time-varying delay by means of a new (m,N)-delay-partitioning approach. Based on an appropriate augmented LKF established in the framework of state vector augmentation, some tighter bounding inequalities (Seuret-Wirtinger’s integral inequality, Peng-Park’s integral inequality and the reciprocally convex approach) have been employed to deal with (time-varying) delay-dependent integral items of the derivative of LKF, therefore, less conservative delaydependent stability criteria can be obtained on account of none of any useful time-varying items are arbitrarily ignored. It’s worth mentioning that, when the delay-partitioning number m is fixed, less conservatism can be achieved by increase of another delay-partitioning number N, but without increasing any computing burden. Finally, one numerical example is provided to show that the proposed conditions are less conservative than existing ones.     

Integrated guidance and control design based on a reference model

In this paper, an Integrated Guidance and Control (IGC) algorithm based on a reference model is proposed for a side-jet missile. First, a IGC structure is introduced, incorporating the response characteristics of the missile control loop into the guidance loop. To describe the response characteristics, then a reference model is built. Next, with the back stepping scheme and sliding mode control algorithm, the reference model is adopted to derive a novel guidance law, which contains response parameters of missile control system to formulate the IGC design. Finally, simulations and comparisons with the time-scale separation design and an existing IGC design, are conducted to verify the proposed IGC algorithm. It can be shown that the proposed algorithm performs better against highly maneuvering target in different missile-target initial position and heading scenarios.     

Angular velocity observer for attitude tracking on SO(3) with the separation property

This paper studies a rigid body attitude tracking control problem with attitude measurements only, when angular velocity measurements are not available. An angular velocity observer is constructed such that the estimated angular velocity is guaranteed to converge to the true angular velocity asymptotically from almost all initial estimates. As it is developed directly on the special orthogonal group, which completely avoids singularities, complexities, or discontinuities caused by minimal attitude representations or quaternions. Then, the presented observer is integrated with a proportional-derivative attitude tracking controller to show a separation type property, where exponential stability is guaranteed for the combined observer and attitude control system.     

An efficient algorithm for the tensor product model transformation

The tensor-product (TP) model transformation was proposed recently as a numerical and automatically executable method which is capable of transforming linear parameter varying (LPV) state-space models into the higher order singular value decomposition (HOSVD) based canonical form of polytopic models. The crucial disadvantage of the TP model transformation is that its computational load explodes with the density of discretization and the dimensionality of the parameter vector of the parameter-varying state-space model. In this paper we propose a new algorithm that leads to considerable reduction of the computation in the TP model transformation. The main idea behind the modified algorithm is to minimize the number of discretized points to acquire as much information as possible. The modified TP model transformation can readily be executed on a regular computer efficiently and concisely, especially in higher dimensional cases when the original TP model transformation fails. The paper also presents numerical examples to show the effectiveness of the new algorithm.