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.     

Central limit theorem for reducible and irreducible open quantum walks

In this work we aim at proving central limit theorems for open quantum walks on \({\mathbb {Z}}^d\). We study the case when there are various classes of vertices in the network. In particular, we investigate two ways of distributing the vertex classes in the network. First, we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a transition invariant distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.     

Code reordering using local random extraction and insertion (LREI) operator for GPGPU-based track-before-detect systems

Track-before-detect (TBD) algorithms are used for tracking systems, where the object’s signal is below the noise floor (low-SNR objects). A lot of computations and memory transfers for real-time signal processing are necessary. GPGPU in parallel processing devices for TBD algorithms is well suited. Finding optimal or suboptimal code, due to lack of documentation for low-level programming of GPGPUs is not possible. High-level code optimization is necessary and the evolutionary approach, based on the single parent and single child is considered, that is local search approach. Brute force search technique is not feasible, because there are N! code variants, where N is the number of motion vectors components. The proposed evolutionary operator—LREI (local random extraction and insertion) allows source code reordering for the reduction of computation time due to better organization of memory transfer and the texture cache content. The starting point, based on the sorting and the minimal execution time metric is proposed. The unbiased random and biased sorting techniques are compared using experimental approach. Tests shows significant improvements of the computation speed, about 8 % over the conventional code for CUDA code. The time period of optimization for the sample code is about 1 h (1,000 iterations) for the considered recursive spatio-temporal TBD algorithm.     

Control of Robot Manipulators in Terms of Quasi-Velocities

In this paper we present new control algorithms for robots with dynamics described in terms of quasi-velocities (Kozłowski, Identification of articulated body inertias and decoupled control of robots in terms of quasi-coordinates. In: Proc. of the 1996 IEEE International Conference on Robotics and Automation, pp. 317–322. IEEE, Piscataway, 1996a; Zeitschrift für Angewandte Mathematik und Mechanik 76(S3):479–480, 1996c; Robot control algorithms in terms of quasi-coordinates. In: Proc. of the 34 Conference on Decision and Control, pp. 3020–3025, Kobe, 11–13 December 1996, 1996d). The equations of motion are written using spatial quantities such as spatial velocities, accelerations, forces, and articulated body inertia matrices (Kozłowski, Standard and diagonalized Lagrangian dynamics: a comparison. In: Proc. of the 1995 IEEE Int. Conf. on Robotics and Automation, pp. 2823–2828. IEEE, Piscataway, 1995b; Rodriguez and Kreutz, Recursive Mass Matrix Factorization and Inversion, An Operator Approach to Open- and Closed-Chain Multibody Dynamics, pp. 88–11. JPL, Dartmouth, 1998). The forward dynamics algorithms incorporate new control laws in terms of normalized quasi-velocities. Two cases are considered: end point trajectory tracking and trajectory tracking algorithm, in general. It is shown that by properly choosing the Lyapunov function candidate a dynamic system with appropriate feedback can be made asymptotically stable and follows the desired trajectory in the task space. All of the control laws have a new architecture in the sense that they are derived, in the so-called quasi-velocity and quasi-force space, and at any instant of time generalized positions and forces can be recovered from order recursions, where denotes the number of degrees of freedom of the manipulator. This paper also contains the proposition of a sliding mode control, originally introduced by Slotine and Li (Int J Rob Res 6(3):49–59, 1987), which has been extended to the sliding mode control in the quasi-velocity and quasi-force space. Experimental results illustrate behavior of the new control schemes and show the potential of the approach in the quasi-velocity and quasi-force space. Authors are with Chair of Control and Systems Engineering.     

On the quantum and randomized approximation of linear functionals on function spaces

We deal with quantum and randomized algorithms for approximating a class of linear continuous functionals. The functionals are defined on a H?lder space of functions f of d variables with r continuous partial derivatives, the rth derivative being a H?lder function with exponent ρ. For a certain class of such linear problems (which includes the integration problem), we define algorithms based on partitioning the domain of f into a large number of small subdomains, and making use of the well-known quantum or randomized algorithms for summation of real numbers. For N information evaluations (quantum queries in the quantum setting), we show upper bounds on the error of order N ^−(γ+1) in the quantum setting, and N ^−(γ+1/2) in the randomized setting, where γ = (r + ρ)/d is the regularity parameter. Hence, we obtain for a wider class of linear problems the same upper bounds as those known for the integration problem. We give examples of functionals satisfying the assumptions, among which we discuss functionals defined on the solution of Fredholm integral equations of the second kind, with complete information about the kernel. We also provide lower bounds, showing in some cases sharpness of the obtained results, and compare the power of quantum, randomized and deterministic algorithms for the exemplary problems.     

Angle-of-arrival localization based on antenna arrays for wireless sensor networks

Among the large number of contributions concerning the localization techniques for wireless sensor networks (WSNs), there is still no simple, energy and cost efficient solution suitable in outdoor scenarios. In this paper, a technique based on antenna arrays and angle-of-arrival (AoA) measurements is carefully discussed. While the AoA algorithms are rarely considered for WSNs due to the large dimensions of directional antennas, some system configurations are investigated that can be easily incorporated in pocket-size wireless devices.A heuristic weighting function that enables decreasing the location errors is introduced. Also, the detailed performance analysis of the presented system is provided. The localization accuracy is validated through realistic Monte-Carlo simulations that take into account the specificity of propagation conditions in WSNs as well as the radio noise effects. Finally, trade-offs between the accuracy, localization time and the number of anchors in a network are addressed.     

Makespan minimization of multi-slot just-in-time scheduling on single and parallel machines

The paper addresses the problem of multi-slot just-in-time scheduling. Unlike the existing literature on this subject, it studies a more general criterion—the minimization of the schedule makespan rather than the minimization of the number of slots used by schedule. It gives an O(nlog ² n)-time optimization algorithm for the single machine problem. For arbitrary number of m>1 identical parallel machines it presents an O(nlog n)-time optimization algorithm for the case when the processing time of each job does not exceed its due date. For the general case on m>1 machines, it proposes a polynomial time constant factor approximation algorithm.     

Collision-free control of an omni-directional vehicle

This study addresses the problem of controlling an omni-directional vehicle with both state and control dependent constraints. The task of the vehicle is to attain its desired final position given in the task space. The control constraints resulting from the physical abilities of actuators driving the vehicle wheels are also taken into account during the robot movement. The problem of collision avoidance is solved here based on an exterior penalty function approach which results in smooth vehicle velocities near obstacles. Provided that, a solution to the aforementioned vehicle task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results carried out for the omni-directional vehicle operating in both a constraint-free task space and task space including obstacles, illustrate the performance of the proposed controllers.