scholarly journals Quantum circuits for incompletely specified two-qubit operators

2005 ◽  
Vol 5 (1) ◽  
pp. 48-56
Author(s):  
V.V. Shende ◽  
I.L. Markov
Keyword(s):  
Degrees Of Freedom ◽  
Unitary Operator ◽  
Quantum Circuits ◽  
Quantum Gates ◽  
Input State ◽  
Projective Measurement ◽  
Practical Challenge ◽  
Necessary And Sufficient ◽  
The Given

While the question ``how many CNOT gates are needed to simulate an arbitrary two-qubit operator'' has been conclusively answered -- three are necessary and sufficient -- previous work on this topic assumes that one wants to simulate a given unitary operator up to global phase. However, in many practical cases additional degrees of freedom are allowed. For example, if the computation is to be followed by a given projective measurement, many dissimilar operators achieve the same output distributions on all input states. Alternatively, if it is known that the input state is $\ket{0}$, the action of the given operator on all orthogonal states is immaterial. In such cases, we say that the unitary operator is incompletely specified; in this work, we take up the practical challenge of satisfying a given specification with the smallest possible circuit. In particular, we identify cases in which such operators can be implemented using fewer quantum gates than are required for generic completely specified operators.

scholarly journals Bipartite graphs with close domination and k-domination numbers

2020 ◽  
Vol 18 (1) ◽  
pp. 873-885
Author(s):  
Gülnaz Boruzanlı Ekinci ◽  
Csilla Bujtás
Keyword(s):  
Positive Integer ◽  
Dominating Set ◽  
Domination Number ◽  
Bipartite Graphs ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Minimum Cardinality ◽  
Vertex Set ◽  
Necessary And Sufficient ◽  
The Given

Abstract Let k be a positive integer and let G be a graph with vertex set V(G) . A subset D\subseteq V(G) is a k -dominating set if every vertex outside D is adjacent to at least k vertices in D . The k -domination number {\gamma }_{k}(G) is the minimum cardinality of a k -dominating set in G . For any graph G , we know that {\gamma }_{k}(G)\ge \gamma (G)+k-2 where \text{Δ}(G)\ge k\ge 2 and this bound is sharp for every k\ge 2 . In this paper, we characterize bipartite graphs satisfying the equality for k\ge 3 and present a necessary and sufficient condition for a bipartite graph to satisfy the equality hereditarily when k=3 . We also prove that the problem of deciding whether a graph satisfies the given equality is NP-hard in general.

A General Analysis of Sequential Social Learning

2021 ◽  
Author(s):  
Itai Arieli ◽  
Manuel Mueller-Frank
Keyword(s):  
Social Learning ◽  
Utility Function ◽  
Posterior Probability ◽  
General Analysis ◽  
Sufficient Condition ◽  
Important Class ◽  
General Utility ◽  
Learning Game ◽  
Necessary And Sufficient ◽  
The Given

This paper analyzes a sequential social learning game with a general utility function, state, and action space. We show that asymptotic learning holds for every utility function if and only if signals are totally unbounded, that is, the support of the private posterior probability of every event contains both zero and one. For the case of finitely many actions, we provide a sufficient condition for asymptotic learning depending on the given utility function. Finally, we establish that for the important class of simple utility functions with finitely many actions and states, pairwise unbounded signals, which generally are a strictly weaker notion than unbounded signals, are necessary and sufficient for asymptotic learning.

The Natural Frequencies of Free and Constrained Non-Uniform Beams

1960 ◽  
Vol 64 (599) ◽  
pp. 697-699 ◽  
Author(s):  
R. P. N. Jones ◽  
S. Mahalingam
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Normal Modes ◽  
Iteration Process ◽  
Conservative System ◽  
Basic System ◽  
Orthogonal Functions ◽  
Added Masses ◽  
The Given

The Rayleigh-Ritz method is well known as an approximate method of determining the natural frequencies of a conservative system, using a constrained deflection form. On the other hand, if a general deflection form (i.e. an unconstrained form) is used, the method provides a theoretically exact solution. An unconstrained form may be obtained by expressing the deflection as an expansion in terms of a suitable set of orthogonal functions, and in selecting such a set, it is convenient to use the known normal modes of a suitably chosen “ basic system.” The given system, whose vibration properties are to be determined, can then be regarded as a “ modified system,” which is derived from the basic system by a variation of mass and elasticity. A similar procedure has been applied to systems with a finite number of degrees of freedom. In the present note the method is applied to simple non-uniform beams, and to beams with added masses and constraints. A concise general solution is obtained, and an iteration process of obtaining a numerical solution is described.

A FRAMEWORK FOR REPRESENTING AND PRODUCING MOVIES ON QUANTUM COMPUTERS

2011 ◽  
Vol 09 (06) ◽  
pp. 1459-1497 ◽  
Author(s):  
ABDULLAH M. ILIYASU ◽  
PHUC Q. LE ◽  
FANGYAN DONG ◽  
KAORU HIROTA
Keyword(s):  
Quantum Circuits ◽  
Quantum Computers ◽  
Transition Rates ◽  
Projective Measurement ◽  
Physical Realization ◽  
Quantum Devices ◽  
Frame Transition ◽  
Key Frames ◽  
Movie Script ◽  
The Physical Realization

Adopting a generalization of the DiVincenzo criteria for the physical realization of quantum devices, a standalone component each, is proposed to prepare, manipulate, and measure the various content required to represent and produce movies on quantum computers. The quantum CD encodes, prepares, and initializes the broad content or key frames conveying the movie script. The quantum player uses the simple motion operations to manipulate the contents of the key frames in order to interpolate the missing viewing frames required to effectively depict the shots and scenes of the movie. The movie reader combines the projective measurement technique and the ancilla-driven quantum computation to retrieve the classical movie sequence comprising of both the key and viewing frames for each shot. At appropriate frame transition rates, this sequence creates the impression of continuity in order to depict the various movements and actions in the movie. Two well-thought-out examples demonstrate the feasibility of the proposed framework. Concatenated, these components together facilitate the proposed framework for quantum movie representation and production, thus, opening the door towards manipulating quantum circuits aimed at applications for information representation and processing.

A Heuristic Application-Specific Path Planner for Robot Motion Planning

1992 ◽  
Author(s):  
David G. Alciatore
Keyword(s):  
Degrees Of Freedom ◽  
Optimal Solution ◽  
Plant Design ◽  
Planning Techniques ◽  
Construction Automation ◽  
Path Planner ◽  
Joint Limits ◽  
The Given ◽  
Application Specific ◽  
Equipment Operator

Abstract This paper presents the development and simulation results of a Heuristic Application-Specific Path Planner (HASPP) that can be used to automatically plan trajectories for a manipulator operating around obstacles. Since the implementation of HASPP is inherently application-specific due to dependence on heuristics, the application of HASPP to an eight degree of freedom Pipe Manipulator is presented as an illustrative example. This development and simulation was implemented on a Silicon Graphics Personal IRIS with the aid of WALKTHRU, a 3-D simulation and animation tool, and software developed in C. HASPP uses extensive knowledge of the manipulator’s workspace and makes certain assumptions about the environment in finding trajectories. The algorithm also makes use of the manipulator’s redundant degrees of freedom to avoid obstacles and joint limits during the trajectory while obtaining a heuristic near-optimal solution. The algorithm is rule-based, governed by heuristics and well-defined geometric tests, providing extremely fast results. It finds “good” trajectories that are optimal within the defined heuristics. When a trajectory is not feasible for the given geometry, the algorithm offers a diagnosis of the limiting constraints. The Pipe Manipulator HASPP implementation has been tested thoroughly with the computer graphics model and it has demonstrated the ability to reliably determine near-optimal collision-free erection trajectories completely automatically. No other planning techniques available in the literature have demonstrated the ability to solve problems as complex as the example presented here. The use of HASPP with simulation offers many application opportunities including plant design constructability studies, assembly and maintenance planning, pre-planning and pre-programming of equipment tasks, and equipment operator assistance. This work was the result of construction automation research sponsored by the National Science Foundation.

scholarly journals Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1026 ◽  
Author(s):  
Martin Gavalec ◽  
Zuzana Němcová
Keyword(s):  
Linear System ◽  
Fuzzy Systems ◽  
Polynomial Algorithm ◽  
Sufficient Conditions ◽  
Recognition Algorithm ◽  
Triangular Norm ◽  
Binary Operations ◽  
Interval Coefficients ◽  
Necessary And Sufficient ◽  
The Given

The max-Łukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Łukasiewicz triangular norm. The behavior of such a system in time depends on the solvability of the corresponding bounded parametric max-linear system. The aim of this study is to describe an algorithm recognizing for which values of the parameter the given bounded parametric max-linear system has a solution—represented by an appropriate state of the fuzzy system in consideration. Necessary and sufficient conditions of the solvability have been found and a polynomial recognition algorithm has been described. The correctness of the algorithm has been verified. The presented polynomial algorithm consists of three parts depending on the entries of the transition matrix and the required state vector. The results are illustrated by numerical examples. The presented results can be also applied in the study of the max-Łukasiewicz systems with interval coefficients. Furthermore, Łukasiewicz arithmetical conjunction can be used in various types of models, for example, in cash-flow system.

Error bounds on multivariate Normal approximations for word count statistics

2002 ◽  
Vol 34 (03) ◽  
pp. 559-586 ◽  
Author(s):  
Haiyan Huang
Keyword(s):  
Covariance Matrix ◽  
Error Bounds ◽  
Multivariate Distribution ◽  
Finite Alphabet ◽  
Multivariate Normal ◽  
Word Count ◽  
First Order ◽  
Normal Approximations ◽  
Necessary And Sufficient ◽  
The Given

Given a sequence S and a collection Ω of d words, it is of interest in many applications to characterize the multivariate distribution of the vector of counts U = (N(S,w 1), …, N(S,w d )), where N(S,w) is the number of times a word w ∈ Ω appears in the sequence S. We obtain an explicit bound on the error made when approximating the multivariate distribution of U by the normal distribution, when the underlying sequence is i.i.d. or first-order stationary Markov over a finite alphabet. When the limiting covariance matrix of U is nonsingular, the error bounds decay at rate O ((log n) / √n) in the i.i.d. case and O ((log n)3 / √n) in the Markov case. In order for U to have a nondegenerate covariance matrix, it is necessary and sufficient that the counted word set Ω is not full, that is, that Ω is not the collection of all possible words of some length k over the given finite alphabet. To supply the bounds on the error, we use a version of Stein's method.

Coordinated Motion Planning of Legged Mobile Manipulator for Tracking the Given End-Effector’s Trajectory

2019 ◽  
Author(s):  
Kondalarao Bhavanibhatla ◽  
Sulthan Suresh-Fazeela ◽  
Dilip Kumar Pratihar
Keyword(s):  
Motion Planning ◽  
Degrees Of Freedom ◽  
Robotic System ◽  
Simulation Software ◽  
Body Motion ◽  
Whole Body ◽  
Mobile Manipulator ◽  
Coordinated Motion ◽  
Multibody Dynamic ◽  
The Given

Abstract In this paper, a novel algorithm is presented to achieve the coordinated motion planning of a Legged Mobile Manipulator (LMM) for tracking the given end-effector’s trajectory. LMM robotic system can be obtained by mounting a manipulator on the top of a multi-legged platform for achieving the capabilities of both manipulation and mobility. To exploit the advantages of these capabilities, the manipulator should be able to accomplish the task, while the hexapod platform moves simultaneously. In the presented approach, the whole-body motion planning is achieved in two steps. In the first step, the robotic system is assumed to be a mobile manipulator, in which the manipulator has two additional translational degrees of freedom at the base. The redundancy of this robotic system is solved by treating it as an optimization problem. Then, in the second step, the omnidirectional motion of the legged platform is achieved with a combination of straight forward and crab motions. The proposed algorithm is tested through a numerical simulation in MATLAB and then, validated on a virtual model of the robot using multibody dynamic simulation software, MSC ADAMS. Multiple trajectories of the end-effector have been tested and the results show that the proposed algorithm accomplishes the given task successfully by providing a singularity-free whole-body motion.

scholarly journals On the integrable deformations of a system related to the motion of two vortices in an ideal incompressible fluid

2019 ◽  
Vol 29 ◽  
pp. 01015 ◽  
Author(s):  
Cristian Lăzureanu ◽  
Ciprian Hedrea ◽  
Camelia Petrişor
Keyword(s):  
Incompressible Fluid ◽  
Mechanical System ◽  
Integrable Systems ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Ideal Incompressible Fluid ◽  
First Integrals ◽  
Integrable Deformation ◽  
Integrable Deformations ◽  
The Given

Altering the first integrals of an integrable system integrable deformations of the given system are obtained. These integrable deformations are also integrable systems, and they generalize the initial system. In this paper we give a method to construct integrable deformations of maximally superintegrable Hamiltonian mechanical systems with two degrees of freedom. An integrable deformation of a maximally superintegrable Hamiltonian mechanical system preserves the number of first integrals, but is not a Hamiltonian mechanical system, generally. We construct integrable deformations of the maximally superintegrable Hamiltonian mechanical system that describes the motion of two vortices in an ideal incompressible fluid, and we show that some of these integrable deformations are Hamiltonian mechanical systems too.

Dynamic system of indices determining technical equipment of railroad infrastructure

2017 ◽  
pp. 354-363
Author(s):  
Alexander Shepel
Keyword(s):  
Dynamic System ◽  
Practical Importance ◽  
Transport Systems ◽  
Technical Equipment ◽  
Railway Stations ◽  
Systems Simulation ◽  
Necessary And Sufficient ◽  
Relationship Of ◽  
The Given ◽  
Optimum Relationship

Objective: To obtain technical equipment of infrastructure and terminal capacity relations in order to determine the necessary gridiron of tracks, as well as to assess efficiency and optimization of existing stations’ functioning. Methods: Based on synthesis and analysis of stations’ operation, as well as transport systems’ simulation modeling theory. Results: Parameters, influencing the present and designed terminal capacity, were identified. Cause-and-effect relations of events, resulting in railway machinery being brought in non-serviceable condition, are established. Dynamic system of indices was suggested, allowing for a more precise solution of the following tasks: to identify the necessary and sufficient gridiron of tracks for passing the specified amount of traffic, to assess the most probable amount of traffic at the station and its loading. Criteria of input and output flows of traffic at the station, as well as lay-over and trains' delays were stated, the former make it possible to analyze the suggested technical equipment and station functioning. Practical importance: On the basis of obtained relations it is possible to specify optimum relationship of trains’ lay-over time at station yards, the reserve of gridiron of tracks’ elements time in use and the number of routes being implemented at the station, as well as the necessary gridiron of tracks within the given аmount of train traffic. The results of the research may be applied in designing new railway stations, as well as optimization of station functioning and reconstruction of the existing stations.

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