A reduced complexity numerical method for optimal gate synthesis

Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate design problem is equivalent to the solution of an associated optimal control problem, the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality free techniques) that determine the optimal control thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, used in previous literature. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on $SU(4)$- a problem that is computationally intractable by grid based approaches.Comment: 8 pages, 4 figure

The Impact of Link Suggestions on User Navigation and User Perception

The study reported in this paper explores the effects of providing web users with link suggestions that are relevant to their tasks. Results indicate that link suggestions were positively received. Furthermore, users perceived sites with link suggestions as more usable and themselves as less disoriented. The average task execution time was significantly lower than in the control condition and users appeared to navigate in a more structured manner. Unexpectedly, men took more advantage from link suggestions than women

Stochastic Game Approach to Air Operations

A Command and Control (C2) problem for Military Air Operations is addressed. Specifically, we consider C2 problems for air vehicles against ground based targets and defensive systems. The problem is viewed as a stochastic game. In this paper, we restrict our attention to the C2 level where the problem may consist of a few UCAVs or aircraft (or possibly teams of vehicles); less than say, a half-dozen enemy SAMs; a few enemy assets (viewed as targets from our standpoint); and some enemy decoys (assumed to mimic SAM radar signatures). At this low level, some targets are mapped out and possible SAM sites that are unavoidably part of the situation are known. One may then employ a discrete stochastic game problem formulation to determine which of these SAMs should optimally be engaged (if any), and by what series of air vehicle operations. Since this is a game model, the optimal opponent strategy is also determined. We provide analysis, numerical implementation, and simulation for full state feedback and measurement feedback control within this C2 context