Chapter 4, Problem 49QAP

I need help to solve a simple problem using Grover’s algorithm, where the solution is not necessarily known beforehand. The problem is a 2×2 binary sudoku with two rules: • No column may contain the same value twice. • No row may contain the same value twice.   Each square in the sudoku is assigned to a variable as follows:   We want to design a quantum circuit that outputs a valid solution to this sudoku. While using Grover’s algorithm for this task is not necessarily practical, the goal is to demonstrate how classical decision problems can be converted into oracles for Grover’s algorithm.   Turning the Problem into a Circuit   To solve this, an oracle needs to be created that helps identify valid solutions. The first step is to construct a classical function within a quantum circuit that checks whether a given state satisfies the sudoku rules.   Since we need to check both columns and rows, there are four conditions to verify: v0 ≠ v1   # Check top row   v2 ≠ v3   # Check bottom row…

7.18 Determine the discharge in the pipe and the pressure at point B. Neglect head losses. Assume α = 1.0 at all locations. 1.5 m Water B 3.5 m 40 cm diameter -20 cm diameter nozzle Problem 7.18

A robot gripper is shown on Fig.1a. The block diagram of the control system is shown in Fig.1b. This system is conditionally stable because it is stable only for a range of the gain K. Using the Routh-Hurwitz criterion method to determine the range of gain for which the system is stable. Find the steady-state error due to unit step input. Sketch the root locus of the system and analyze its stability. Find the value of K so that the phase margin is minimum, and record the values of the phase margin, gain margin, Mr, and BW. Then draw the Bode plot of the system and discuss its stability using the Nyquist stability method. What is the value of this maximum overshoot for both large and small values of K due to unit step input? Draw the response of the open-loop and closed-loop of the system according to the unit step system for k=15, 25, 50. Discuss how to improve the system response if needed.