Chapter 7, Problem 18QAP

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…

A 1.8m x 1.8m footing is located at a depth of 1 m below the ground surface in a deep deposit of compacted sand (f'= 33 , f' = 28 , γ = 17.5 kN/m). Calculate the ultimate net bearing capacity considering several factors (e.g., shape, depth, and inclination) when the groundwater table is located (a) at 5 m below the footing base, (b) at the ground surface, (c) at the footing base, and (d) at 1.5 m below the footing base. Also, explain the effects of the groundwater levels in the bearing capacities of the footing with your own words. If the information is not given for the calculation, please assume it reasonably.

1 Vo V₁ V3 V₂ V₂ 2