Positive Train Control (PTC): Positive train control (PTC) is a system which is used to prevent the train accidents caused by the human errors, such as train-to-train collisions, derailments caused due to excess speed, and unauthorized incursion into work zones. PTC system provides audible and visual signals to the crew member regarding the slowing and stopping of the train. For this purpose very high frequency wireless communication system is required.

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.NET Interactive Solving Sudoku using Grover's Algorithm We will now solve a simple problem using Grover's algorithm, for which we do not necessarily know the solution beforehand. Our problem is a 2x2 binary sudoku, which in our case has two simple rules: •No column may contain the same value twice •No row may contain the same value twice If we assign each square in our sudoku to a variable like so: 1 V V₁ V3 V2 we want our circuit to output a solution to this sudoku. Note that, while this approach of using Grover's algorithm to solve this problem is not practical (you can probably find the solution in your head!), the purpose of this example is to demonstrate the conversion of classical decision problems into oracles for Grover's algorithm. Turning the Problem into a Circuit We want to create an oracle that will help us solve this problem, and we will start by creating a circuit that identifies a correct solution, we simply need to create a classical function on a quantum circuit that…

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Chapter 2, Problem 1CTQ1

Program Plan Intro

Positive Train Control (PTC):

Positive train control (PTC) is a system which is used to prevent the train accidents caused by the human errors, such as train-to-train collisions, derailments caused due to excess speed, and unauthorized incursion into work zones.

PTC system provides audible and visual signals to the crew member regarding the slowing and stopping of the train.

For this purpose very high frequency wireless communication system is required.

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.NET Interactive Solving Sudoku using Grover's Algorithm We will now solve a simple problem using Grover's algorithm, for which we do not necessarily know the solution beforehand. Our problem is a 2x2 binary sudoku, which in our case has two simple rules: •No column may contain the same value twice •No row may contain the same value twice If we assign each square in our sudoku to a variable like so: 1 V V₁ V3 V2 we want our circuit to output a solution to this sudoku. Note that, while this approach of using Grover's algorithm to solve this problem is not practical (you can probably find the solution in your head!), the purpose of this example is to demonstrate the conversion of classical decision problems into oracles for Grover's algorithm. Turning the Problem into a Circuit We want to create an oracle that will help us solve this problem, and we will start by creating a circuit that identifies a correct solution, we simply need to create a classical function on a quantum circuit that…

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