Sign-Magnitude Representation: Generally, the numbers consists of a sign and a value (magnitude). Sign is used to indicate whether the number is positive or negative. Positive numbers are represented as unsigned numbers. Negative numbers are represented with a negative sign “-” in front of the numbers. Example: +21, -45, 34. Representing the numbers in this way is known as sign-magnitude. Binary number system uses only two bits “0 and “1”. Binary number system uses Most Significant Bit (MSB) to represent the positive and negative binary numbers. MSB is used to represent the sign and remaining bits are used to represent the magnitude value. If the sign bit is “0” then it indicates that the binary number is positive. If the sign bit is “1” then it indicates that the binary number is negative. Number Line: Number line is a line used to represent the real numbers in a horizontal line. Every point in a horizontal line represents a real number. Positive numbers are represented to the right of zero and negative numbers are represented to the left of zero. Number line is mainly used for the operation of basic addition and subtraction performed on negative numbers.

Question

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…

Answer 1

Question

Chapter 3, Problem 43E

Program Plan Intro

Sign-Magnitude Representation:

Generally, the numbers consists of a sign and a value (magnitude).

Sign is used to indicate whether the number is positive or negative.

Positive numbers are represented as unsigned numbers.

Negative numbers are represented with a negative sign “-” in front of the numbers.

Example: +21, -45, 34.

Representing the numbers in this way is known as sign-magnitude.

Binary number system uses only two bits “0 and “1”.

Binary number system uses Most Significant Bit (MSB) to represent the positive and negative binary numbers.

MSB is used to represent the sign and remaining bits are used to represent the magnitude value.

If the sign bit is “0” then it indicates that the binary number is positive.

If the sign bit is “1” then it indicates that the binary number is negative.

Number Line:

Number line is a line used to represent the real numbers in a horizontal line.

Every point in a horizontal line represents a real number.

Positive numbers are represented to the right of zero and negative numbers are represented to the left of zero.

Number line is mainly used for the operation of basic addition and subtraction performed on negative numbers.

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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…

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