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   v0 ≠ v2   # Check left column   v1 ≠ v3   # Check right column   The process consists of three main steps: 1. Creating a reversible classical circuit that verifies a correct solution. 2. Converting this circuit into an oracle. 3. Using Grover’s algorithm to solve for a valid state.   Refer to the image below for the variable assignments within the sudoku grid. this needs to run in Qiskit 1.0. Please don't use AI, ChatGPT or LLM

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  

v0 ≠ v2   # Check left column  

v1 ≠ v3   # Check right column  

The process consists of three main steps:

1. Creating a reversible classical circuit that verifies a correct solution.

2. Converting this circuit into an oracle.

3. Using Grover’s algorithm to solve for a valid state.

Refer to the image below for the variable assignments within the sudoku grid.

this needs to run in Qiskit 1.0. Please don't use AI, ChatGPT or LLM