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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 checks whether the state of our variable bits is a valid solution. Since we need to check down both columns and across both rows, there are 4 conditions we need to check: v0 v1 # check along top row v2 # v3 v0 # v2 v1 # check along bottom row # check down left column v3 # check down right column 1. Create a reversible classical circuit that identifies a correct solution 2. Turn this circuit into an oracle 3. Use Grover's algorithm to solve this oracle

.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 checks whether the state of our variable bits is a valid solution. Since we need to check down both columns and across both rows, there are 4 conditions we need to check: v0 v1 # check along top row v2 # v3 v0 # v2 v1 # check along bottom row # check down left column v3 # check down right column 1. Create a reversible classical circuit that identifies a correct solution 2. Turn this circuit into an oracle 3. Use Grover's algorithm to solve this oracle

C++ for Engineers and Scientists
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter4: Selection Structures
Section: Chapter Questions
Problem 14PP
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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 checks whether the state of our variable bits is a valid solution. Since we need to check down both columns and across both rows, there are 4 conditions we need to check: v0 v1 # check along top row v2 # v3 v0 # v2 v1 # check along bottom row # check down left column v3 # check down right column 1. Create a reversible classical circuit that identifies a correct solution 2. Turn this circuit into an oracle 3. Use Grover's algorithm to solve this oracle
Transcribed Image Text:.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 checks whether the state of our variable bits is a valid solution. Since we need to check down both columns and across both rows, there are 4 conditions we need to check: v0 v1 # check along top row v2 # v3 v0 # v2 v1 # check along bottom row # check down left column v3 # check down right column 1. Create a reversible classical circuit that identifies a correct solution 2. Turn this circuit into an oracle 3. Use Grover's algorithm to solve this oracle
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