feat: extra sudoku with qa

extra-sudoku/pom.xml

@@ -0,0 +1,42 @@
+<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 https://maven.apache.org/xsd/maven-4.0.0.xsd">
+  <modelVersion>4.0.0</modelVersion>
+  <groupId>com.javaqc</groupId>
+  <artifactId>extra-sudoku</artifactId>
+  <version>0.0.1-SNAPSHOT</version>
+
+	  <properties>
+		<project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
+		<project.reporting.outputEncoding>UTF-8</project.reporting.outputEncoding>
+		<java.version>21</java.version>
+	</properties>
+
+	<dependencies>
+
+		 <dependency>
+	      <groupId>org.redfx</groupId>
+	      <artifactId>strangefx</artifactId>
+	      <version>0.1.4</version>
+	    </dependency>
+	    <dependency>
+	      <groupId>org.openjfx</groupId>
+	      <artifactId>javafx-controls</artifactId>
+	      <version>18.0.2</version>
+	    </dependency>
+
+	</dependencies>
+
+	<build>
+		<finalName>quantum-sudoku</finalName>
+		<plugins>
+			<plugin>
+				<groupId>org.apache.maven.plugins</groupId>
+				<artifactId>maven-compiler-plugin</artifactId>
+				<version>3.13.0</version>
+				<configuration>
+				<source>21</source>
+				<target>21</target>
+				</configuration>
+			</plugin>
+		</plugins>
+	</build>
+</project>

extra-sudoku/src/main/java/com/javaqc/sudoku/SudokuTwoByTwo.java

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+package com.javaqc.sudoku;
+
+import org.redfx.strange.Program;
+import org.redfx.strange.Qubit;
+import org.redfx.strange.Result;
+import org.redfx.strange.Step;
+import org.redfx.strange.gate.Cnot;
+import org.redfx.strange.gate.Hadamard;
+import org.redfx.strange.gate.RotationX;
+import org.redfx.strange.gate.RotationZ;
+import org.redfx.strange.gate.X;
+import org.redfx.strange.local.SimpleQuantumExecutionEnvironment;
+
+
+public class SudokuTwoByTwo {
+	// Quantum Annealing
+    public static void main(String[] args) {
+        int nQubits = 4;
+        Program program = new Program(nQubits);
+
+        // Parameter adjustment for better simulator visibility
+        double gamma = 1.2; // Increased to enforce penalty
+        double beta = 0.8;  // Increased to allow more state transitions
+
+        // --- STEP 1: Preparation ---
+        /* Board
+         * Q0,Q1
+         * Q2,Q3
+         * 		bit =	decimal
+         * Where 0 	= 	1
+         * 		 1 	= 	2         
+         * */
+
+        Step prep = new Step();
+        prep.addGate(new X(0)); // Fix Q0 = Value 2; Identity Gate for value 1
+        prep.addGate(new Hadamard(1));
+        prep.addGate(new Hadamard(2));
+        prep.addGate(new Hadamard(3));
+        program.addStep(prep);
+
+        // --- ANNEALING LAYERS ---
+        int layers = 5; // Increasing the number of layers helps with convergence
+
+        for (int p = 0; p < layers; p++) {
+            // 2. COST: Sudoku Constraints
+            // Applying interaction across all constraints
+            int[][] constraints = { { 0, 1 }, { 2, 3 }, { 0, 2 }, { 1, 3 } };
+            for (int[] pair : constraints) {
+                // Ising Interaction: CNOT -> Rz -> CNOT
+                Step s1 = new Step(new Cnot(pair[0], pair[1]));
+                program.addStep(s1);
+
+                Step s2 = new Step(new RotationZ(gamma, pair[1]));
+                program.addStep(s2);
+
+                Step s3 = new Step(new Cnot(pair[0], pair[1]));
+                program.addStep(s3);
+            }
+
+            // 3. MIXING (Mixer Layer)
+            Step mixer = new Step();
+            for (int i = 1; i < nQubits; i++) {
+                mixer.addGate(new RotationX(beta, i));
+            }
+            program.addStep(mixer);
+
+            // Parameter decay (Simulating the "cooling" process)
+            gamma += 0.1;
+            beta *= 0.9;
+        }
+
+        // Execution
+        SimpleQuantumExecutionEnvironment sqee = new SimpleQuantumExecutionEnvironment();
+        Result result = sqee.runProgram(program);
+        Qubit[] qubits = result.getQubits();
+
+        System.out.println("=== Sudoku 2x2: Fixed (0,0)=2 ===");
+        for (int i = 0; i < qubits.length; i++) {
+            double probValue2 = qubits[i].getProbability();
+            // Rounding for easier reading
+            System.out.printf("Cell Q%d: Value 1 (%.1f%%) | Value 2 (%.1f%%)\n", 
+                i, (1.0 - probValue2) * 100, probValue2 * 100);
+        }
+
+        // Execute the program multiple times to see actual solutions collapse
+        System.out.println("\n=== Solution Sampling (10 attempts) ===");
+        for (int shot = 0; shot < 10; shot++) {
+            Result shotResult = sqee.runProgram(program);
+            Qubit[] shotQubits = shotResult.getQubits();
+
+            System.out.print("Attempt " + shot + ": [");
+            for (int i = 0; i < nQubits; i++) {
+                // measure() returns 0 or 1, collapsing the state
+                int value = shotQubits[i].measure() + 1; // +1 to convert 0,1 to 1,2
+                System.out.print(value + (i < nQubits - 1 ? " " : ""));
+            }
+            System.out.println("]");
+        }
+    }
+}