Create ComplexSimulation.qs

ComplexSimulation.qs

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+namespace Quantum.ComplexSimulation {
+    open Microsoft.Quantum.Canon;
+    open Microsoft.Quantum.Intrinsic;
+    open Microsoft.Quantum.Measurement;
+
+    // Quantum Fourier Transform (QFT) - A key part of the algorithm for frequency analysis
+    operation QFT(qubits: Qubit[]) : Unit {
+        let n = Length(qubits);
+
+        for (i in 0..n-1) {
+            // Apply Hadamard gate to each qubit
+            H(qubits[i]);
+
+            for (j in i+1..n-1) {
+                // Apply controlled rotation for each qubit pair
+                let angle = 1.0 / (2.0 ^ (j - i + 1));
+                CR(qubits[j], qubits[i], angle * PI);
+            }
+        }
+
+        // Apply final Hadamard gate
+        ApplyToEach(H, qubits);
+
+        // Reverse the qubit order (to make the result readable)
+        ApplyToEach(X, qubits);
+    }
+
+    // Quantum Simulation of a complex system with differential equations (e.g., Schrödinger equation)
+    operation QuantumDifferentialEquationSolver() : Unit {
+        // Simulating a simple quantum system (Schrödinger equation)
+        mutable qubits = Qubit[5];  // Number of qubits for the system state
+
+        using (qubits) {
+            // Prepare the system in a superposition state
+            ApplyToEach(H, qubits);
+
+            // Simulate a quantum evolution (solving the Schrödinger equation)
+            for (i in 0..4) {
+                // Apply a series of rotations to simulate evolution
+                let angle = 2.0 * PI / (2.0 ^ (i + 1));
+                Rz(angle, qubits[i]);  // Rotation around the Z-axis
+                Ry(angle, qubits[i]);  // Rotation around the Y-axis
+            }
+
+            // Perform a Quantum Fourier Transform to analyze the frequencies of the system
+            QFT(qubits);
+
+            // Measure the qubits to observe the final state
+            let result = M(qubits[0]);
+            if (result == Zero) {
+                Message("The system evolved into state 0.");
+            } else {
+                Message("The system evolved into state 1.");
+            }
+        }
+    }
+
+    // Main function to run the quantum system simulation
+    operation RunComplexQuantumSimulation() : Unit {
+        // Run the quantum differential equation solver simulation
+        QuantumDifferentialEquationSolver();
+    }
+}