Update code.py

Author: mhjensen

doc/Programs/HHL/code.py

@@ -20,14 +20,15 @@
 
 # --- Compute and display the classical solution ---
 print("Classical solution x (unnormalized):", x_classical)
-We normalize \ket{b} so it becomes a valid quantum state .  In our example A has eigenvalues \lambda_1=0.25,\lambda_2=0.75.  The classical solution is x=A^{-1}b, which we compute and show for reference.
+
 # Solve Ax = b classically for comparison
 x_classical = np.linalg.solve(A, b)
 print("Classical solution (unnormalized):", x_classical)
 
 # Build the initial quantum state |00>_phase ⊗ |b>_main ⊗ |0>_ancilla
-phase0 = np.zeros(4, dtype=complex); phase0[0] = 1.0  # |00> in 2-qubit space (dim=4)
-anc0 = np.array([1.0+0j, 0+0j])  # single-qubit |0>
+phase0 = np.zeros(4, dtype=complex);
+phase0[0] = 1.0  # |00> in 2-qubit space (dim=4)
+anc0 = np.array([1.0+0j, 0+0j]) # single-qubit |0>
 state = np.kron(phase0, np.kron(b, anc0))
 
 # Apply H on both phase qubits: (H⊗H⊗I⊗I) on 4-qubit state
@@ -61,13 +62,13 @@
 # Compute eigenvalues and rotation angles
 eigvals, _ = np.linalg.eigh(A)
 lam1, lam2 = eigvals
-C = lam1  # smallest eigenvalue = 0.25
+C = lam1 # smallest eigenvalue = 0.25
 theta1 = 2*np.arcsin(C/lam1)
 theta2 = 2*np.arcsin(C/lam2)
 
 # Rotation matrices on ancilla
 def R_y(angle):
-    return np.array([[np.cos(angle/2), -np.sin(angle/2)],[np.sin(angle/2),  np.cos(angle/2)]], dtype=complex)
+    return np.array([[np.cos(angle/2), -np.sin(angle/2)],[np.sin(angle/2), np.cos(angle/2)]], dtype=complex)
 R1 = R_y(theta1)
 R2 = R_y(theta2)