Update app.py

app.py

@@ -127,9 +127,7 @@ problem = QuadraticProgram("my_qubo")
 problem.binary_var("x0")
 problem.binary_var("x1")
 
-# Objective: minimize H = x0 + 2*x1 + (1)*x0*x1
-#  - linear coefficients => x0: 1, x1: 2
-#  - quadratic coefficient => (x0, x1): 1
+# Objective: minimize: H = x0 + 2*x1 + x0*x1
 problem.minimize(
     linear={"x0": 1, "x1": 2},
     quadratic={("x0", "x1"): 1}
@@ -139,10 +137,8 @@ problem.minimize(
 print("\n--- Quadratic Program ---")
 print(problem.export_as_lp_string())
 
-# 2) Set up a QAOA solver on the qasm_simulator
+# 2) Set up QAOA solver on the qasm_simulator
 backend = Aer.get_backend('qasm_simulator')
-
-# Configure the quantum instance
 quantum_instance = QuantumInstance(
     backend=backend,
     shots=512,
@@ -150,24 +146,22 @@ quantum_instance = QuantumInstance(
     seed_transpiler=42
 )
 
-# Create a QAOA instance
 qaoa = QAOA(
-    optimizer=SPSA(maxiter=50),  # or COBYLA(), NFT(), etc.
-    reps=2,                      # Number of QAOA layers
+    optimizer=SPSA(maxiter=50),
+    reps=2,  # number of QAOA layers
     quantum_instance=quantum_instance
 )
 
-# Wrap QAOA in a MinimumEigenOptimizer
 solver = MinimumEigenOptimizer(qaoa)
 
 # 3) Solve the QUBO
 result = solver.solve(problem)
 
-# Print results
 print("\n--- QAOA Results ---")
 print("Optimal solution:", result.x)
 print("Objective value:", result.fval)
 
+
     """,
     "9. DNA Sequence Matching with Grover's Algorithm": """
 from qiskit import QuantumCircuit, transpile