diff --git a/presentation/spin_chain/time_evolution.py b/presentation/spin_chain/time_evolution.py
index 712d65f..74db889 100644
--- a/presentation/spin_chain/time_evolution.py
+++ b/presentation/spin_chain/time_evolution.py
@@ -7,14 +7,14 @@ from hamiltonian import H
 
 from scipy.linalg import expm
 
-nqbits = 4
-g = 0.5
-N = 400
+nqbits = 2
+g = 0.20
+N = 50
 t_stop = 9
 delta_t = 0.05
 qbits = list(range(nqbits))
 
-n_sample = 200
+n_sample = 400
 measure = 0b10
 
 
@@ -28,27 +28,32 @@ for t in np.arange(0, t_stop, delta_t):
     for _ in range(N):
         state = T_time_slice(qbits, t, g, N) * state
 
-    result = sample(state, measure, n_sample)
+    #result = sample(state, measure, n_sample)
 
-    results_qc.append(result[0] / n_sample)
+    #results_qc.append(result[0] / n_sample)
+
+    amplitude = np.sqrt(np.sum(np.abs(state._qm_state[[False if (i & measure) else True for i in range(2**nqbits)]])**2))
+    results_qc.append(amplitude)
 
     # Simulation using matrices
     np_zero_state = np.zeros(2**nqbits)
     np_zero_state[0] = 1
 
-    T = expm(-1j * t * H(nqbits, g))
-    #for Tv in T:
-    #    print(np.sum(np.abs(Tv)))
-    #    assert np.isclose(np.sum(np.abs(Tv)), 1)
+    itH = np.matrix(-1j * t * H(nqbits, g))
+    T = expm(itH)
+
     np_state = T.dot(np_zero_state)
-    amplitude = np.sum(np.abs(np_state[[False if (i & measure) else True for i in range(2**nqbits)]]))
+    amplitude = np.sqrt(np.sum(np.abs(np_state[[False if (i & measure) else True for i in range(2**nqbits)]])**2))
     results_np.append(amplitude)
 
     print(f"simulating... {int(t/t_stop*100)} %  ", end="\r")
 print()
 print("done.")
 
-h0, = plt.plot(np.arange(0, t_stop, delta_t), results_qc, label=f"Quantum computing {n_sample} samples")
+errors_trotter = np.arange(0, t_stop, delta_t)**2 / N**2
+
+
+h0 = plt.errorbar(np.arange(0, t_stop, delta_t), results_qc, yerr=errors_trotter, label=f"Quantum computing ({n_sample} samples, {N} trotterization steps)")
 h1, = plt.plot(np.arange(0, t_stop, delta_t), results_np, label="Classical simulation using explicit transfer matrix")
 plt.xlabel("t")
 plt.ylabel(r"$|0\rangle$ probability amplitude for second spin")