| import time
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| import jax
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| import jax.numpy as jnp
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| import numpy as np
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| import pandas as pd
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| import matplotlib.pyplot as plt
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| import dense_evolution as de
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|
|
| jax.config.update("jax_enable_x64", True)
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|
|
| N_Q = 6
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| sim = de.DenseSVSimulator(n_qubits=N_Q, use_gpu=False, use_float32=False)
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| t_hopping = 2.11
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|
|
| def calcola_energia_vqe(theta):
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| ansatz_circuit = []
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| ansatz_circuit.append(['x', 0])
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|
|
| for q in range(N_Q - 1):
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| ansatz_circuit.append(['cx', q + 1, q])
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| ansatz_circuit.append(['ry', q + 1, float(theta)])
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| ansatz_circuit.append(['cx', q, q + 1])
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| ansatz_circuit.append(['ry', q + 1, -float(theta)])
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| ansatz_circuit.append(['cx', q + 1, q])
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|
|
| sim.set_initial_state()
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| sim.run_circuit_jit_beast_mode(ansatz_circuit)
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| statevector = sim.get_statevector()
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|
|
| dim = len(statevector)
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| indices = np.arange(dim)
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| total_kinetic = 0.0
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|
|
| for q in range(N_Q):
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| q_next = (q + 1) % N_Q
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| mask = (1 << q) | (1 << q_next)
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| psi_flipped = statevector[indices ^ mask]
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|
|
| xx_exp = np.real(np.sum(np.conj(statevector) * psi_flipped))
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| bit_i = (indices & (1 << q)) >> q
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| bit_j = (indices & (1 << q_next)) >> q_next
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| phase = np.where(bit_i == bit_j, -1.0, 1.0)
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| yy_exp = np.real(np.sum(np.conj(statevector) * psi_flipped * phase))
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|
|
| total_kinetic += float(xx_exp + yy_exp)
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|
|
| return - (t_hopping / 2.0) * total_kinetic
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|
|
| punti_theta = np.linspace(0.0, 2 * np.pi, 3500)
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| dati_gradiente = []
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| h = 1e-5
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|
|
| print("============================================================")
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| print("🔬 COMPUTING EXACT ANALYTICAL VQE GRADIENT LANDSCAPE (3500 STEPS)")
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| print("============================================================")
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|
|
| t_global_start = time.perf_counter()
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|
|
| for idx, theta in enumerate(punti_theta):
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| E_plus = calcola_energia_vqe(theta + h)
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| E_minus = calcola_energia_vqe(theta - h)
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| gradiente_reale = (E_plus - E_minus) / (2 * h)
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|
|
| E_attuale = calcola_energia_vqe(theta)
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|
|
| if (idx + 1) % 250 == 0 or idx == 0 or idx == len(punti_theta) - 1:
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| print(f"Step {idx+1:04d}/3500 | Theta: {theta:.3f} rad | Energia: {E_attuale:+.4f} eV | Gradiente: {gradiente_reale:+.6f}")
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|
|
| dati_gradiente.append({
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| "Theta": theta,
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| "Energia": E_attuale,
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| "Gradiente": gradiente_reale
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| })
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|
|
| df = pd.DataFrame(dati_gradiente)
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| df.to_csv("vqe_gradient_landscape.csv", index=False)
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|
|
| plt.style.use('dark_background')
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| fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(10, 8), sharex=True)
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|
|
| ax1.plot(df["Theta"], df["Energia"], color='#00FFFF', linewidth=2.5, label='VQE Energy Surface E(θ)')
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| ax1.set_ylabel("Energy (eV)", color='#888888')
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| ax1.grid(True, linestyle='--', alpha=0.2, color='#444444')
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| ax1.legend(loc="upper right")
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| ax1.set_title("VQE Energy Landscape & Exact Numerical Gradients", fontsize=11, fontweight='bold', pad=15)
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|
|
| ax2.plot(df["Theta"], df["Gradiente"], color='#FFFF00', linewidth=2, label='Exact Gradient (dE/dθ)')
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| ax2.axhline(0.0, color='#888888', linestyle=':', alpha=0.5)
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| ax2.set_xlabel("Variational Parameter θ (radians)", color='#888888')
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| ax2.set_ylabel("Gradient Magnitude", color='#888888')
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| ax2.grid(True, linestyle='--', alpha=0.2, color='#444444')
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| ax2.legend(loc="upper right")
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|
|
| plt.tight_layout()
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| plt.savefig("vqe_gradient_landscape.png", dpi=300)
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|
|
| tempo_totale = time.perf_counter() - t_global_start
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| print("============================================================")
|
| print(f"✅ MAPPA DEI GRADIENTI COMPLETATA IN {tempo_totale:.2f} s")
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| print("============================================================")
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|
|
|
|
