added and deleted codes

Author: mhjensen

doc/src/week15/figures/pqc.png

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+import pennylane as qml
+from pennylane import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.animation import FuncAnimation
+from collections import Counter
+
+# Config
+num_visible = 2
+num_hidden = 2
+num_qubits = num_visible + num_hidden
+epochs = 50
+shots = 1000
+
+dev = qml.device("default.qubit", wires=num_qubits, shots=shots)
+
+# Target data (biased toward '11' and '00')
+target_bitstrings = ['11', '11', '11', '00', '00', '01']
+target_counts = Counter(target_bitstrings)
+target_probs = {
+    format(i, f'0{num_visible}b'): target_counts.get(format(i, f'0{num_visible}b'), 0) / len(target_bitstrings)
+    for i in range(2**num_visible)
+}
+
+
+# Ansatz
+def vqbm_ansatz(params):
+    for i in range(num_qubits):
+        qml.RY(params[i], wires=i)
+    for i in range(num_qubits - 1):
+        qml.CNOT(wires=[i, i + 1])
+    for i in range(num_qubits):
+        qml.RZ(params[i + num_qubits], wires=i)
+
+# Hamiltonian
+def generate_hamiltonian():
+    coeffs = []
+    observables = []
+    for i in range(num_qubits):
+        coeffs.append(np.random.uniform(-1, 1))
+        observables.append(qml.PauliZ(wires=i))
+    for i in range(num_qubits):
+        for j in range(i + 1, num_qubits):
+            coeffs.append(np.random.uniform(-1, 1))
+            observables.append(qml.PauliZ(wires=i) @ qml.PauliZ(wires=j))
+    return qml.Hamiltonian(coeffs, observables)
+
+H = generate_hamiltonian()
+
+
+@qml.qnode(dev)
+def energy_expectation(params):
+    vqbm_ansatz(params)
+    return qml.expval(H)
+
+@qml.qnode(dev)
+def sample_circuit(params):
+    vqbm_ansatz(params)
+    return qml.sample(wires=range(num_visible))
+
+# Helper: Convert samples to bitstring histogram
+def get_distribution(samples):
+    bitstrings = ["".join(str(bit) for bit in s) for s in samples]
+    counts = Counter(bitstrings)
+    total = sum(counts.values())
+    return {
+        format(i, f'0{num_visible}b'): counts.get(format(i, f'0{num_visible}b'), 0) / total
+        for i in range(2**num_visible)
+    }
+
+# Training and storing distributions
+params = 0.01 * np.random.randn(2 * num_qubits, requires_grad=True)
+opt = qml.AdamOptimizer(stepsize=0.1)
+history = []
+
+for epoch in range(epochs):
+    params = opt.step(energy_expectation, params)
+    learned_dist = get_distribution(sample_circuit(params))
+    history.append(learned_dist)
+    if epoch % 10 == 0:
+        print(f"Epoch {epoch} energy: {energy_expectation(params):.4f}")
+
+# Animation setup
+states = [format(i, f'0{num_visible}b') for i in range(2**num_visible)]
+
+fig, ax = plt.subplots()
+bar1 = ax.bar(states, [0]*len(states), color='skyblue', label="VQBM")
+bar2 = ax.bar(states, [target_probs[s] for s in states], color='orange', alpha=0.6, label="Target")
+ax.set_ylim(0, 1)
+ax.set_ylabel("Probability")
+ax.set_title("VQBM Learning Over Epochs")
+ax.legend()
+
+def update(frame):
+    dist = history[frame]
+    for i, state in enumerate(states):
+        bar1[i].set_height(dist[state])
+    ax.set_title(f"Epoch {frame}")
+
+ani = FuncAnimation(fig, update, frames=len(history), repeat=False)
+plt.show()
+
+
+"""
+Define a target distribution (e.g., classical binary data).
+At each epoch:
+Train the model.
+Sample the VQBM output.
+Compute histogram probabilities.
+
+Store results for animation.
+Use matplotlib.animation to animate VQBM’s learned distribution converging to the target.
+Trains a VQBM using an energy-based loss.
+Samples from the circuit at each epoch.
+Animates how the model’s output distribution converges toward the target.
+"""