feat(circle): add probability to arrow

src/grovers_visualizer/main.py

@@ -66,7 +66,7 @@ def main() -> None:
         plot_amplitudes_live(ax_bar, bars, sv, basis_states, step_label, iteration, target_state, optimal_iterations)
         draw_grover_circle(ax_circle, iteration, optimal_iterations, theta, state_angle)
 
-        plt.pause(1)
+        plt.pause(0.5)
 
     # Start with Hadamard
     qc = QuantumCircuit(n_qubits)

src/grovers_visualizer/plot.py

@@ -8,7 +8,7 @@ from matplotlib.patches import Circle
 from qiskit.quantum_info import Statevector
 
 from .state import QubitState
-from .utils import get_bar_color, is_optimal_iteration
+from .utils import get_bar_color, is_optimal_iteration, sign
 
 
 def plot_amplitudes_live(
@@ -34,6 +34,8 @@ def plot_amplitudes_live(
     for l in ax.lines:  # Remove previous mean line(s)
         l.remove()
 
+    # Draw axes and mean
+    ax.axhline(0, color="black", linewidth=0.5)
     ax.axhline(float(mean), color="red", linestyle="--", label="Mean")
 
     if not ax.get_legend():
@@ -71,7 +73,7 @@ def draw_grover_circle(
 
     angle = state_angle + iteration * theta
     x, y = cos(angle), sin(angle)
-    is_optimal = optimal_iterations and is_optimal_iteration(iteration, optimal_iterations)
+    is_optimal = is_optimal_iteration(iteration, optimal_iterations)
 
     # Arrow color: green at optimal, blue otherwise
     color = "green" if is_optimal else "blue"
@@ -79,6 +81,20 @@ def draw_grover_circle(
 
     # Probability of target state is y^2
     prob = y**2
-    ax.set_title(
+
-        f"Grover State Vector Rotation\nIteration {iteration} | Probability of target: {prob:.2f}{' (optimal)' if is_optimal else ''}"
+    # Draw the value at the tip of the arrow
+    ax.text(
+        x,
+        y,
+        f"{prob * sign(y):.2f}",
+        color=color,
+        fontsize=10,
+        ha="left" if x >= 0 else "right",
+        va="bottom" if y >= 0 else "top",
+        fontweight="bold",
+        bbox={"facecolor": "white", "edgecolor": "none", "alpha": 0.7, "boxstyle": "round,pad=0.2"},
+    )
+
+    ax.set_title(
+        f"Grover State Vector Rotation\nIteration {iteration} | Probability of target: {prob}{' (optimal)' if is_optimal else ''}"
     )

src/grovers_visualizer/utils.py

@@ -1,6 +1,6 @@
 from collections.abc import Iterator
 from itertools import product
-from math import floor, pi, sqrt
+from math import copysign, floor, pi, sqrt
 
 from .state import QubitState
 
@@ -17,7 +17,7 @@ def optimal_grover_iterations(n_qubits: int) -> int:
 
 
 def is_optimal_iteration(iteration: int, optimal_iteration: int) -> bool:
-    return iteration % optimal_iteration == 0 and iteration != 0
+    return iteration == optimal_iteration
 
 
 def get_bar_color(state: str, target_state: QubitState | None, iteration: int, optimal_iteration: int | None) -> str:
@@ -27,3 +27,7 @@ def get_bar_color(state: str, target_state: QubitState | None, iteration: int, o
     if optimal_iteration and is_optimal_iteration(iteration, optimal_iteration):
         return "green"
     return "orange"
+
+
+def sign(x: float) -> int:
+    return int(copysign(1, x))