Update decoherence.py

quantum/decoherence.py

@@ -1 +1,64 @@
-print("Hello World")
+from __future__ import annotations
+from dataclasses import dataclass
+from typing import List
+
+@dataclass
+class QuantumState:
+    """
+    Represents a single-qubit state with amplitudes for the |0> and |1> basis states.
+    """
+    alpha: complex
+    beta: complex
+
+    def apply_decoherence(self, rate: float) -> "QuantumState":
+        """
+        Apply a simple exponential decoherence to the amplitudes.
+
+        Parameters
+        ----------
+        rate : float
+            A value between 0 and 1 controlling how quickly coherence decays.
+
+        Returns
+        -------
+        QuantumState
+            A new state with scaled amplitudes.
+        """
+        # Ensure rate is within [0, 1]
+        rate = max(0.0, min(1.0, rate))
+        factor = (1.0 - rate) ** 0.5
+        return QuantumState(alpha=self.alpha * factor, beta=self.beta * factor)
+
+
+def simulate_decoherence(state: QuantumState, rate: float, steps: int) -> List[QuantumState]:
+    """
+    Simulate decoherence by repeatedly applying a decoherence model to a state.
+
+    Parameters
+    ----------
+    state : QuantumState
+        Initial qubit state.
+    rate : float
+        Decoherence rate between 0 and 1.
+    steps : int
+        Number of iterations to simulate.
+
+    Returns
+    -------
+    List[QuantumState]
+        Sequence of states after each step.
+    """
+    results: List[QuantumState] = []
+    current = state
+    for _ in range(steps):
+        current = current.apply_decoherence(rate)
+        results.append(current)
+    return results
+
+
+if __name__ == "__main__":
+    # Demonstration: start in an equal superposition and simulate decoherence
+    initial = QuantumState(alpha=1+0j, beta=1+0j)
+    trajectory = simulate_decoherence(initial, rate=0.2, steps=5)
+    for idx, st in enumerate(trajectory, 1):
+        print(f"Step {idx}: {st}")