Update coherence.py

quantum/coherence.py

@@ -1 +1,59 @@
-print("Hello World")
+from __future__ import annotations
+from dataclasses import dataclass
+
+@dataclass
+class QubitState:
+    """
+    Represents a single qubit state |psi> = alpha|0> + beta|1>.
+
+    Attributes
+    ----------
+    alpha : complex
+        Amplitude of the |0> basis state.
+    beta : complex
+        Amplitude of the |1> basis state.
+    """
+    alpha: complex
+    beta: complex
+
+    def normalize(self) -> None:
+        """
+        Normalize the qubit so that |alpha|^2 + |beta|^2 = 1.
+
+        Raises
+        ------
+        ValueError
+            If the norm is zero and normalization cannot be performed.
+        """
+        norm = (abs(self.alpha)**2 + abs(self.beta)**2) ** 0.5
+        if norm == 0:
+            raise ValueError("Norm is zero; cannot normalize.")
+        self.alpha /= norm
+        self.beta /= norm
+
+
+def coherence_measure(state: QubitState) -> float:
+    """
+    Compute a simple coherence measure based on the off-diagonal terms of the density matrix.
+
+    For a pure state, the magnitude of alpha*beta† is a proxy for superposition/coherence.
+
+    Parameters
+    ----------
+    state : QubitState
+        The qubit state for which to compute coherence.
+
+    Returns
+    -------
+    float
+        The magnitude of the product of alpha and the complex conjugate of beta.
+    """
+    return abs(state.alpha * state.beta.conjugate())
+
+
+if __name__ == "__main__":
+    # Demonstration of coherence measurement
+    qubit = QubitState(alpha=1+0j, beta=1+0j)
+    qubit.normalize()
+    print("Normalized qubit:", qubit)
+    print("Coherence:", coherence_measure(qubit))