@@ -10,7 +10,7 @@ by the associated classical bitstring.

 import numpy as np

-__all__ = ["from_classical", "is_normalized", "num_qubits", "zero"]  # type: ignore

+__all__ = ["from_classical", "is_normalized", "is_normalizable", "normalize", "num_qubits", "zero"]  # type: ignore

 def from_classical(bitstring):

@@ -59,7 +59,22 @@ def num_qubits(state):

 def is_normalized(state: np.ndarray) -> bool:

     """Return True if and only if 'state' is normalized."""

-    return np.allclose(np.linalg.norm(state), 1)

+    return np.isclose(np.linalg.norm(state), 1)

+

+

+def is_normalizable(v: np.ndarray) -> bool:

+    """Return True if and only if 'v' is normalizable."""

+    # If the norm is too small then normalizing a vector using

+    # the norm will yield a vector that is not normalized to machine

+    # precision.

+    return bool(np.linalg.norm(v) ** 2 > np.finfo(float).smallest_normal)

+

+

+def normalize(state: np.ndarray) -> np.ndarray:

+    """Return a normalized state, given a potentially un-normalized one."""

+    if not is_normalizable(state):

+        raise ValueError("State is not normalizable")

+    return state / np.linalg.norm(state)

 def _check_valid_state(state):