Merge pull request qutip#1688 from AGaliciaMartinez/hadamard_transfor…

…m_efficient Improve Hadamard transform efficiency by up to ~70x.
hodgestar · Feb 4, 2022 · 5642874 · 5642874
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diff --git a/qutip/qip/operations/gates.py b/qutip/qip/operations/gates.py
@@ -924,11 +924,9 @@ def hadamard_transform(N=1):
         Quantum object representation of the N-qubit Hadamard gate.
 
     """
-    data = 2 ** (-N / 2) * np.array([[(-1) ** _hamming_distance(i & j)
-                                      for i in range(2 ** N)]
-                                     for j in range(2 ** N)])
+    H = Qobj([[1, 1], [1, -1]]) / np.sqrt(2)
 
-    return Qobj(data, dims=[[2] * N, [2] * N])
+    return tensor([H] * N)
 
 
 def _flatten(lst):

diff --git a/qutip/tests/test_gates.py b/qutip/tests/test_gates.py
@@ -332,6 +332,20 @@ def test_cnot_explicit(self):
                              [0, 0, 0, 1, 0, 0, 0, 0]])
         np.testing.assert_allclose(test, expected, atol=1e-15)
 
+
+    def test_hadamard_explicit(self):
+        test = gates.hadamard_transform(3).full()
+        expected = np.array([[ 1,  1,  1,  1,  1,  1,  1,  1],
+                            [ 1, -1,  1, -1,  1, -1,  1, -1],
+                            [ 1,  1, -1, -1,  1,  1, -1, -1],
+                            [ 1, -1, -1,  1,  1, -1, -1,  1],
+                            [ 1,  1,  1,  1, -1, -1, -1, -1],
+                            [ 1, -1,  1, -1, -1,  1, -1,  1],
+                            [ 1,  1, -1, -1, -1, -1,  1,  1],
+                            [ 1, -1, -1,  1, -1,  1,  1, -1]])
+        expected = expected/np.sqrt(8)
+        np.testing.assert_allclose(test, expected)
+
     def test_cyclic_permutation(self):
         operators = [qutip.sigmax(), qutip.sigmaz()]
         test = gates.expand_operator(qutip.tensor(*operators), N=3,