Add order parameter to backend.calculate_norm

doc/source/api-reference/qibo.rst

@@ -655,7 +655,7 @@ Parametric ZX interaction (RZX)
     :member-order: bysource
 
 Parametric XX-YY interaction (RXXYY)
-""""""""""""""""""""""""""""""""""
+""""""""""""""""""""""""""""""""""""
 
 .. autoclass:: qibo.gates.RXXYY
     :members:

src/qibo/backends/abstract.py

@@ -326,13 +326,29 @@ def entanglement_entropy(self, rho):  # pragma: no cover
         raise_error(NotImplementedError)
 
     @abc.abstractmethod
-    def calculate_norm(self, state):  # pragma: no cover
-        """Calculate norm of a state vector."""
+    def calculate_norm(self, state, order=2):  # pragma: no cover
+        """Calculate norm of a state vector. Default is :math:`2`-norm.
+
+        For specifications on possible values of the parameter ``order``
+        for the ``tensorflow`` backend, please refer to
+        `tensorflow.norm <https://www.tensorflow.org/api_docs/python/tf/norm>`_.
+        For all other backends, please refer to
+        `numpy.linalg.norm <https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html>`_.
+        """
         raise_error(NotImplementedError)
 
     @abc.abstractmethod
-    def calculate_norm_density_matrix(self, state):  # pragma: no cover
-        """Calculate norm (trace) of a density matrix."""
+    def calculate_norm_density_matrix(self, state, order="nuc"):  # pragma: no cover
+        """Calculate norm of a density matrix. Default is the ``nuclear`` norm.
+
+        If ``order="nuc"``, it returns the nuclear norm of ``state``,
+        assuming ``state`` is Hermitian (also known as trace norm).
+        For specifications on the other  possible values of the
+        parameter ``order`` for the ``tensorflow`` backend, please refer to
+        `tensorflow.norm <https://www.tensorflow.org/api_docs/python/tf/norm>`_.
+        For all other backends, please refer to
+        `numpy.linalg.norm <https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html>`_.
+        """
         raise_error(NotImplementedError)
 
     @abc.abstractmethod

src/qibo/backends/numpy.py

@@ -673,13 +673,13 @@ def entanglement_entropy(self, rho):
         entropy = self.np.sum(masked_eigvals * spectrum) / self.np.log(2.0)
         return entropy, spectrum
 
-    def calculate_norm(self, state):
+    def calculate_norm(self, state, order=2):
         state = self.cast(state)
-        return self.np.sqrt(self.np.sum(self.np.abs(state) ** 2))
+        return self.np.linalg.norm(state, ord=order)
 
-    def calculate_norm_density_matrix(self, state):
+    def calculate_norm_density_matrix(self, state, order="nuc"):
         state = self.cast(state)
-        return self.np.trace(state)
+        return self.np.linalg.norm(state, ord=order)
 
     def calculate_overlap(self, state1, state2):
         state1 = self.cast(state1)

src/qibo/backends/tensorflow.py

@@ -306,6 +306,16 @@ def entanglement_entropy(self, rho):
         entropy = self.np.sum(masked_eigvals * spectrum) / self.np.log(2.0)
         return entropy, spectrum
 
+    def calculate_norm(self, state, order=2):
+        state = self.cast(state)
+        return self.tf.norm(state, ord=order)
+
+    def calculate_norm_density_matrix(self, state, order="nuc"):
+        state = self.cast(state)
+        if order == "nuc":
+            return self.np.trace(state)
+        return self.tf.norm(state, ord=order)
+
     def calculate_eigenvalues(self, matrix, k=6):
         return self.tf.linalg.eigvalsh(matrix)
 

src/qibo/quantum_info/metrics.py

@@ -359,7 +359,11 @@ def trace_distance(state, target, check_hermitian: bool = False, backend=None):
     difference = state - target
     if check_hermitian is True:
         hermitian = bool(
-            backend.calculate_norm(np.transpose(np.conj(difference)) - difference)
+            float(
+                backend.calculate_norm_density_matrix(
+                    np.transpose(np.conj(difference)) - difference, order=2
+                )
+            )
             <= PRECISION_TOL
         )
         if (
@@ -724,14 +728,18 @@ def process_fidelity(channel, target=None, check_unitary: bool = False, backend=
     dim = int(np.sqrt(channel.shape[0]))
 
     if check_unitary is True:
-        norm_channel = backend.calculate_norm(
-            np.dot(np.conj(np.transpose(channel)), channel) - np.eye(dim**2)
+        norm_channel = float(
+            backend.calculate_norm_density_matrix(
+                np.dot(np.conj(np.transpose(channel)), channel) - np.eye(dim**2)
+            )
         )
         if target is None and norm_channel > PRECISION_TOL:
             raise_error(TypeError, "Channel is not unitary and Target is None.")
         if target is not None:
-            norm_target = backend.calculate_norm(
-                np.dot(np.conj(np.transpose(target)), target) - np.eye(dim**2)
+            norm_target = float(
+                backend.calculate_norm(
+                    np.dot(np.conj(np.transpose(target)), target) - np.eye(dim**2)
+                )
             )
             if (norm_channel > PRECISION_TOL) and (norm_target > PRECISION_TOL):
                 raise_error(TypeError, "Neither channel is unitary.")
@@ -1131,10 +1139,12 @@ def _check_hermitian_or_not_gpu(matrix, backend=None):
     if backend is None:  # pragma: no cover
         backend = GlobalBackend()
 
-    hermitian = bool(
-        backend.calculate_norm(np.transpose(np.conj(matrix)) - matrix) < PRECISION_TOL
+    norm = backend.calculate_norm_density_matrix(
+        np.transpose(np.conj(matrix)) - matrix, order=2
     )
 
+    hermitian = bool(float(norm) <= PRECISION_TOL)
+
     if hermitian is False and backend.__class__.__name__ in [
         "CupyBackend",
         "CuQuantumBackend",

src/qibo/quantum_info/superoperator_transformations.py

@@ -453,8 +453,10 @@ def choi_to_kraus(
         backend = GlobalBackend()
 
     if validate_cp:
-        norm = backend.calculate_norm(
-            choi_super_op - np.transpose(np.conj(choi_super_op))
+        norm = float(
+            backend.calculate_norm_density_matrix(
+                choi_super_op - np.transpose(np.conj(choi_super_op)), order=2
+            )
         )
         if norm > PRECISION_TOL:
             non_cp = True
@@ -2065,7 +2067,7 @@ def function(x0, operators):
         for prob, oper in zip(x0, operators):
             operator += prob * oper
 
-        return float(backend.calculate_norm(target - operator))
+        return float(backend.calculate_norm_density_matrix(target - operator, order=2))
 
     # initial parameters as flat distribution
     x0 = [1.0 / (len(kraus_ops) + 1)] * len(kraus_ops)

src/qibo/quantum_info/utils.py

@@ -245,11 +245,9 @@ def hellinger_distance(prob_dist_p, prob_dist_q, validate: bool = False, backend
         if np.abs(np.sum(prob_dist_q) - 1.0) > PRECISION_TOL:
             raise_error(ValueError, "Second probability array must sum to 1.")
 
-    distance = backend.calculate_norm(
-        np.sqrt(prob_dist_p) - np.sqrt(prob_dist_q)
-    ) / np.sqrt(2)
-
-    distance = float(distance)
+    distance = float(
+        backend.calculate_norm(np.sqrt(prob_dist_p) - np.sqrt(prob_dist_q)) / np.sqrt(2)
+    )
 
     return distance
 

tests/test_callbacks.py

@@ -7,6 +7,7 @@
 # Absolute testing tolerance for the cases of zero entanglement entropy
 from qibo.config import PRECISION_TOL
 from qibo.models import AdiabaticEvolution, Circuit
+from qibo.quantum_info.random_ensembles import random_density_matrix, random_statevector
 
 
 def test_abstract_callback_properties():
@@ -324,17 +325,18 @@ def test_state_callback(backend, density_matrix, copy):
     backend.assert_allclose(statec[1], target_state1)
 
 
+@pytest.mark.parametrize("seed", list(range(1, 5 + 1)))
 @pytest.mark.parametrize("density_matrix", [False, True])
-def test_norm(backend, density_matrix):
+def test_norm(backend, density_matrix, seed):
     norm = callbacks.Norm()
     if density_matrix:
         norm.nqubits = 1
-        state = np.random.random((2, 2)) + 1j * np.random.random((2, 2))
+        state = random_density_matrix(2**norm.nqubits, seed=seed, backend=backend)
         target_norm = np.trace(state)
         final_norm = norm.apply_density_matrix(backend, state)
     else:
         norm.nqubits = 2
-        state = np.random.random(4) + 1j * np.random.random(4)
+        state = random_statevector(2**norm.nqubits, seed=seed, backend=backend)
         target_norm = np.sqrt((np.abs(state) ** 2).sum())
         final_norm = norm.apply(backend, state)
 

tests/test_gates_channels.py

@@ -94,19 +94,29 @@ def test_kraus_channel(backend, pauli_order):
     channel = gates.KrausChannel(0, [a_1, a_2])
 
     backend.assert_allclose(
-        backend.calculate_norm(channel.to_liouville(backend=backend) - test_superop)
+        float(
+            backend.calculate_norm_density_matrix(
+                channel.to_liouville(backend=backend) - test_superop, order=2
+            )
+        )
         < PRECISION_TOL,
         True,
     )
     backend.assert_allclose(
-        backend.calculate_norm(channel.to_choi(backend=backend) - test_choi)
+        float(
+            backend.calculate_norm_density_matrix(
+                channel.to_choi(backend=backend) - test_choi, order=2
+            )
+        )
         < PRECISION_TOL,
         True,
     )
     backend.assert_allclose(
-        backend.calculate_norm(
-            channel.to_pauli_liouville(pauli_order=pauli_order, backend=backend)
-            - test_pauli
+        float(
+            backend.calculate_norm(
+                channel.to_pauli_liouville(pauli_order=pauli_order, backend=backend)
+                - test_pauli
+            )
         )
         < PRECISION_TOL,
         True,
@@ -212,7 +222,11 @@ def test_pauli_noise_channel(backend, pauli_order):
     liouville = gates.PauliNoiseChannel(0, list(zip(basis, pnp))).to_pauli_liouville(
         normalize=True, pauli_order=pauli_order, backend=backend
     )
-    norm = backend.calculate_norm(backend.to_numpy(liouville) - test_representation)
+    norm = float(
+        backend.calculate_norm_density_matrix(
+            backend.to_numpy(liouville) - test_representation, order=2
+        )
+    )
 
     assert norm < PRECISION_TOL
 
@@ -341,7 +355,11 @@ def test_thermal_relaxation_channel(backend, t_1, t_2, time, excpop):
     target_state = backend.cast(target_state, dtype=target_state.dtype)
 
     backend.assert_allclose(
-        backend.calculate_norm(final_state - target_state) < PRECISION_TOL, True
+        float(
+            backend.calculate_norm_density_matrix(final_state - target_state, order=2)
+        )
+        < PRECISION_TOL,
+        True,
     )
 
 

tests/test_models_circuit_features.py

@@ -352,7 +352,7 @@ def test_repeated_execute_probs_and_freqs(backend, nqubits):
     test_probabilities = backend.cast(test_probabilities, dtype=float)
     print(result.probabilities())
     backend.assert_allclose(
-        backend.calculate_norm(result.probabilities() - test_probabilities)
+        float(backend.calculate_norm(result.probabilities() - test_probabilities))
         < PRECISION_TOL,
         True,
     )

tests/test_quantum_info_metrics.py

@@ -156,12 +156,7 @@ def test_entropy(backend, base, check_hermitian):
         test = 0.8613531161467861
 
     backend.assert_allclose(
-        backend.calculate_norm(
-            entropy(state, base, check_hermitian=check_hermitian, backend=backend)
-            - test
-        )
-        < PRECISION_TOL,
-        True,
+        entropy(state, base, check_hermitian=check_hermitian, backend=backend), test
     )
 
 
@@ -520,8 +515,8 @@ def test_process_fidelity_and_infidelity(backend):
         channel = backend.cast(channel, dtype=channel.dtype)
         test = process_fidelity(channel, check_unitary=True, backend=backend)
     with pytest.raises(TypeError):
-        channel = np.random.rand(d**2, d**2)
-        target = np.random.rand(d**2, d**2)
+        channel = 10 * np.random.rand(d**2, d**2)
+        target = 10 * np.random.rand(d**2, d**2)
         channel = backend.cast(channel, dtype=channel.dtype)
         target = backend.cast(target, dtype=target.dtype)
         test = process_fidelity(channel, target, check_unitary=True, backend=backend)