Fixing the tools for plotting Pauli vec (Qiskit#10619)

* fixing the plot for pauli_vec to scaled to pm 1

* testing

* linting

* ref figure

* Update docstring to define Paulivector

* add reno

---------

Co-authored-by: Julien Gacon <gaconju@gmail.com>

Author: jaygambetta

qiskit/visualization/state_visualization.py

@@ -627,14 +627,17 @@ def plot_state_city(
 def plot_state_paulivec(
     state, title="", figsize=None, color=None, ax=None, *, rho=None, filename=None
 ):
-    r"""Plot the paulivec representation of a quantum state.
+    r"""Plot the Pauli-vector representation of a quantum state as bar graph.
 
-    Plot a bargraph of the density matrix of a quantum state using as a basis all
-    possible tensor products of Pauli operators and identities, that is,
-    :math:`\{\bigotimes_{i=0}^{N-1}P_i\}_{P_i\in \{I,X,Y,Z\}}`, where
-    :math:`N` is the number of qubits.
+    The Pauli-vector of a density matrix :math:`\rho` is defined by the expectation of each
+    possible tensor product of single-qubit Pauli operators (including the identity), that is
 
+    .. math ::
 
+        \rho = \frac{1}{2^n} \sum_{\sigma \in \{I, X, Y, Z\}^{\otimes n}}
+               \mathrm{Tr}(\sigma \rho) \sigma.
+
+    This function plots the coefficients :math:`\mathrm{Tr}(\sigma\rho)` as bar graph.
 
     Args:
         state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state.
@@ -1574,4 +1577,4 @@ def _paulivec_data(state):
     rho = SparsePauliOp.from_operator(DensityMatrix(state))
     if rho.num_qubits is None:
         raise VisualizationError("Input is not a multi-qubit quantum state.")
-    return rho.paulis.to_labels(), np.real(rho.coeffs)
+    return rho.paulis.to_labels(), np.real(rho.coeffs * 2**rho.num_qubits)

releasenotes/notes/paulivecplot-normalization-5dd3cf3393c75afb.yaml

@@ -0,0 +1,7 @@
+---
+fixes:
+  - |
+    Fixed :func:`plot_state_paulivec`, which previously damped the state coefficients by a factor of
+    :math:`2^n`, where :math:`n` is the number of qubits. Now the bar graph correctly displays
+    the coefficients as :math:`\mathrm{Tr}(\sigma\rho)`, where :math:`\rho` is the state to 
+    be plotted and :math:`\sigma` iterates over all possible tensor products of single-qubit Paulis.

test/python/visualization/test_state_plot_tools.py

@@ -0,0 +1,55 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2022.
+#
+# This code is licensed under the Apache License, Version 2.0. You may
+# obtain a copy of this license in the LICENSE.txt file in the root directory
+# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
+#
+# Any modifications or derivative works of this code must retain this
+# copyright notice, and modified files need to carry a notice indicating
+# that they have been altered from the originals.
+
+"""Tests for functions used in state visualization"""
+
+import unittest
+import numpy as np
+
+from qiskit.quantum_info import Statevector
+from qiskit.visualization.state_visualization import _paulivec_data
+from qiskit.test import QiskitTestCase
+
+
+class TestStatePlotTools(QiskitTestCase):
+    """State Plotting Tools"""
+
+    def test_state_paulivec(self):
+        """Test paulivec."""
+
+        sv = Statevector.from_label("+-rl")
+        output = _paulivec_data(sv)
+        labels = [
+            "IIII",
+            "IIIY",
+            "IIYI",
+            "IIYY",
+            "IXII",
+            "IXIY",
+            "IXYI",
+            "IXYY",
+            "XIII",
+            "XIIY",
+            "XIYI",
+            "XIYY",
+            "XXII",
+            "XXIY",
+            "XXYI",
+            "XXYY",
+        ]
+        values = [1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1]
+        self.assertEqual(output[0], labels)
+        self.assertTrue(np.allclose(output[1], values))
+
+
+if __name__ == "__main__":
+    unittest.main(verbosity=2)