qinfo module deprecations and removals (#5911)

**Context:**

As part of our v0.39 deprecation cycle, `qinfo` will be deprecated. All
PRs for deprecating each function can be merged to here,

**Description of the Change:**

Deprecates `qinfo`. Specifically:

- [x] deprecate `qinfo.mutual_info`:
#5917
- [x] deprecate `qinfo.reduced_dm`:
#5915
- [x] deprecate `qinfo.purity`:
#5916
- [x] deprecate `qinfo.vn_entropy`:
#5912
- [x] deprecate `qinfo.vn_entanglement_entropy`
#5914
- [x] deprecate `qinfo.fidelity`:
#5915
- [x] deprecate `qinfo.relative_entropy`:
#5915
- [x] deprecate `qinfo.trace_distance`
- [x] remove `qinfo.classical_fisher`
- [x] remove `qinfo.quantum_fisher`

**Benefits:**

Desired UI and less redundancies.

**Possible Drawbacks:**

None

**Related GitHub Issues:**

[sc-67217] [sc-67216] [sc-66716] [sc-66715] [sc-66714] [sc-66713]
[sc-67664] [sc-67665] [sc-67663] [sc-67446]

---------

Co-authored-by: Mudit Pandey <mudit.pandey@xanadu.ai>
Co-authored-by: Astral Cai <astral.cai@xanadu.ai>
Co-authored-by: Ahmed Darwish <exclass9.24@gmail.com>
Co-authored-by: Cristian Emiliano Godinez Ramirez <57567043+EmilianoG-byte@users.noreply.github.com>
Co-authored-by: Ali Asadi <10773383+maliasadi@users.noreply.github.com>
Co-authored-by: albi3ro <chrissie.c.l@gmail.com>
Co-authored-by: Christina Lee <christina@xanadu.ai>
Co-authored-by: ringo-but-quantum <github-ringo-but-quantum@xanadu.ai>
Co-authored-by: David Wierichs <david.wierichs@xanadu.ai>
Co-authored-by: Thomas R. Bromley <49409390+trbromley@users.noreply.github.com>
Co-authored-by: Korbinian Kottmann <43949391+Qottmann@users.noreply.github.com>
Co-authored-by: Tonmoy Bhattacharya <ultraton_16@yahoo.com>
Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
Co-authored-by: Vincent Michaud-Rioux <vincent.michaud-rioux@xanadu.ai>
Co-authored-by: Matthew Silverman <matthews@xanadu.ai>
Co-authored-by: Guillermo Alonso-Linaje <65235481+KetpuntoG@users.noreply.github.com>
Co-authored-by: Utkarsh <utkarshazad98@gmail.com>
Co-authored-by: soranjh <40344468+soranjh@users.noreply.github.com>
Co-authored-by: Romain Moyard <rmoyard@gmail.com>
Co-authored-by: Diksha Dhawan <40900030+ddhawan11@users.noreply.github.com>
Co-authored-by: soranjh <soran.jahangiri@gmail.com>
Co-authored-by: Jorge J. Martínez de Lejarza <61199780+gmlejarza@users.noreply.github.com>
Co-authored-by: anthayes92 <34694788+anthayes92@users.noreply.github.com>
Co-authored-by: Alex Preciado <alex.preciado@xanadu.ai>
Co-authored-by: Mikhail Andrenkov <mikhail@xanadu.ai>
Co-authored-by: Jack Brown <jack@xanadu.ai>
Co-authored-by: Austin Huang <65315367+austingmhuang@users.noreply.github.com>
Co-authored-by: Pietropaolo Frisoni <pietropaolo.frisoni@xanadu.ai>
Co-authored-by: Justin Pickering <79890410+justinpickering@users.noreply.github.com>
Co-authored-by: lillian542 <38584660+lillian542@users.noreply.github.com>
Co-authored-by: Will <wmaxwell90@gmail.com>
Co-authored-by: Josh Izaac <josh146@gmail.com>
Co-authored-by: Lee James O'Riordan <mlxd@users.noreply.github.com>
Co-authored-by: Pietropaolo Frisoni <pietropfrisoni@gmail.com>

doc/code/qml_qinfo.rst

@@ -4,6 +4,13 @@ qml.qinfo
 Overview
 --------
 
+.. warning::
+
+    The ``qinfo`` module is deprecated and scheduled to be removed in v0.40. Most quantum information transforms
+    are available as measurement processes (see the :mod:`~pennylane.measurements` module for more details).
+    Additionally, the transforms are also available as standalone functions in the :mod:`~pennylane.math` and
+    :mod:`~pennylane.gradients` modules.
+
 This module provides a collection of methods to return quantum information quantities from :class:`~.QNode`
 returning :func:`~pennylane.state`.
 
@@ -15,8 +22,4 @@ Transforms
 .. automodapi:: pennylane.qinfo.transforms
     :no-heading:
     :no-inherited-members:
-    :skip: metric_tensor
-    :skip: adjoint_metric_tensor
     :skip: transform
-    :skip: classical_fisher
-    :skip: quantum_fisher

doc/development/deprecations.rst

@@ -9,12 +9,18 @@ deprecations are listed below.
 Pending deprecations
 --------------------
 
+* The ``qml.qinfo`` module has been deprecated. Please see the respective functions in the ``qml.math`` and ``qml.measurements``
+  modules instead.
+
+  - Deprecated in v0.39
+  - Will be removed in v0.40
+
 * ``Device``, ``QubitDevice``, and ``QutritDevice`` will no longer be imported top level in v0.40.  They instead
   we be available as ``qml.devices.LegacyDevice``, ``qml.devices.QubitDevice``, and ``qml.devices.QutritDevice``
   respectively.
 
   - Deprecated top level access in v0.39
-  - Top level access removed in v0.40
+  - Top level access will be removed in v0.40
 
 * `QNode.gradient_fn` is deprecated. Please use `QNode.diff_method` instead. `QNode.get_gradient_fn` can also be used to
   process the diff method.
@@ -27,12 +33,6 @@ Pending deprecations
   - Deprecated in v0.38
   - Will be removed in v0.39
 
-* The functions ``qml.qinfo.classical_fisher`` and ``qml.qinfo.quantum_fisher`` are deprecated since they are being migrated
-  to the ``qml.gradients`` module. Therefore, ``qml.gradients.classical_fisher`` and ``qml.gradients.quantum_fisher`` should be used instead.
-
-  - Deprecated and Duplicated in v0.38
-  - Will be removed in v0.39
-
 * The ``simplify`` argument in ``qml.Hamiltonian`` and ``qml.ops.LinearCombination`` is deprecated. 
   Instead, ``qml.simplify()`` can be called on the constructed operator.
 
@@ -89,6 +89,12 @@ Other deprecations
 Completed deprecation cycles
 ----------------------------
 
+* The functions ``qml.qinfo.classical_fisher`` and ``qml.qinfo.quantum_fisher`` have been removed and migrated to the ``qml.gradients``
+  module. Therefore, ``qml.gradients.classical_fisher`` and ``qml.gradients.quantum_fisher`` should be used instead.
+
+  - Deprecated in v0.38
+  - Removed in v0.39
+
 * All of the legacy devices (any with the name ``default.qubit.{autograd,torch,tf,jax,legacy}``) are removed. Use ``default.qubit`` instead,
   as it supports backpropagation for the many backends the legacy devices support.
 

doc/releases/changelog-dev.md

@@ -63,6 +63,10 @@
 
 <h3>Breaking changes 💔</h3>
 
+* The functions `qml.qinfo.classical_fisher` and `qml.qinfo.quantum_fisher` have been removed and migrated to the `qml.gradients`
+  module. Therefore, `qml.gradients.classical_fisher` and `qml.gradients.quantum_fisher` should be used instead.
+  [(#5911)](https://github.com/PennyLaneAI/pennylane/pull/5911)
+
 * Remove support for Python 3.9.
   [(#6223)](https://github.com/PennyLaneAI/pennylane/pull/6223)
 
@@ -93,6 +97,10 @@
 
 <h3>Deprecations 👋</h3>
 
+* The `qml.qinfo` module has been deprecated. Please see the respective functions in the `qml.math` and
+  `qml.measurements` modules instead.
+  [(#5911)](https://github.com/PennyLaneAI/pennylane/pull/5911)
+
 * The ``QubitStateVector`` template is deprecated.
    Instead, use ``StatePrep``.
    [(#6172)](https://github.com/PennyLaneAI/pennylane/pull/6172)
@@ -140,10 +148,12 @@ This release contains contributions from (in alphabetical order):
 Guillermo Alonso,
 Utkarsh Azad,
 Astral Cai,
+Isaac De Vlugt,
 Lillian M. A. Frederiksen,
 Pietropaolo Frisoni,
 Emiliano Godinez,
 Christina Lee,
 William Maxwell,
 Lee J. O'Riordan,
+Mudit Pandey,
 David Wierichs,

pennylane/devices/default_mixed.py

@@ -763,8 +763,9 @@ def execute(self, circuit, **kwargs):
                     self.measured_wires = self.wires
                     return super().execute(circuit, **kwargs)
                 if isinstance(m, (VnEntropyMP, MutualInfoMP)):
-                    # VnEntropy, MutualInfo: Computed for the state prior to measurement. So, readout
-                    # error need not be applied on the corresponding device wires.
+                    # VnEntropy, MutualInfo: Computed for the state
+                    # prior to measurement. So, readout error need not be applied to the
+                    # corresponding device wires.
                     continue
                 wires_list.append(m.wires)
             self.measured_wires = qml.wires.Wires.all_wires(wires_list)

pennylane/measurements/mutual_info.py

@@ -74,7 +74,7 @@ def circuit_mutual(x):
         using the classical backpropagation differentiation method (``diff_method="backprop"``)
         with a compatible device and finite differences (``diff_method="finite-diff"``).
 
-    .. seealso:: :func:`~.vn_entropy`, :func:`pennylane.qinfo.transforms.mutual_info` and :func:`pennylane.math.mutual_info`
+    .. seealso:: :func:`~pennylane.vn_entropy`, :func:`pennylane.math.mutual_info`
     """
     wires0 = qml.wires.Wires(wires0)
     wires1 = qml.wires.Wires(wires1)

pennylane/measurements/purity.py

@@ -57,7 +57,7 @@ def circuit_purity(p):
     >>> circuit_purity(0.1)
     array(0.7048)
 
-    .. seealso:: :func:`pennylane.qinfo.transforms.purity` and :func:`pennylane.math.purity`
+    .. seealso:: :func:`pennylane.math.purity`
     """
     wires = Wires(wires)
     return PurityMP(wires=wires)

pennylane/measurements/vn_entropy.py

@@ -61,11 +61,11 @@ def circuit_entropy(x):
 
     .. note::
 
-        Calculating the derivative of :func:`~.vn_entropy` is currently supported when
+        Calculating the derivative of :func:`~pennylane.vn_entropy` is currently supported when
         using the classical backpropagation differentiation method (``diff_method="backprop"``)
         with a compatible device and finite differences (``diff_method="finite-diff"``).
 
-    .. seealso:: :func:`pennylane.qinfo.transforms.vn_entropy` and :func:`pennylane.math.vn_entropy`
+    .. seealso:: :func:`pennylane.math.vn_entropy`
     """
     wires = Wires(wires)
     return VnEntropyMP(wires=wires, log_base=log_base)
@@ -74,7 +74,7 @@ def circuit_entropy(x):
 class VnEntropyMP(StateMeasurement):
     """Measurement process that computes the Von Neumann entropy of the system prior to measurement.
 
-    Please refer to :func:`vn_entropy` for detailed documentation.
+    Please refer to :func:`~pennylane.vn_entropy` for detailed documentation.
 
     Args:
         wires (.Wires): The wires the measurement process applies to.

pennylane/qinfo/__init__.py

@@ -18,8 +18,6 @@
     vn_entropy,
     purity,
     mutual_info,
-    classical_fisher,
-    quantum_fisher,
     fidelity,
     relative_entropy,
     trace_distance,