Add VnEntanglementEntropyMP measurement process (#6270)

**Context:**
With the qinfo deprecations in progress, it makes sense to have users
still be able to easily access the VN entanglement entropy.

**Description of the Change:**
Add a `VnEntanglementEntropyMP` and associated
`qml.vn_entanglement_entropy` function

**Benefits:**

**Possible Drawbacks:**

**Related GitHub Issues:**

---------

Co-authored-by: Isaac De Vlugt <isaacdevlugt@gmail.com>
Co-authored-by: Isaac De Vlugt <34751083+isaacdevlugt@users.noreply.github.com>
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>
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Co-authored-by: Will <wmaxwell90@gmail.com>
Co-authored-by: Josh Izaac <josh146@gmail.com>
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Co-authored-by: Pietropaolo Frisoni <pietropfrisoni@gmail.com>

doc/releases/changelog-dev.md

@@ -3,6 +3,10 @@
 # Release 0.39.0-dev (development release)
 
 <h3>New features since last release</h3>
+
+* A new `qml.vn_entanglement_entropy` measurement process has been added which measures the
+  Von Neumann entanglement entropy of a quantum state.
+  [(#5911)](https://github.com/PennyLaneAI/pennylane/pull/5911)
 
 <h3>Improvements 🛠</h3>
 

pennylane/__init__.py

@@ -67,6 +67,7 @@
     state,
     var,
     vn_entropy,
+    vn_entanglement_entropy,
     purity,
     mutual_info,
     classical_shadow,
@@ -183,23 +184,23 @@ def __getattr__(name):
     if name == "QubitDevice":
         warn(
             "QubitDevice will no longer be accessible top level. Please access "
-            " the class as pennylane.devices.QubitDevice",
+            "the class as pennylane.devices.QubitDevice",
             PennyLaneDeprecationWarning,
         )
         return pennylane.devices._qubit_device.QubitDevice  # pylint:disable=protected-access
 
     if name == "QutritDevice":
         warn(
             "QutritDevice will no longer be accessible top level. Please access "
-            " the class as pennylane.devices.QutritDevice",
+            "the class as pennylane.devices.QutritDevice",
             PennyLaneDeprecationWarning,
         )
         return pennylane.devices._qutrit_device.QutritDevice  # pylint:disable=protected-access
 
     if name == "Device":
         warn(
             "Device will no longer be accessible top level. Please access "
-            " the class as pennylane.devices.LegacyDevice",
+            "the class as pennylane.devices.LegacyDevice",
             PennyLaneDeprecationWarning,
         )
         return pennylane.devices._legacy_device.Device  # pylint:disable=protected-access

pennylane/devices/_qubit_device.py

@@ -50,6 +50,7 @@
     StateMeasurement,
     StateMP,
     VarianceMP,
+    VnEntanglementEntropyMP,
     VnEntropyMP,
 )
 from pennylane.operation import Operation, operation_derivative
@@ -718,6 +719,29 @@ def statistics(
                     )
                 result = self.vn_entropy(wires=obs.wires, log_base=obs.log_base)
 
+            elif isinstance(m, VnEntanglementEntropyMP):
+                if self.wires.labels != tuple(range(self.num_wires)):
+                    raise qml.QuantumFunctionError(
+                        "Returning the Von Neumann entanglement entropy is not supported when using custom wire labels"
+                    )
+
+                if self._shot_vector is not None:
+                    raise NotImplementedError(
+                        "Returning the Von Neumann entanglement entropy is not supported with shot vectors."
+                    )
+
+                if self.shots is not None:
+                    warnings.warn(
+                        "Requested Von Neumann entanglement entropy with finite shots; the returned "
+                        "state information is analytic and is unaffected by sampling. To silence "
+                        "this warning, set shots=None on the device.",
+                        UserWarning,
+                    )
+                wires0, wires1 = obs.raw_wires
+                result = self.vn_entanglement_entropy(
+                    wires0=wires0, wires1=wires1, log_base=obs.log_base
+                )
+
             elif isinstance(m, MutualInfoMP):
                 if self.wires.labels != tuple(range(self.num_wires)):
                     raise qml.QuantumFunctionError(
@@ -777,6 +801,7 @@ def statistics(
                     VarianceMP,
                     ProbabilityMP,
                     VnEntropyMP,
+                    VnEntanglementEntropyMP,
                     MutualInfoMP,
                     ShadowExpvalMP,
                 ),
@@ -1008,14 +1033,44 @@ def vn_entropy(self, wires, log_base):
         """
         try:
             state = self.density_matrix(wires=self.wires)
-        except qml.QuantumFunctionError as e:  # pragma: no cover
+        except (qml.QuantumFunctionError, NotImplementedError) as e:  # pragma: no cover
             raise NotImplementedError(
                 f"Cannot compute the Von Neumman entropy with device {self.name} that is not capable of returning the "
                 f"state. "
             ) from e
         wires = wires.tolist()
         return qml.math.vn_entropy(state, indices=wires, c_dtype=self.C_DTYPE, base=log_base)
 
+    def vn_entanglement_entropy(self, wires0, wires1, log_base):
+        r"""Returns the Von Neumann entanglement entropy prior to measurement.
+
+        .. math::
+
+            S(\rho_A) = -\text{Tr}[\rho_A \log \rho_A] = -\text{Tr}[\rho_B \log \rho_B] = S(\rho_B)
+
+        Args:
+            wires0 (Sequence[int] or int): the wires of the first subsystem
+            wires1 (Sequence[int] or int): the wires of the second subsystem
+            log_base (float): Base for the logarithm.
+
+        Returns:
+            float: returns the Von Neumann entropy
+        """
+        try:
+            state = self.density_matrix(wires=self.wires)
+        except (qml.QuantumFunctionError, NotImplementedError) as e:  # pragma: no cover
+            raise NotImplementedError(
+                f"Cannot compute the Von Neumman entropy with device {self.name} that is not capable of returning the "
+                f"state. "
+            ) from e
+
+        wires0 = wires0.tolist()
+        wires1 = wires1.tolist()
+
+        return qml.math.vn_entanglement_entropy(
+            state, indices0=wires0, indices1=wires1, c_dtype=self.C_DTYPE, base=log_base
+        )
+
     def mutual_info(self, wires0, wires1, log_base):
         r"""Returns the mutual information prior to measurement:
 
@@ -1035,7 +1090,7 @@ def mutual_info(self, wires0, wires1, log_base):
         """
         try:
             state = self.density_matrix(wires=self.wires)
-        except qml.QuantumFunctionError as e:  # pragma: no cover
+        except (qml.QuantumFunctionError, NotImplementedError) as e:  # pragma: no cover
             raise NotImplementedError(
                 f"Cannot compute the mutual information with device {self.name} that is not capable of returning the "
                 f"state. "

pennylane/devices/_qutrit_device.py

@@ -183,6 +183,28 @@ def vn_entropy(self, wires, log_base):
             "Unsupported return type specified for observable Von Neumann entropy"
         )
 
+    def vn_entanglement_entropy(self, wires0, wires1, log_base):
+        r"""Returns the Von Neumann entanglement entropy prior to measurement.
+
+        .. math::
+
+            S(\rho_A) = -\text{Tr}[\rho_A \log \rho_A] = -\text{Tr}[\rho_B \log \rho_B] = S(\rho_B)
+
+        Args:
+            wires0 (Sequence[int] or int): the wires of the first subsystem
+            wires1 (Sequence[int] or int): the wires of the second subsystem
+            log_base (float): Base for the logarithm.
+
+        Returns:
+            float: returns the Von Neumann entropy
+        """
+        # TODO: Add support for VnEntanglementEntropy return type. Currently, qml.math is hard coded to calculate this for qubit
+        # states (see `qml.math.vn_entanglement_entropy()`), so it needs to be updated before VnEntanglementEntropy can be supported for qutrits.
+        # For now, if a user tries to request this return type, an error will be raised.
+        raise qml.QuantumFunctionError(
+            "Unsupported return type specified for observable Von Neumann entanglement entropy"
+        )
+
     def mutual_info(self, wires0, wires1, log_base):
         r"""Returns the mutual information prior to measurement:
 

pennylane/devices/default_mixed.py

@@ -41,6 +41,7 @@
     SampleMP,
     StateMP,
     VarianceMP,
+    VnEntanglementEntropyMP,
     VnEntropyMP,
 )
 from pennylane.operation import Channel
@@ -637,6 +638,9 @@ def _snapshot_measurements(self, density_matrix, measurement):
                 density_matrix, indices=map_wires, c_dtype=self.C_DTYPE, base=base
             )
 
+        elif isinstance(measurement, VnEntanglementEntropyMP):
+            snap_result = measurement.process_density_matrix(density_matrix, wire_order=self.wires)
+
         elif isinstance(measurement, MutualInfoMP):
             base = measurement.log_base
             wires0, wires1 = list(map(self.map_wires, measurement.raw_wires))
@@ -762,9 +766,9 @@ def execute(self, circuit, **kwargs):
                     # not specified or all wires specified.
                     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 to the
+                if isinstance(m, (VnEntropyMP, VnEntanglementEntropyMP, MutualInfoMP)):
+                    # VnEntropy, VnEntanglementEntropyMP, MutualInfo: Computed for the state
+                    # prior to measurement. So, readout error need not be applied on the
                     # corresponding device wires.
                     continue
                 wires_list.append(m.wires)

pennylane/measurements/__init__.py

@@ -288,6 +288,7 @@ def circuit(x):
     StateMeasurement,
     Variance,
     VnEntropy,
+    VnEntanglementEntropy,
 )
 from .mid_measure import MeasurementValue, MidMeasureMP, measure, find_post_processed_mcms
 from .mutual_info import MutualInfoMP, mutual_info
@@ -298,3 +299,4 @@ def circuit(x):
 from .state import DensityMatrixMP, StateMP, density_matrix, state
 from .var import VarianceMP, var
 from .vn_entropy import VnEntropyMP, vn_entropy
+from .vn_entanglement_entropy import VnEntanglementEntropyMP, vn_entanglement_entropy

pennylane/measurements/measurements.py

@@ -46,6 +46,7 @@ class ObservableReturnTypes(Enum):
     State = "state"
     MidMeasure = "measure"
     VnEntropy = "vnentropy"
+    VnEntanglementEntropy = "vnentanglemententropy"
     MutualInfo = "mutualinfo"
     Shadow = "shadow"
     ShadowExpval = "shadowexpval"
@@ -90,6 +91,9 @@ def __repr__(self):
 VnEntropy = ObservableReturnTypes.VnEntropy
 """Enum: An enumeration which represents returning Von Neumann entropy before measurements."""
 
+VnEntanglementEntropy = ObservableReturnTypes.VnEntanglementEntropy
+"""Enum: An enumeration which represents returning Von Neumann entanglement entropy before measurements."""
+
 MutualInfo = ObservableReturnTypes.MutualInfo
 """Enum: An enumeration which represents returning the mutual information before measurements."""