Add support for non-hermitian operators in AerPauliExpectation (#7857)

* Added support for non-hermitian operators in AerPauliExpectation

Fixes #415

QEOM creates a dictionary of operators to evaluate on the groundstate.
When using the noisy simulators (qasm_simulator or aer_simulator), one
could either use PauliExpectation (with noise) or AerPauliExpectation
(without noise). PauliExpectation works with non-hermitian operators
but internal methods of AerPauliExpectation raised an Error.
This is a workaround to this limitation.
Note that using include_custom=True on qasm allows the VQE to use a
local AerPauliExpectation without using the "expectation" input.
This does not apply to QEOM and one should explicitly define the
"expectation" input of the VQE for it to apply globally.

* Added support for non-hermitian operators in AerPauliExpectation

Fixes #415

QEOM creates a dictionary of operators to evaluate on the groundstate.
When using the noisy simulators (qasm_simulator or aer_simulator), one
could either use PauliExpectation (with noise) or AerPauliExpectation
(without noise). PauliExpectation works with non-hermitian operators
but internal methods of AerPauliExpectation raised an Error.
This is a workaround to this limitation.
Note that using include_custom=True on qasm allows the VQE to use a
local AerPauliExpectation without using the "expectation" input.
This does not apply to QEOM and one should explicitly define the
"expectation" input of the VQE for it to apply globally.

* Add a test case for non-hermitian operators.

* Add a test case for non-hermitian operators.

* Add a test case for non-hermitian operators.

* Update test/python/opflow/test_aer_pauli_expectation.py

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

* Update aer_pauli_expectation.py

Use a generator instead of list

* Update qiskit/opflow/expectations/aer_pauli_expectation.py

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

* Update releasenotes/notes/add-support-non-hermitian-op-aerpauliexpectation-653d8e16de4eca07.yaml

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

* Add a test case for PauliOp

* Change the test cases from using ~StateFn() to using StateFn(, is_measurement=True)

* Fix the formatting

Co-authored-by: Julien Gacon <gaconju@gmail.com>
Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>

qiskit/opflow/expectations/aer_pauli_expectation.py

@@ -43,13 +43,36 @@ def convert(self, operator: OperatorBase) -> OperatorBase:
         AerSnapshot-based expectation circuits.
 
         Args:
-            operator: The operator to convert.
+            operator: The operator to convert. If it contains non-hermitian terms, the
+                operator is decomposed into hermitian and anti-hermitian parts.
 
         Returns:
             The converted operator.
         """
+
         if isinstance(operator, OperatorStateFn) and operator.is_measurement:
-            return self._replace_pauli_sums(operator.primitive) * operator.coeff
+            if isinstance(operator.primitive, ListOp):
+                is_herm = all((op.is_hermitian() for op in operator.primitive.oplist))
+            else:
+                is_herm = operator.primitive.is_hermitian()
+
+            if not is_herm:
+                pauli_sum_re = (
+                    self._replace_pauli_sums(
+                        1 / 2 * (operator.primitive + operator.primitive.adjoint()).reduce()
+                    )
+                    * operator.coeff
+                )
+                pauli_sum_im = (
+                    self._replace_pauli_sums(
+                        1 / 2j * (operator.primitive - operator.primitive.adjoint()).reduce()
+                    )
+                    * operator.coeff
+                )
+                pauli_sum = (pauli_sum_re + 1j * pauli_sum_im).reduce()
+            else:
+                pauli_sum = self._replace_pauli_sums(operator.primitive) * operator.coeff
+            return pauli_sum
         elif isinstance(operator, ListOp):
             return operator.traverse(self.convert)
         else:

releasenotes/notes/add-support-non-hermitian-op-aerpauliexpectation-653d8e16de4eca07.yaml

@@ -0,0 +1,5 @@
+features:
+  - |
+    Added the support of non-hermitian operators for :class:`~qiskit.opflow.AerPauliExpectation`.
+    This for instance enables using Aer's fast snapshot expectation value in algorithms such as
+    :class:`~qiskit.algorithms.QEOM`.

test/python/opflow/test_aer_pauli_expectation.py

@@ -38,6 +38,7 @@
     Y,
     Z,
     Zero,
+    MatrixOp,
 )
 from qiskit.utils import QuantumInstance
 
@@ -120,6 +121,29 @@ def test_pauli_expect_state_vector(self):
 
         np.testing.assert_array_almost_equal(sampled.eval(), [0, 0, 1, -1], decimal=1)
 
+    def test_pauli_expect_non_hermitian_matrixop(self):
+        """pauli expect state vector with non hermitian operator test"""
+        states_op = ListOp([One, Zero, Plus, Minus])
+
+        op_mat = np.array([[0, 1], [2, 3]])
+        op = MatrixOp(op_mat)
+
+        converted_meas = self.expect.convert(StateFn(op, is_measurement=True) @ states_op)
+        sampled = self.sampler.convert(converted_meas)
+
+        np.testing.assert_array_almost_equal(sampled.eval(), [3, 0, 3, 0], decimal=1)
+
+    def test_pauli_expect_non_hermitian_pauliop(self):
+        """pauli expect state vector with non hermitian operator test"""
+        states_op = ListOp([One, Zero, Plus, Minus])
+
+        op = 1j * X
+
+        converted_meas = self.expect.convert(StateFn(op, is_measurement=True) @ states_op)
+        sampled = self.sampler.convert(converted_meas)
+
+        np.testing.assert_array_almost_equal(sampled.eval(), [0, 0, 1j, -1j], decimal=1)
+
     def test_pauli_expect_op_vector_state_vector(self):
         """pauli expect op vector state vector test"""
         paulis_op = ListOp([X, Y, Z, I])