Extend CommutativeInverseCancellation to cancel pairs of gates up-t…

…o-phase (#11248)

* pass, tests, reno

* using assertAlmostEqual for checking floating-point calculations

* renaming

* improving description

* simplifying code based on review

* renaming; changing order of arguments; propagating max_qubits to commutativity checker; docs improvements

* doc-string improvements

qiskit/quantum_info/operators/predicates.py

@@ -21,7 +21,7 @@
 RTOL_DEFAULT = 1e-5
 
 
-def matrix_equal(mat1, mat2, ignore_phase=False, rtol=RTOL_DEFAULT, atol=ATOL_DEFAULT):
+def matrix_equal(mat1, mat2, ignore_phase=False, rtol=RTOL_DEFAULT, atol=ATOL_DEFAULT, props=None):
     """Test if two arrays are equal.
 
     The final comparison is implemented using Numpy.allclose. See its
@@ -38,6 +38,9 @@ def matrix_equal(mat1, mat2, ignore_phase=False, rtol=RTOL_DEFAULT, atol=ATOL_DE
             matrices [Default: False]
         rtol (double): the relative tolerance parameter [Default {}].
         atol (double): the absolute tolerance parameter [Default {}].
+        props (dict | None): if not ``None`` and ``ignore_phase`` is ``True``
+            returns the phase difference between the two matrices under
+            ``props['phase_difference']``
 
     Returns:
         bool: True if the matrices are equal or False otherwise.
@@ -59,16 +62,25 @@ def matrix_equal(mat1, mat2, ignore_phase=False, rtol=RTOL_DEFAULT, atol=ATOL_DE
         return False
 
     if ignore_phase:
+        phase_difference = 0
+
         # Get phase of first non-zero entry of mat1 and mat2
         # and multiply all entries by the conjugate
         for elt in mat1.flat:
             if abs(elt) > atol:
-                mat1 = np.exp(-1j * np.angle(elt)) * mat1
+                angle = np.angle(elt)
+                phase_difference -= angle
+                mat1 = np.exp(-1j * angle) * mat1
                 break
         for elt in mat2.flat:
             if abs(elt) > atol:
+                angle = np.angle(elt)
+                phase_difference += angle
                 mat2 = np.exp(-1j * np.angle(elt)) * mat2
                 break
+        if props is not None:
+            props["phase_difference"] = phase_difference
+
     return np.allclose(mat1, mat2, rtol=rtol, atol=atol)
 
 

qiskit/transpiler/passes/optimization/commutative_inverse_cancellation.py

@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2017, 2021.
+# (C) Copyright IBM 2017, 2024.
 #
 # 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
@@ -14,13 +14,30 @@
 
 
 from qiskit.dagcircuit import DAGCircuit, DAGOpNode
+from qiskit.quantum_info import Operator
+from qiskit.quantum_info.operators.predicates import matrix_equal
 from qiskit.transpiler.basepasses import TransformationPass
 from qiskit.circuit.commutation_checker import CommutationChecker
 
 
 class CommutativeInverseCancellation(TransformationPass):
     """Cancel pairs of inverse gates exploiting commutation relations."""
 
+    def __init__(self, matrix_based: bool = False, max_qubits: int = 4):
+        """
+        Args:
+            matrix_based: If ``True``, uses matrix representations to check whether two
+                operations are inverse of each other. This makes the checks more powerful,
+                and, in addition, allows canceling pairs of operations that are inverse up to a
+                phase, while updating the global phase of the circuit accordingly.
+                Generally this leads to more reductions at the expense of increased runtime.
+            max_qubits: Limits the number of qubits in matrix-based commutativity and
+                inverse checks.
+        """
+        self._matrix_based = matrix_based
+        self._max_qubits = max_qubits
+        super().__init__()
+
     def _skip_node(self, node):
         """Returns True if we should skip this node for the analysis."""
         if not isinstance(node, DAGOpNode):
@@ -36,9 +53,31 @@ def _skip_node(self, node):
             return True
         if node.op.is_parameterized():
             return True
-        # ToDo: possibly also skip nodes on too many qubits
         return False
 
+    def _check_inverse(self, node1, node2):
+        """Checks whether op1 and op2 are inverse up to a phase, that is whether
+        ``op2 = e^{i * d} op1^{-1})`` for some phase difference ``d``.
+        If this is the case, we can replace ``op2 * op1`` by `e^{i * d} I``.
+        The input to this function is a pair of DAG nodes.
+        The output is a tuple representing whether the two nodes
+        are inverse up to a phase and that phase difference.
+        """
+        phase_difference = 0
+        if not self._matrix_based:
+            is_inverse = node1.op.inverse() == node2.op
+        elif len(node2.qargs) > self._max_qubits:
+            is_inverse = False
+        else:
+            mat1 = Operator(node1.op.inverse()).data
+            mat2 = Operator(node2.op).data
+            props = {}
+            is_inverse = matrix_equal(mat1, mat2, ignore_phase=True, props=props)
+            if is_inverse:
+                # mat2 = e^{i * phase_difference} mat1
+                phase_difference = props["phase_difference"]
+        return is_inverse, phase_difference
+
     def run(self, dag: DAGCircuit):
         """
         Run the CommutativeInverseCancellation pass on `dag`.
@@ -55,6 +94,7 @@ def run(self, dag: DAGCircuit):
 
         removed = [False for _ in range(circ_size)]
 
+        phase_update = 0
         cc = CommutationChecker()
 
         for idx1 in range(0, circ_size):
@@ -71,10 +111,14 @@ def run(self, dag: DAGCircuit):
                     not self._skip_node(topo_sorted_nodes[idx2])
                     and topo_sorted_nodes[idx2].qargs == topo_sorted_nodes[idx1].qargs
                     and topo_sorted_nodes[idx2].cargs == topo_sorted_nodes[idx1].cargs
-                    and topo_sorted_nodes[idx2].op == topo_sorted_nodes[idx1].op.inverse()
                 ):
-                    matched_idx2 = idx2
-                    break
+                    is_inverse, phase = self._check_inverse(
+                        topo_sorted_nodes[idx1], topo_sorted_nodes[idx2]
+                    )
+                    if is_inverse:
+                        phase_update += phase
+                        matched_idx2 = idx2
+                        break
 
                 if not cc.commute(
                     topo_sorted_nodes[idx1].op,
@@ -83,6 +127,7 @@ def run(self, dag: DAGCircuit):
                     topo_sorted_nodes[idx2].op,
                     topo_sorted_nodes[idx2].qargs,
                     topo_sorted_nodes[idx2].cargs,
+                    max_num_qubits=self._max_qubits,
                 ):
                     break
 
@@ -94,4 +139,7 @@ def run(self, dag: DAGCircuit):
             if removed[idx]:
                 dag.remove_op_node(topo_sorted_nodes[idx])
 
+        if phase_update != 0:
+            dag.global_phase += phase_update
+
         return dag

releasenotes/notes/commutative-inv-cancellation-uptophase-028525d21b199cef.yaml

@@ -0,0 +1,27 @@
+---
+features:
+  - |
+    Added two new arguments ``matrix_based`` and ``max_qubits`` to the
+    constructor of :class:`.CommutativeInverseCancellation` transpiler pass.
+    When ``matrix_based`` is ``True`` the pass uses matrix representations to
+    check whether two operations are inverse of each other. This makes the
+    checks more powerful, and in addition allows canceling pairs of operations
+    that are inverse up to a phase, while updating the global phase of the circuit
+    accordingly. Generally this leads to more reductions at the expense of increased
+    runtime. The argument ``max_qubits`` limits the number of qubits in matrix-based
+    commutativity and inverse checks. For example::
+
+        import numpy as np
+        from qiskit.circuit import QuantumCircuit
+        from qiskit.transpiler import PassManager
+        from qiskit.transpiler.passes import CommutativeInverseCancellation
+
+        circuit = QuantumCircuit(1)
+        circuit.rz(np.pi / 4, 0)
+        circuit.p(-np.pi / 4, 0)
+
+        passmanager = PassManager(CommutativeInverseCancellation(matrix_based=True))
+        new_circuit = passmanager.run(circuit)
+
+    The pass is able to cancel the ``RZ`` and ``P`` gates, while adjusting the circuit's global
+    phase to :math:`\frac{15 \pi}{8}`.