EchoRZXWeylDecomposition Transpiler Pass

qiskit/quantum_info/synthesis/two_qubit_decompose.py

@@ -28,16 +28,16 @@
 import io
 import base64
 import warnings
-from typing import ClassVar, Optional
+from typing import ClassVar, Optional, Type
 
 import logging
 
 import numpy as np
 import scipy.linalg as la
 
 from qiskit.circuit.quantumregister import QuantumRegister
-from qiskit.circuit.quantumcircuit import QuantumCircuit
-from qiskit.circuit.library.standard_gates import CXGate, RXGate, RYGate, RZGate
+from qiskit.circuit.quantumcircuit import QuantumCircuit, Gate
+from qiskit.circuit.library.standard_gates import CXGate, RXGate, RYGate, RZGate, RXXGate
 from qiskit.exceptions import QiskitError
 from qiskit.quantum_info.operators import Operator
 from qiskit.quantum_info.synthesis.weyl import weyl_coordinates, transform_to_magic_basis
@@ -556,6 +556,151 @@ def specialize(self):
         self.K2r = np.asarray(RYGate(k2rtheta)) @ np.asarray(RXGate(k2rlambda))
 
 
+class TwoQubitControlledUDecomposer:
+    """Decompose two-qubit unitary in terms of a desired U ~ Ud(α, 0, 0) ~ Ctrl-U gate
+    that is locally equivalent to an RXXGate."""
+
+    def __init__(self, rxx_equivalent_gate: Type[Gate]):
+        """Initialize the KAK decomposition.
+
+        Args:
+            rxx_equivalent_gate: Gate that is locally equivalent to an RXXGate:
+            U ~ Ud(α, 0, 0) ~ Ctrl-U gate.
+        Raises:
+            QiskitError: If the gate is not locally equivalent to an RXXGate.
+        """
+        # Do a few spot checks that the KAK decomposition gives (x, 0, 0)
+        for test_angle in [0.2, 0.3, np.pi / 2]:
+            decomp = TwoQubitWeylDecomposition(Operator(rxx_equivalent_gate(test_angle)).data)
+            if not np.allclose([decomp.b, decomp.c], [0, 0]):
+                raise QiskitError(
+                    f"{rxx_equivalent_gate.__name__} is not equivalent to an RXXGate."
+                )
+
+        self.rxx_equivalent_gate = rxx_equivalent_gate
+
+    def __call__(self, unitary, *, atol=DEFAULT_ATOL) -> QuantumCircuit:
+        """Returns the Weyl decomposition in circuit form.
+
+        Note: atol ist passed to OneQubitEulerDecomposer.
+        """
+
+        # pylint: disable=attribute-defined-outside-init
+        self.decomposer = TwoQubitWeylDecomposition(unitary)
+
+        oneq_decompose = OneQubitEulerDecomposer("ZYZ")
+        c1l, c1r, c2l, c2r = (
+            oneq_decompose(k, atol=atol)
+            for k in (
+                self.decomposer.K1l,
+                self.decomposer.K1r,
+                self.decomposer.K2l,
+                self.decomposer.K2r,
+            )
+        )
+        circ = QuantumCircuit(2, global_phase=self.decomposer.global_phase)
+        circ.compose(c2r, [0], inplace=True)
+        circ.compose(c2l, [1], inplace=True)
+        self._weyl_gate(circ)
+        circ.compose(c1r, [0], inplace=True)
+        circ.compose(c1l, [1], inplace=True)
+        return circ
+
+    def _to_rxx_gate(self, angle: float):
+        """
+        Takes an angle and returns the circuit equivalent to an RXXGate with the
+        RXX equivalent gate as the two-qubit unitary.
+
+        Args:
+            angle: Rotation angle (in this case one of the Weyl parameters a, b, or c)
+
+        Returns:
+            Circuit: Circuit equivalent to an RXXGate.
+
+        Raises:
+            QiskitError: If the circuit is not equivalent to an RXXGate.
+        """
+
+        # The user-provided RXXGate equivalent gate may be locally equivalent to the RXXGate
+        # but with some scaling in the rotation angle. For example, RXXGate(angle) has Weyl
+        # parameters (angle, 0, 0) for angle in [0, pi/2] but the user provided gate, i.e.
+        # :code:`self.rxx_equivalent_gate(angle)` might produce the Weyl parameters
+        # (scale * angle, 0, 0) where scale != 1. This is the case for the CPhaseGate.
+        circ = QuantumCircuit(2)
+        circ.rxx(angle, 0, 1)
+        decomposer_rxx = TwoQubitWeylControlledEquiv(Operator(circ).data)
+
+        circ = QuantumCircuit(2)
+        circ.append(self.rxx_equivalent_gate(angle), qargs=[0, 1])
+        decomposer_equiv = TwoQubitWeylControlledEquiv(Operator(circ).data)
+
+        scale = decomposer_rxx.a / decomposer_equiv.a
+
+        circ = QuantumCircuit(2)
+        circ.append(self.rxx_equivalent_gate(scale * angle), qargs=[0, 1])
+        decomposer_inv = TwoQubitWeylControlledEquiv(Operator(circ).data)
+
+        oneq_decompose = OneQubitEulerDecomposer("ZYZ")
+
+        # Express the RXXGate in terms of the user-provided RXXGate equivalent gate.
+        rxx_circ = QuantumCircuit(2, global_phase=-decomposer_inv.global_phase)
+        rxx_circ.compose(oneq_decompose(decomposer_inv.K2r).inverse(), inplace=True, qubits=[0])
+        rxx_circ.compose(oneq_decompose(decomposer_inv.K2l).inverse(), inplace=True, qubits=[1])
+        rxx_circ.compose(circ, inplace=True)
+        rxx_circ.compose(oneq_decompose(decomposer_inv.K1r).inverse(), inplace=True, qubits=[0])
+        rxx_circ.compose(oneq_decompose(decomposer_inv.K1l).inverse(), inplace=True, qubits=[1])
+
+        # Ensure the circuit is equivalent to an RXXGate.
+        qc_rxx = QuantumCircuit(2)
+        qc_rxx.append(RXXGate(angle), qargs=[0, 1])
+        if not np.allclose(Operator(rxx_circ).data, Operator(qc_rxx).data):
+            raise QiskitError(f"Failed to reproduce RXXGate for angle {angle}.")
+
+        return rxx_circ
+
+    def _weyl_gate(self, circ: QuantumCircuit, atol=1.0e-13):
+        """Appends Ud(a, b, c) to the circuit."""
+
+        circ_rxx = self._to_rxx_gate(-2 * self.decomposer.a)
+        circ.compose(circ_rxx, inplace=True)
+
+        # translate the RYYGate(b) into a circuit based on the desired Ctrl-U gate.
+        if abs(self.decomposer.b) > atol:
+            circ_ryy = QuantumCircuit(2)
+            circ_ryy.sdg(0)
+            circ_ryy.sdg(1)
+            circ_ryy.compose(self._to_rxx_gate(-2 * self.decomposer.b), inplace=True)
+            circ_ryy.s(0)
+            circ_ryy.s(1)
+            circ.compose(circ_ryy, inplace=True)
+
+        # translate the RZZGate(c) into a circuit based on the desired Ctrl-U gate.
+        if abs(self.decomposer.c) > atol:
+            # Since the Weyl chember is here defined as a > b > |c| we may have
+            # negative c. This will cause issues in _to_rxx_gate
+            # as TwoQubitWeylControlledEquiv will map (c, 0, 0) to (|c|, 0, 0).
+            # We therefore produce RZZGate(|c|) and append its inverse to the
+            # circuit if c < 0.
+            gamma, invert = -2 * self.decomposer.c, False
+            if gamma > 0:
+                gamma *= -1
+                invert = True
+
+            circ_rzz = QuantumCircuit(2)
+            circ_rzz.h(0)
+            circ_rzz.h(1)
+            circ_rzz.compose(self._to_rxx_gate(gamma), inplace=True)
+            circ_rzz.h(0)
+            circ_rzz.h(1)
+
+            if invert:
+                circ.compose(circ_rzz.inverse(), inplace=True)
+            else:
+                circ.compose(circ_rzz, inplace=True)
+
+        return circ
+
+
 class TwoQubitWeylMirrorControlledEquiv(TwoQubitWeylDecomposition):
     """U ~ Ud(𝜋/4, 𝜋/4, α) ~ SWAP . Ctrl-U
 

qiskit/transpiler/passes/optimization/echo_rzx_weyl_decomposition.py

@@ -0,0 +1,127 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2017, 2021.
+#
+# 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.
+
+"""Weyl decomposition of two-qubit gates in terms of echoed cross-resonance gates."""
+
+from typing import Tuple
+
+from qiskit import QuantumRegister
+from qiskit.circuit.library.standard_gates import RZXGate, HGate, XGate
+
+from qiskit.transpiler.basepasses import TransformationPass
+from qiskit.transpiler.exceptions import TranspilerError
+from qiskit.transpiler.layout import Layout
+
+from qiskit.dagcircuit import DAGCircuit
+from qiskit.converters import circuit_to_dag
+
+from qiskit.providers import basebackend
+
+import qiskit.quantum_info as qi
+from qiskit.quantum_info.synthesis.two_qubit_decompose import TwoQubitControlledUDecomposer
+
+
+class EchoRZXWeylDecomposition(TransformationPass):
+    """Rewrite two-qubit gates using the Weyl decomposition.
+
+    This transpiler pass rewrites two-qubit gates in terms of echoed cross-resonance gates according
+    to the Weyl decomposition. A two-qubit gate will be replaced with at most six non-echoed RZXGates.
+    Each pair of RZXGates forms an echoed RZXGate.
+    """
+
+    def __init__(self, backend: basebackend):
+        """EchoRZXWeylDecomposition pass."""
+        self._inst_map = backend.defaults().instruction_schedule_map
+        super().__init__()
+
+    def _is_native(self, qubit_pair: Tuple) -> bool:
+        """Return the direction of the qubit pair that is native, i.e. with the shortest schedule."""
+        cx1 = self._inst_map.get("cx", qubit_pair)
+        cx2 = self._inst_map.get("cx", qubit_pair[::-1])
+        return cx1.duration < cx2.duration
+
+    @staticmethod
+    def _echo_rzx_dag(theta):
+        rzx_dag = DAGCircuit()
+        qr = QuantumRegister(2)
+        rzx_dag.add_qreg(qr)
+        rzx_dag.apply_operation_back(RZXGate(theta / 2), [qr[0], qr[1]], [])
+        rzx_dag.apply_operation_back(XGate(), [qr[0]], [])
+        rzx_dag.apply_operation_back(RZXGate(-theta / 2), [qr[0], qr[1]], [])
+        rzx_dag.apply_operation_back(XGate(), [qr[0]], [])
+        return rzx_dag
+
+    @staticmethod
+    def _reverse_echo_rzx_dag(theta):
+        reverse_rzx_dag = DAGCircuit()
+        qr = QuantumRegister(2)
+        reverse_rzx_dag.add_qreg(qr)
+        reverse_rzx_dag.apply_operation_back(HGate(), [qr[0]], [])
+        reverse_rzx_dag.apply_operation_back(HGate(), [qr[1]], [])
+        reverse_rzx_dag.apply_operation_back(RZXGate(theta / 2), [qr[1], qr[0]], [])
+        reverse_rzx_dag.apply_operation_back(XGate(), [qr[1]], [])
+        reverse_rzx_dag.apply_operation_back(RZXGate(-theta / 2), [qr[1], qr[0]], [])
+        reverse_rzx_dag.apply_operation_back(XGate(), [qr[1]], [])
+        reverse_rzx_dag.apply_operation_back(HGate(), [qr[0]], [])
+        reverse_rzx_dag.apply_operation_back(HGate(), [qr[1]], [])
+        return reverse_rzx_dag
+
+    def run(self, dag: DAGCircuit):
+        """Run the EchoRZXWeylDecomposition pass on `dag`.
+
+        Rewrites two-qubit gates in an arbitrary circuit in terms of echoed cross-resonance
+        gates by computing the Weyl decomposition of the corresponding unitary. Modifies the
+        input dag.
+
+        Args:
+            dag (DAGCircuit): DAG to map.
+
+        Returns:
+            DAGCircuit: The rearranged dag.
+
+        Raises:
+            TranspilerError: If the circuit cannot be mapped.
+        """
+
+        if len(dag.qregs) > 1:
+            raise TranspilerError(
+                "EchoRZXWeylDecomposition expects a single qreg input DAG,"
+                f"but input DAG had qregs: {dag.qregs}."
+            )
+
+        trivial_layout = Layout.generate_trivial_layout(*dag.qregs.values())
+
+        decomposer = TwoQubitControlledUDecomposer(RZXGate)
+
+        for node in dag.two_qubit_ops():
+
+            unitary = qi.Operator(node.op).data
+            dag_weyl = circuit_to_dag(decomposer(unitary))
+            dag.substitute_node_with_dag(node, dag_weyl)
+
+        for node in dag.two_qubit_ops():
+            if node.name == "rzx":
+                control = node.qargs[0]
+                target = node.qargs[1]
+
+                physical_q0 = trivial_layout[control]
+                physical_q1 = trivial_layout[target]
+
+                is_native = self._is_native((physical_q0, physical_q1))
+
+                theta = node.op.params[0]
+                if is_native:
+                    dag.substitute_node_with_dag(node, self._echo_rzx_dag(theta))
+                else:
+                    dag.substitute_node_with_dag(node, self._reverse_echo_rzx_dag(theta))
+
+        return dag

releasenotes/notes/echo-rzx-weyl-decomposition-ef72345a58bea9e0.yaml

@@ -0,0 +1,4 @@
+---
+features:
+  - |
+   Added a new transpiler pass :class:`qiskit.transpiler.passes.optimization.EchoRZXWeylDecomposition` that allows users to decompose an arbitrary two-qubit gate in terms of echoed RZX-gates by leveraging Cartan's decomposition. In combination with other transpiler passes this can be used to transpile arbitrary circuits to RZX-gate-based and pulse-efficient circuits that implement the same unitary. 

test/python/quantum_info/test_synthesis.py

@@ -37,7 +37,13 @@
     CXGate,
     CZGate,
     iSwapGate,
+    SwapGate,
     RXXGate,
+    RYYGate,
+    RZZGate,
+    RZXGate,
+    CPhaseGate,
+    CRZGate,
     RXGate,
     RYGate,
     RZGate,
@@ -60,6 +66,7 @@
     TwoQubitWeylGeneral,
     two_qubit_cnot_decompose,
     TwoQubitBasisDecomposer,
+    TwoQubitControlledUDecomposer,
     Ud,
     decompose_two_qubit_product_gate,
 )
@@ -1302,6 +1309,36 @@ def test_approx_supercontrolled_decompose_phase_3_use_random(self, seed, delta=0
         self.check_approx_decomposition(tgt_unitary, decomposer, num_basis_uses=3)
 
 
+@ddt
+class TestTwoQubitControlledUDecompose(CheckDecompositions):
+    """Test TwoQubitControlledUDecomposer() for exact decompositions and raised exceptions"""
+
+    @combine(seed=range(10), name="seed_{seed}")
+    def test_correct_unitary(self, seed):
+        """Verify unitary for different gates in the decomposition"""
+        unitary = random_unitary(4, seed=seed)
+        for gate in [RXXGate, RYYGate, RZZGate, RZXGate, CPhaseGate, CRZGate]:
+            decomposer = TwoQubitControlledUDecomposer(gate)
+            circ = decomposer(unitary)
+            self.assertEqual(Operator(unitary), Operator(circ))
+
+    def test_rxx_not_reproducible(self):
+        """Test that an exception is raised if RXXGate cannot be reproduced"""
+        unitary = random_unitary(4)
+        for gate in [CXGate, CZGate]:
+            decomposer = TwoQubitControlledUDecomposer(gate)
+            with self.assertRaises(QiskitError) as exc:
+                decomposer(unitary)
+            self.assertIn("Failed to reproduce RXXGate for angle", exc.exception.message)
+
+    def test_not_rxx_equivalent(self):
+        """Test that an exception is raised if the gate is not equivalent to an RXXGate"""
+        gate = SwapGate
+        with self.assertRaises(QiskitError) as exc:
+            TwoQubitControlledUDecomposer(gate)
+        self.assertIn("is not equivalent to an RXXGate.", exc.exception.message)
+
+
 class TestDecomposeProductRaises(QiskitTestCase):
     """Check that exceptions are raised when 2q matrix is not a product of 1q unitaries"""