two-qubit decomposition into sqrt(iSWAP) + approximation

qiskit/circuit/library/__init__.py

@@ -110,6 +110,7 @@
    SdgGate
    SwapGate
    iSwapGate
+   SiSwapGate
    SXGate
    SXdgGate
    TGate

qiskit/circuit/library/pauli_evolution.py

@@ -19,7 +19,7 @@
 
 from qiskit.circuit.gate import Gate
 from qiskit.circuit.parameterexpression import ParameterExpression
-from qiskit.synthesis import EvolutionSynthesis, LieTrotter
+from qiskit.synthesis.evolution import EvolutionSynthesis, LieTrotter
 from qiskit.quantum_info import Pauli, SparsePauliOp
 
 

qiskit/circuit/library/standard_gates/__init__.py

@@ -59,6 +59,7 @@
    CSdgGate
    SwapGate
    iSwapGate
+   SiSwapGate
    SXGate
    SXdgGate
    TGate
@@ -90,6 +91,7 @@
 from .s import SGate, SdgGate, CSGate, CSdgGate
 from .swap import SwapGate, CSwapGate
 from .iswap import iSwapGate
+from .siswap import SiSwapGate
 from .sx import SXGate, SXdgGate, CSXGate
 from .dcx import DCXGate
 from .t import TGate, TdgGate
@@ -158,6 +160,7 @@ def get_standard_gate_name_mapping():
         CSdgGate(),
         SwapGate(),
         iSwapGate(),
+        SiSwapGate(),
         SXdgGate(),
         TGate(),
         TdgGate(),

qiskit/circuit/library/standard_gates/equivalence_library.py

@@ -41,6 +41,7 @@
     SwapGate,
     CSwapGate,
     iSwapGate,
+    SiSwapGate,
     SXGate,
     SXdgGate,
     CSXGate,
@@ -762,6 +763,23 @@
     def_iswap.append(inst, qargs, cargs)
 _sel.add_equivalence(iSwapGate(), def_iswap)
 
+# SiSwapGate
+#
+#      ┌──────────┐           ┌────────────┐┌────────────┐
+# q_0: ┤0         ├      q_0: ┤0           ├┤0           ├
+#      │  Siswap  │  ≡        │  Rxx(-π/4) ││  Ryy(-π/4) │
+# q_1: ┤1         ├      q_1: ┤1           ├┤1           ├
+#      └──────────┘           └────────────┘└────────────┘
+
+q = QuantumRegister(2, "q")
+def_siswap = QuantumCircuit(q)
+for inst, qargs, cargs in [
+    (RXXGate(-pi / 4), [q[0], q[1]], []),
+    (RYYGate(-pi / 4), [q[0], q[1]], []),
+]:
+    def_siswap.append(inst, qargs, cargs)
+_sel.add_equivalence(SiSwapGate(), def_siswap)
+
 # SXGate
 #               global phase: π/4
 #    ┌────┐        ┌─────┐┌───┐┌─────┐

qiskit/circuit/library/standard_gates/siswap.py

@@ -0,0 +1,77 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2017, 2023.
+#
+# 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.
+
+"""sqrt(iSWAP) gate."""
+
+import numpy as np
+from qiskit.circuit.gate import Gate
+
+
+class SiSwapGate(Gate):
+    r"""sqrt(iSWAP) gate.
+
+    A 2-qubit symmetric gate from the iSWAP (or XY) family.
+    It has Weyl chamber coordinates (π/8, π/8, 0).
+
+    Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
+    with the :meth:`~qiskit.circuit.QuantumCircuit.SiSwap` method.
+
+    .. parsed-literal::
+
+                 ┌────────────┐┌────────────┐
+            q_0: ┤0           ├┤0           ├
+                 │  Rxx(-π/4) ││  Ryy(-π/4) │
+            q_1: ┤1           ├┤1           ├
+                 └────────────┘└────────────┘
+
+    .. math::
+        B\ q_0, q_1 =
+            \begin{pmatrix}
+                1       & 0                  & 0                     & 0     \\
+                0       & \frac{1}{\sqrt{2}} & \frac{i}{\sqrt{2}}     & 0     \\
+                0       & \frac{i}{\sqrt{2}} & \frac{1}{\sqrt{2}}     & 0     \\
+                0       & 0                  & 0                     & 1
+            \end{pmatrix}
+    """
+
+    def __init__(self):
+        """Create new SiSwap gate."""
+        super().__init__("siswap", 2, [])
+
+    def _define(self):
+        """
+        gate siswap a, b { rxx(-pi/4) a, b; ryy(-pi/4) a, b; }
+        """
+        # pylint: disable=cyclic-import
+        from qiskit.circuit.quantumcircuit import QuantumRegister, QuantumCircuit
+        from .rxx import RXXGate
+        from .ryy import RYYGate
+
+        q = QuantumRegister(2, "q")
+        qc = QuantumCircuit(q, name=self.name)
+        rules = [(RXXGate(-np.pi / 4), [q[0], q[1]], []), (RYYGate(-np.pi / 4), [q[0], q[1]], [])]
+        for instr, qargs, cargs in rules:
+            qc._append(instr, qargs, cargs)
+
+        self.definition = qc
+
+    def __array__(self, dtype=None):
+        """Return a numpy.array for the DCX gate."""
+        return np.array(
+            [
+                [1, 0, 0, 0],
+                [0, 1 / np.sqrt(2), 1j / np.sqrt(2), 0],
+                [0, 1j / np.sqrt(2), 1 / np.sqrt(2), 0],
+                [0, 0, 0, 1],
+            ],
+            dtype=dtype,
+        )

qiskit/quantum_info/synthesis/two_qubit_decompose.py

@@ -1092,17 +1092,17 @@ def __call__(
         basis_fidelity: Optional[float] = None,
         approximate: bool = True,
         *,
-        _num_basis_uses: int = None,
+        _num_basis_uses: Optional[int] = None,
     ) -> QuantumCircuit:
         """Decompose a two-qubit `unitary` over fixed basis + SU(2) using the best approximation given
         that each basis application has a finite `basis_fidelity`.
 
         Args:
-            unitary (Operator or ndarray): 4x4 unitary to synthesize.
-            basis_fidelity (float or None): Fidelity to be assumed for applications of KAK Gate.
+            unitary: 4x4 unitary to synthesize.
+            basis_fidelity: Fidelity to be assumed for applications of KAK Gate.
                 If given, overrides basis_fidelity given at init.
-            approximate (bool): Approximates if basis fidelities are less than 1.0.
-            _num_basis_uses (int): force a particular approximation by passing a number in [0, 3].
+            approximate: Approximates if basis fidelities are less than 1.0.
+            _num_basis_uses: force a particular approximation by passing a number in [0, 3].
         Returns:
             QuantumCircuit: Synthesized circuit.
         Raises:

qiskit/quantum_info/synthesis/xx_decompose/decomposer.py

@@ -15,7 +15,6 @@
 """
 from __future__ import annotations
 import heapq
-import math
 from operator import itemgetter
 from typing import Callable
 
@@ -27,31 +26,13 @@
 from qiskit.quantum_info.operators import Operator
 from qiskit.quantum_info.synthesis.one_qubit_decompose import ONE_QUBIT_EULER_BASIS_GATES
 from qiskit.quantum_info.synthesis.two_qubit_decompose import TwoQubitWeylDecomposition
+from qiskit.synthesis.su4.utils import average_infidelity
 
 from .circuits import apply_reflection, apply_shift, canonical_xx_circuit
 from .utilities import EPSILON
 from .polytopes import XXPolytope
 
 
-def _average_infidelity(p, q):
-    """
-    Computes the infidelity distance between two points p, q expressed in positive canonical
-    coordinates.
-    """
-
-    a0, b0, c0 = p
-    a1, b1, c1 = q
-
-    return 1 - 1 / 20 * (
-        4
-        + 16
-        * (
-            math.cos(a0 - a1) ** 2 * math.cos(b0 - b1) ** 2 * math.cos(c0 - c1) ** 2
-            + math.sin(a0 - a1) ** 2 * math.sin(b0 - b1) ** 2 * math.sin(c0 - c1) ** 2
-        )
-    )
-
-
 class XXDecomposer:
     """
     A class for optimal decomposition of 2-qubit unitaries into 2-qubit basis gates of XX type
@@ -155,7 +136,7 @@ def _best_decomposition(canonical_coordinate, available_strengths):
 
             strength_polytope = XXPolytope.from_strengths(*[x / 2 for x in sequence])
             candidate_point = strength_polytope.nearest(canonical_coordinate)
-            candidate_cost = sequence_cost + _average_infidelity(
+            candidate_cost = sequence_cost + average_infidelity(
                 canonical_coordinate, candidate_point
             )
 

qiskit/synthesis/__init__.py

@@ -79,6 +79,13 @@
    SolovayKitaevDecomposition
    generate_basic_approximations
 
+SU(4) (2-qubit unitary) Synthesis
+===============
+
+.. autosummary::
+   :toctree: ../stubs/
+
+   SiSwapDecomposer
 """
 
 from .evolution import (
@@ -109,3 +116,4 @@
     synth_cnotdihedral_general,
 )
 from .discrete_basis import SolovayKitaevDecomposition, generate_basic_approximations
+from .su4 import SiSwapDecomposer

qiskit/synthesis/su4/__init__.py

@@ -0,0 +1,15 @@
+# This code is part of Qiskit.
+#
+# (C) Copyright IBM 2023.
+#
+# 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.
+
+"""Two-qubit unitary synthesis methods."""
+
+from .siswap_decompose import SiSwapDecomposer