Decomposition of arbitrary two-qubit unitaries. (#1552)

* Initial commit. * Add scaffolding and helper function. * Temp commit. * Progress!! * Update su2su2 implementation. * Temp commit. * Implementation that essentially works. Need testing. * Remove perms. * Works about half the time. * Tidy a bit. * Small tweaks. * Temporary work. * Working version, minus tests. * Fix compute matrix in tests. Add check for tensor product structure. * Move decomposition tests to decomposition. * Update some tests. Add to docs. * Remove old test file. * Run black. * Apply suggestions from code review Co-authored-by: Josh Izaac <josh146@gmail.com> * Make E matrix numpy constant. * Vectorize permutation matrix construction. * Replace column negation with matrix multiplication. * Fix decomposition to work in all interfaces. Fix tests to match. * qml.math to math * Remove unneeded variables. * Calculate the required number of CNOTs from tr(gammaU). * Split into multiple cases. 0, 2, and 3-CNOT cases are currently functional. * Add broken version. * Update with integration tests. * Improve documentation. * Run black. * Fix matrix ordering. * RUn black. * Apply suggestions from code review Co-authored-by: Josh Izaac <josh146@gmail.com> * Update error message. Change all qml.math to math. * Fix tests. * Change error to warning. * Remove unused warnings. * Run black. * Test CNOT number computation. * Fix bug in zyz decomposition and tidy tests. * Update CHANGELOG. * Tweak comments. * Add single-CNOT case. * Separate out utility functions and clean up file. * Cast to 1j to handle square root of negative values. * Partially working 2-CNOT case. * Revert qnode file. * Fix CHANGELOG. * Fix CHANGELOG. * Revert test files. * Revert test_qnode. * Run black. * Temporary commit. * Working 2-CNOT case! * Run black. * It works! * Fix test. * Documentation and code factor fixes. * Tweak documentation. * Apply suggestions from code review Co-authored-by: Josh Izaac <josh146@gmail.com> * Move functions back from utils to module. * Make ASCII circuits in docstrings pretty. * Make single-qubit constant matrices top-level. * Rearrange CNOT check. Move matrix to top level. * Streamline conversion to SO(4). * Remove LAST_COL_NEG. * Fix conj. * Update docs and add developer notes. * Update CHANGELOG. * Fix CHANGELOG. * Fix docstring. * Fix decomposition so expansion works. * Fix QMC test. * Fix transform so expand works. * Remove unused import. * Add length checks. * Apply suggestions from code review * Update changelog. * Remove parameter shift test case. * Tweak docstring. * Apply suggestions from code review Co-authored-by: Josh Izaac <josh146@gmail.com> * Add SU(4) invalid check. * Add test case for 3-qubit QubitUnitary in unitary_to_rot. * Massive simplification. Co-authored-by: Olivia Di Matteo <dimatteo.olivia@gmail.com> Co-authored-by: Josh Izaac <josh146@gmail.com>
PennyLaneAI · Sep 16, 2021 · 3871332 · 3871332
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diff --git a/doc/_static/two_qubit_decomposition_2_cnots.svg b/doc/_static/two_qubit_decomposition_2_cnots.svg
diff --git a/doc/_static/two_qubit_decomposition_3_cnots.svg b/doc/_static/two_qubit_decomposition_3_cnots.svg
diff --git a/doc/releases/changelog-dev.md b/doc/releases/changelog-dev.md
@@ -4,6 +4,42 @@
 
 <h3>New features since last release</h3>
 
+* Arbitrary two-qubit unitaries can now be decomposed into elementary gates. This
+  functionality has been incorporated into the `qml.transforms.unitary_to_rot` transform, and is
+  available separately as `qml.transforms.two_qubit_decomposition`.
+  [(#1552)](https://github.com/PennyLaneAI/pennylane/pull/1552)
+
+  As an example, consider the following randomly-generated matrix and circuit that uses it:
+
+  ```python
+  U = np.array([
+      [-0.03053706-0.03662692j,  0.01313778+0.38162226j, 0.4101526 -0.81893687j, -0.03864617+0.10743148j],
+      [-0.17171136-0.24851809j,  0.06046239+0.1929145j, -0.04813084-0.01748555j, -0.29544883-0.88202604j],
+      [ 0.39634931-0.78959795j, -0.25521689-0.17045233j, -0.1391033 -0.09670952j, -0.25043606+0.18393466j],
+      [ 0.29599198-0.19573188j,  0.55605806+0.64025769j, 0.06140516+0.35499559j,  0.02674726+0.1563311j ]
+  ])
+
+  dev = qml.device('default.qubit', wires=2)
+
+  @qml.qnode(dev)
+  @qml.transforms.unitary_to_rot
+  def circuit(x, y):
+      qml.RX(x, wires=0)
+      qml.QubitUnitary(U, wires=[0, 1])
+      qml.RY(y, wires=0)
+      return qml.expval(qml.PauliZ(wires=0))
+  ```
+
+  If we run the circuit, we can see the new decomposition:
+
+  ```pycon
+  >>> circuit(0.3, 0.4)
+  tensor(-0.70520073, requires_grad=True)
+  >>> print(qml.draw(circuit)(0.3, 0.4))
+  0: ──RX(0.3)─────────────────Rot(-3.5, 0.242, 0.86)──╭X──RZ(0.176)───╭C─────────────╭X──Rot(5.56, 0.321, -2.09)───RY(0.4)──┤ ⟨Z⟩ 
+  1: ──Rot(-1.64, 2.69, 1.58)──────────────────────────╰C──RY(-0.883)──╰X──RY(-1.47)──╰C──Rot(-1.46, 0.337, 0.587)───────────┤
+  ```
+
 * The transform for the Jacobian of the classical preprocessing within a QNode,
   `qml.transforms.classical_jacobian`, now takes a keyword argument `argnum` to specify
   the QNode argument indices with respect to which the Jacobian is computed.
@@ -107,4 +143,4 @@
 
 This release contains contributions from (in alphabetical order):
 
-Josh Izaac, Christina Lee, David Wierichs.
+Olivia Di Matteo, Josh Izaac, Christina Lee, David Wierichs.
diff --git a/pennylane/ops/qubit/matrix_ops.py b/pennylane/ops/qubit/matrix_ops.py
@@ -86,7 +86,14 @@ def decomposition(U, wires):
             decomp_ops = qml.transforms.decompositions.zyz_decomposition(U, wire)
             return decomp_ops
 
-        raise NotImplementedError("Decompositions only supported for single-qubit unitaries")
+        if qml.math.shape(U) == (4, 4):
+            wires = Wires(wires)
+            decomp_ops = qml.transforms.two_qubit_decomposition(U, wires)
+            return decomp_ops
+
+        raise NotImplementedError(
+            "Decompositions only supported for single- and two-qubit unitaries."
+        )
 
     def adjoint(self):
         return QubitUnitary(qml.math.T(qml.math.conj(self.matrix)), wires=self.wires)

diff --git a/pennylane/transforms/__init__.py b/pennylane/transforms/__init__.py
@@ -71,6 +71,7 @@
     :toctree: api
 
     ~transforms.zyz_decomposition
+    ~transforms.two_qubit_decomposition
 
 Transforms that act on tapes
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -105,7 +106,7 @@
 from .classical_jacobian import classical_jacobian
 from .compile import compile
 from .control import ControlledOperation, ctrl
-from .decompositions import zyz_decomposition
+from .decompositions import zyz_decomposition, two_qubit_decomposition
 from .draw import draw
 from .hamiltonian_expand import hamiltonian_expand
 from .invisible import invisible

diff --git a/pennylane/transforms/decompositions/__init__.py b/pennylane/transforms/decompositions/__init__.py
@@ -16,3 +16,4 @@
 """
 
 from .single_qubit_unitary import zyz_decomposition
+from .two_qubit_unitary import two_qubit_decomposition