Adds Single Excitation operations

.github/CHANGELOG.md

@@ -2,6 +2,27 @@
 
 <h3>New features since last release</h3>
 
+* Added the `SingleExcitation` two-qubit operation, which is useful for quantum 
+  chemistry applications. [(#1121)](https://github.com/PennyLaneAI/pennylane/pull/1121)
+
+  It can be used to perform an SO(2) rotation in the subspace 
+  spanned by the states :math:`|01\rangle` and :math:`|10\rangle`. 
+  For example, the following circuit performs the transformation
+  :math:`|10\rangle \rightarrow \cos(\phi/2)|10\rangle - \sin(\phi/2)|01\rangle`:    
+
+  ```python
+  dev = qml.device('default.qubit', wires=2)
+
+  @qml.qnode(dev)
+  def circuit(phi):
+      qml.PauliX(wires=0)
+      qml.SingleExcitation(phi, wires=[0, 1])
+  ```
+
+  The `SingleExcitation` operation supports analytical gradients on hardware
+  using only four expectation value calculations, following results from
+  [Kottmann et al.](https://arxiv.org/abs/2011.05938)
+
 * Added the function ``finite_diff()`` to compute finite-difference
   approximations to the gradient and the second-order derivatives of
   arbitrary callable functions.
@@ -371,8 +392,8 @@
 
 This release contains contributions from (in alphabetical order):
 
-Thomas Bromley, Olivia Di Matteo, Kyle Godbey, Diego Guala, Josh Izaac, Daniel Polatajko, Chase Roberts,
-Sankalp Sanand, Pritish Sehzpaul, Maria Schuld, Antal Száva.
+Juan Miguel Arrazola, Thomas Bromley, Olivia Di Matteo, Kyle Godbey, Diego Guala, Josh Izaac,
+Daniel Polatajko, Chase Roberts, Sankalp Sanand, Pritish Sehzpaul, Maria Schuld, Antal Száva.
 
 # Release 0.14.1 (current release)
 

doc/conf.py

@@ -46,7 +46,7 @@
     "sphinx.ext.intersphinx",
     "sphinx_automodapi.automodapi",
     'sphinx_copybutton',
-    "m2r"
+    # "m2r"
 ]
 
 source_suffix = ['.rst', '.md']

doc/introduction/operations.rst

@@ -85,6 +85,9 @@ Qubit gates
     ~pennylane.MultiControlledX
     ~pennylane.DiagonalQubitUnitary
     ~pennylane.QFT
+    ~pennylane.SingleExcitation
+    ~pennylane.SingleExcitationPlus
+    ~pennylane.SingleExcitationMinus
 
 :html:`</div>`
 

pennylane/devices/autograd_ops.py

@@ -180,3 +180,47 @@ def MultiRZ(theta, n):
         array[complex]: diagonal part of the multi-qubit rotation matrix
     """
     return np.exp(-1j * theta / 2 * pauli_eigs(n))
+
+
+def SingleExcitation(phi):
+    r"""Single excitation rotation.
+
+    Args:
+        phi (float): rotation angle
+
+    Returns:
+        array[float]: Single excitation rotation matrix
+    """
+    c = np.cos(phi / 2)
+    s = np.sin(phi / 2)
+    return np.array([[1, 0, 0, 0], [0, c, -s, 0], [0, s, c, 0], [0, 0, 0, 1]])
+
+
+def SingleExcitationPlus(phi):
+    r"""Single excitation rotation with positive phase-shift outside the rotation subspace.
+
+    Args:
+        phi (float): rotation angle
+
+    Returns:
+        array[complex]: Single excitation rotation matrix with positive phase-shift
+    """
+    c = np.cos(phi / 2)
+    s = np.sin(phi / 2)
+    e = np.exp(1j * phi / 2)
+    return np.array([[e, 0, 0, 0], [0, c, -s, 0], [0, s, c, 0], [0, 0, 0, e]])
+
+
+def SingleExcitationMinus(phi):
+    r"""Single excitation rotation with negative phase-shift outside the rotation subspace.
+
+    Args:
+        phi (float): rotation angle
+
+    Returns:
+       array[complex]: Single excitation rotation matrix with negative phase-shift
+    """
+    c = np.cos(phi / 2)
+    s = np.sin(phi / 2)
+    e = np.exp(-1j * phi / 2)
+    return np.array([[e, 0, 0, 0], [0, c, -s, 0], [0, s, c, 0], [0, 0, 0, e]])

pennylane/devices/default_mixed.py

@@ -96,6 +96,9 @@ class DefaultMixed(QubitDevice):
         "PhaseFlip",
         "QubitChannel",
         "QFT",
+        "SingleExcitation",
+        "SingleExcitationPlus",
+        "SingleExcitationMinus",
     }
 
     def __init__(self, wires, *, shots=1000, analytic=True, cache=0):

pennylane/devices/default_qubit.py

@@ -125,6 +125,9 @@ class DefaultQubit(QubitDevice):
         "CRZ",
         "CRot",
         "QFT",
+        "SingleExcitation",
+        "SingleExcitationPlus",
+        "SingleExcitationMinus",
     }
 
     observables = {"PauliX", "PauliY", "PauliZ", "Hadamard", "Hermitian", "Identity"}

pennylane/devices/default_qubit_autograd.py

@@ -95,6 +95,9 @@ class DefaultQubitAutograd(DefaultQubit):
         "CRZ": autograd_ops.CRZ,
         "CRot": autograd_ops.CRot,
         "MultiRZ": autograd_ops.MultiRZ,
+        "SingleExcitation": autograd_ops.SingleExcitation,
+        "SingleExcitationPlus": autograd_ops.SingleExcitationPlus,
+        "SingleExcitationMinus": autograd_ops.SingleExcitationMinus,
     }
 
     C_DTYPE = np.complex128

pennylane/devices/default_qubit_jax.py

@@ -145,6 +145,9 @@ def circuit():
         "CRY": jax_ops.CRY,
         "CRZ": jax_ops.CRZ,
         "MultiRZ": jax_ops.MultiRZ,
+        "SingleExcitation": jax_ops.SingleExcitation,
+        "SingleExcitationPlus": jax_ops.SingleExcitationPlus,
+        "SingleExcitationMinus": jax_ops.SingleExcitationMinus,
     }
 
     C_DTYPE = jnp.complex64

pennylane/devices/default_qubit_tf.py

@@ -143,6 +143,9 @@ class DefaultQubitTF(DefaultQubit):
         "CRY": tf_ops.CRY,
         "CRZ": tf_ops.CRZ,
         "CRot": tf_ops.CRot,
+        "SingleExcitation": tf_ops.SingleExcitation,
+        "SingleExcitationPlus": tf_ops.SingleExcitationPlus,
+        "SingleExcitationMinus": tf_ops.SingleExcitationMinus,
     }
 
     C_DTYPE = tf.complex128

pennylane/devices/jax_ops.py

@@ -180,3 +180,47 @@ def MultiRZ(theta, n):
         array[complex]: diagonal part of the multi-qubit rotation matrix
     """
     return jnp.exp(-1j * theta / 2 * pauli_eigs(n))
+
+
+def SingleExcitation(phi):
+    r"""Single excitation rotation.
+
+    Args:
+        phi (float): rotation angle
+
+    Returns:
+        jnp.Tensor[float]: Single excitation rotation matrix
+    """
+    c = jnp.cos(phi / 2)
+    s = jnp.sin(phi / 2)
+    return jnp.array([[1, 0, 0, 0], [0, c, -s, 0], [0, s, c, 0], [0, 0, 0, 1]])
+
+
+def SingleExcitationPlus(phi):
+    r"""Single excitation rotation with positive phase-shift outside the rotation subspace.
+
+    Args:
+        phi (float): rotation angle
+
+    Returns:
+        jnp.Tensor[complex]: Single excitation rotation matrix with positive phase-shift
+    """
+    c = jnp.cos(phi / 2)
+    s = jnp.sin(phi / 2)
+    e = jnp.exp(1j * phi / 2)
+    return jnp.array([[e, 0, 0, 0], [0, c, -s, 0], [0, s, c, 0], [0, 0, 0, e]])
+
+
+def SingleExcitationMinus(phi):
+    r"""Single excitation rotation with negative phase-shift outside the rotation subspace.
+
+    Args:
+        phi (float): rotation angle
+
+    Returns:
+        tf.Tensor[complex]: Single excitation rotation matrix with negative phase-shift
+    """
+    c = jnp.cos(phi / 2)
+    s = jnp.sin(phi / 2)
+    e = jnp.exp(-1j * phi / 2)
+    return jnp.array([[e, 0, 0, 0], [0, c, -s, 0], [0, s, c, 0], [0, 0, 0, e]])

pennylane/devices/tests/test_gates.py

@@ -68,6 +68,9 @@
     "SX": qml.SX(wires=[0]),
     "Toffoli": qml.Toffoli(wires=[0, 1, 2]),
     "QFT": qml.QFT(wires=[0, 1, 2]),
+    "SingleExcitation": qml.SingleExcitation(0, wires=[0, 1]),
+    "SingleExcitationPlus": qml.SingleExcitationPlus(0, wires=[0, 1]),
+    "SingleExcitationMinus": qml.SingleExcitationMinus(0, wires=[0, 1]),
 }
 
 all_ops = ops.keys()

pennylane/devices/tf_ops.py

@@ -191,3 +191,50 @@ def CRot(a, b, c):
         :math:`|0\rangle\langle 0|\otimes \mathbb{I}+|1\rangle\langle 1|\otimes R(a,b,c)`
     """
     return tf.linalg.diag(CRZ(c)) @ (CRY(b) @ tf.linalg.diag(CRZ(a)))
+
+
+def SingleExcitation(phi):
+    r"""Single excitation rotation.
+
+    Args:
+        phi (float): rotation angle
+
+    Returns:
+        tf.Tensor[float]: Single excitation rotation matrix
+    """
+    phi = tf.cast(phi, dtype=C_DTYPE)
+    c = tf.cos(phi / 2)
+    s = tf.sin(phi / 2)
+    return tf.convert_to_tensor([[1, 0, 0, 0], [0, c, -s, 0], [0, s, c, 0], [0, 0, 0, 1]])
+
+
+def SingleExcitationPlus(phi):
+    r"""Single excitation rotation with positive phase-shift outside the rotation subspace.
+
+    Args:
+        phi (float): rotation angle
+
+    Returns:
+        tf.Tensor[complex]: Single excitation rotation matrix with positive phase-shift
+    """
+    phi = tf.cast(phi, dtype=C_DTYPE)
+    c = tf.cos(phi / 2)
+    s = tf.sin(phi / 2)
+    e = tf.exp(1j * phi / 2)
+    return tf.convert_to_tensor([[e, 0, 0, 0], [0, c, -s, 0], [0, s, c, 0], [0, 0, 0, e]])
+
+
+def SingleExcitationMinus(phi):
+    r"""Single excitation rotation with negative phase-shift outside the rotation subspace.
+
+    Args:
+        phi (float): rotation angle
+
+    Returns:
+        tf.Tensor[complex]: Single excitation rotation matrix with negative phase-shift
+    """
+    phi = tf.cast(phi, dtype=C_DTYPE)
+    c = tf.cos(phi / 2)
+    s = tf.sin(phi / 2)
+    e = tf.exp(-1j * phi / 2)
+    return tf.convert_to_tensor([[e, 0, 0, 0], [0, c, -s, 0], [0, s, c, 0], [0, 0, 0, e]])