qml.OrbitalRotation

class OrbitalRotation(phi, wires)[source]

Bases: pennylane.operation.Operation

Spin-adapted spatial orbital rotation.

For two neighbouring spatial orbitals \(\{|\Phi_{0}\rangle, |\Phi_{1}\rangle\}\), this operation performs the following transformation

\[\begin{split}&|\Phi_{0}\rangle = \cos(\phi/2)|\Phi_{0}\rangle - \sin(\phi/2)|\Phi_{1}\rangle\\ &|\Phi_{1}\rangle = \cos(\phi/2)|\Phi_{0}\rangle + \sin(\phi/2)|\Phi_{1}\rangle,\end{split}\]

with the same orbital operation applied in the \(\alpha\) and \(\beta\) spin orbitals.

../../_images/orbital_rotation_decomposition_extended.png

Here, \(G(\phi)\) represents a single-excitation Givens rotation, implemented in PennyLane as the SingleExcitation operation.

Details:

  • Number of wires: 4

  • Number of parameters: 1

  • Gradient recipe: The OrbitalRotation operator satisfies the four-term parameter-shift rule (see Appendix F, https://arxiv.org/abs/2104.05695)

Parameters
  • phi (float) – rotation angle \(\phi\)

  • wires (Sequence[int]) – the wires the operation acts on

Example

>>> dev = qml.device('default.qubit', wires=4)
>>> @qml.qnode(dev)
... def circuit(phi):
...     qml.BasisState(np.array([1, 1, 0, 0]), wires=[0, 1, 2, 3])
...     qml.OrbitalRotation(phi, wires=[0, 1, 2, 3])
...     return qml.state()
>>> circuit(0.1)
array([ 0.        +0.j,  0.        +0.j,  0.        +0.j,
        0.00249792+0.j,  0.        +0.j,  0.        +0.j,
       -0.04991671+0.j,  0.        +0.j,  0.        +0.j,
       -0.04991671+0.j,  0.        +0.j,  0.        +0.j,
        0.99750208+0.j,  0.        +0.j,  0.        +0.j,
        0.        +0.j])

base_name

Get base name of the operator.

basis

The basis of an operation, or for controlled gates, of the target operation.

control_wires

Returns the control wires.

eigvals

Eigenvalues of an instantiated operator.

generator

grad_method

grad_recipe

Gradient recipe for the parameter-shift method.

hash

returns an integer hash uniquely representing the operator

id

String for the ID of the operator.

inverse

Boolean determining if the inverse of the operation was requested.

matrix

Matrix representation of an instantiated operator in the computational basis.

name

Get and set the name of the operator.

num_params

num_wires

parameters

Current parameter values.

single_qubit_rot_angles

The parameters required to implement a single-qubit gate as an equivalent Rot gate, up to a global phase.

string_for_inverse

wires

Wires of this operator.

base_name

Get base name of the operator.

basis = None

The basis of an operation, or for controlled gates, of the target operation. If not None, should take a value of "X", "Y", or "Z".

For example, X and CNOT have basis = "X", whereas ControlledPhaseShift and RZ have basis = "Z".

Type

str or None

control_wires

Returns the control wires. For operations that are not controlled, this is an empty Wires object of length 0.

Returns

The control wires of the operation.

Return type

Wires

eigvals
generator = [array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j,          0.+0.j,  0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,         -0.-1.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j,          0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+1.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j],        [ 0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,  0.+0.j,          0.+0.j,  0.+0.j]]), -0.5]
grad_method = 'A'
grad_recipe = ([[0.4267766952966368, 1, 1.5707963267948966], [-0.4267766952966368, 1, -1.5707963267948966], [-0.07322330470336313, 1, 4.71238898038469], [0.07322330470336313, 1, -4.71238898038469]],)

Gradient recipe for the parameter-shift method.

This is a tuple with one nested list per operation parameter. For parameter \(\phi_k\), the nested list contains elements of the form \([c_i, a_i, s_i]\) where \(i\) is the index of the term, resulting in a gradient recipe of

\[\frac{\partial}{\partial\phi_k}f = \sum_{i} c_i f(a_i \phi_k + s_i).\]

If None, the default gradient recipe containing the two terms \([c_0, a_0, s_0]=[1/2, 1, \pi/2]\) and \([c_1, a_1, s_1]=[-1/2, 1, -\pi/2]\) is assumed for every parameter.

Type

tuple(Union(list[list[float]], None)) or None

hash

returns an integer hash uniquely representing the operator

Type

int

id

String for the ID of the operator.

inverse

Boolean determining if the inverse of the operation was requested.

matrix
name

Get and set the name of the operator.

num_params = 1
num_wires = 4
parameters

Current parameter values.

single_qubit_rot_angles

The parameters required to implement a single-qubit gate as an equivalent Rot gate, up to a global phase.

Returns

A list of values \([\phi, \theta, \omega]\) such that \(RZ(\omega) RY(\theta) RZ(\phi)\) is equivalent to the original operation.

Return type

tuple[float, float, float]

string_for_inverse = '.inv'
wires

Wires of this operator.

Returns

wires

Return type

Wires

adjoint()

Create an operation that is the adjoint of this one.

decompose()

Decomposes this operator into products of other operators.

decomposition(phi, wires)

Defines a decomposition of this operator into products of other operators.

expand()

Returns a tape containing the decomposed operations, rather than a list.

get_parameter_shift(idx[, shift])

Multiplier and shift for the given parameter, based on its gradient recipe.

inv()

Inverts the operation, such that the inverse will be used for the computations by the specific device.

label([decimals, base_label])

A customizable string representation of the operator.

queue([context])

Append the operator to the Operator queue.

adjoint()[source]

Create an operation that is the adjoint of this one.

Adjointed operations are the conjugated and transposed version of the original operation. Adjointed ops are equivalent to the inverted operation for unitary gates.

Parameters

do_queue – Whether to add the adjointed gate to the context queue.

Returns

The adjointed operation.

decompose()

Decomposes this operator into products of other operators.

Returns

list[Operation]

static decomposition(phi, wires)[source]

Defines a decomposition of this operator into products of other operators.

Parameters
  • params (tuple[float, int, array]) – operator parameters

  • wires (Union(Sequence[int], Wires)) – wires the operator acts on

Returns

list[Operation]

expand()

Returns a tape containing the decomposed operations, rather than a list.

Returns

Returns a quantum tape that contains the operations decomposition, or if not implemented, simply the operation itself.

Return type

JacobianTape

get_parameter_shift(idx, shift=1.5707963267948966)

Multiplier and shift for the given parameter, based on its gradient recipe.

Parameters

idx (int) – parameter index

Returns

list of multiplier, coefficient, shift for each term in the gradient recipe

Return type

list[[float, float, float]]

inv()

Inverts the operation, such that the inverse will be used for the computations by the specific device.

This method concatenates a string to the name of the operation, to indicate that the inverse will be used for computations.

Any subsequent call of this method will toggle between the original operation and the inverse of the operation.

Returns

operation to be inverted

Return type

Operator

label(decimals=None, base_label=None)

A customizable string representation of the operator.

Parameters
  • decimals=None (int) – If None, no parameters are included. Else, specifies how to round the parameters.

  • base_label=None (str) – overwrite the non-parameter component of the label

Returns

label to use in drawings

Return type

str

Example:

>>> op = qml.RX(1.23456, wires=0)
>>> op.label()
"RX"
>>> op.label(decimals=2)
"RX\n(1.23)"
>>> op.label(base_label="my_label")
"my_label"
>>> op.label(decimals=2, base_label="my_label")
"my_label\n(1.23)"
>>> op.inv()
>>> op.label()
"RX⁻¹"
queue(context=<class 'pennylane.queuing.QueuingContext'>)

Append the operator to the Operator queue.

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