# qml.MottonenStatePreparation¶

class MottonenStatePreparation(state_vector, wires, do_queue=True, id=None)[source]

Prepares an arbitrary state on the given wires using a decomposition into gates developed by Möttönen et al. (2004).

The state is prepared via a sequence of uniformly controlled rotations. A uniformly controlled rotation on a target qubit is composed from all possible controlled rotations on the qubit and can be used to address individual elements of the state vector.

In the work of Möttönen et al., inverse state preparation is executed by first equalizing the phases of the state vector via uniformly controlled Z rotations, and then rotating the now real state vector into the direction of the state $$|0\rangle$$ via uniformly controlled Y rotations.

This code is adapted from code written by Carsten Blank for PennyLane-Qiskit.

Note

The final state is only equal to the input state vector up to a global phase.

Warning

Due to non-trivial classical processing of the state vector, this template is not always fully differentiable.

Parameters
• state_vector (tensor_like) – Input array of shape (2^n,), where n is the number of wires the state preparation acts on. The input array must be normalized.

• wires (Iterable) – wires that the template acts on

Example

MottonenStatePreparation creates any arbitrary state on the given wires depending on the input state vector.

dev = qml.device('default.qubit', wires=3)

@qml.qnode(dev)
def circuit(state):
qml.MottonenStatePreparation(state_vector=state, wires=range(3))
return qml.state()

state = np.array([1, 2j, 3, 4j, 5, 6j, 7, 8j])
state = state / np.linalg.norm(state)


The resulting circuit is:

>>> print(qml.draw(circuit)(state))
0: ──RY(2.35)──╭C─────────────╭C─────────────────╭C─────────────────────────────╭C──╭C─────────╭C──────╭C──────╭C──╭┤ State
1: ──RY(2.09)──╰X──RY(0.213)──╰X──╭C─────────────│───────────────╭C─────────────│───╰X─────────╰X──╭C──│───╭C──│───├┤ State
2: ──RY(1.88)─────────────────────╰X──RY(0.102)──╰X──RY(0.0779)──╰X──RY(0.153)──╰X───RZ(1.57)──────╰X──╰X──╰X──╰X──╰┤ State


The state preparation can be checked by running:

>>> print(np.allclose(state * np.exp(1j * -0.785396), circuit(state)))
True


The state is equal to the input state upto a global phase. This phase is given by np.exp(1j * -0.785396) in this example.

 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 Generator of the operation. 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 Number of trainable parameters that this operator expects to be fed via the dynamic *params argument. 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

Generator of the operation.

A length-2 list [generator, scaling_factor], where

• generator is an existing PennyLane operation class or $$2\times 2$$ Hermitian array that acts as the generator of the current operation

• scaling_factor represents a scaling factor applied to the generator operation

For example, if $$U(\theta)=e^{i0.7\theta \sigma_x}$$, then $$\sigma_x$$, with scaling factor $$s$$, is the generator of operator $$U(\theta)$$:

generator = [PauliX, 0.7]


Default is [None, 1], indicating the operation has no generator.

grad_method = None
grad_recipe = None

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
num_wires = -1
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([do_queue]) Create an operation that is the adjoint of this one. Decomposes this operator into products of other operators. decomposition(*params, wires) Defines a decomposition of this operator into products of other operators. 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. 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(do_queue=False)

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

decompose()

Decomposes this operator into products of other operators.

Returns

list[Operation]

static decomposition(*params, wires)

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()[source]

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.