# qml.templates.subroutines.Permute¶

class Permute(permutation, wires, do_queue=True)[source]

Applies a permutation to a set of wires.

Parameters
• permutation (list) – A list of wire labels that represents the new ordering of wires after the permutation. The list may consist of integers or strings, so long as they match the labels of wires.

• wires (Iterable or Wires) – Wires that the permutation acts on. Accepts an iterable of numbers or strings, or a Wires object.

Raises

ValueError – if inputs do not have the correct format

Example

import pennylane as qml

dev = qml.device('default.qubit', wires=5)

@qml.qnode(dev)
def apply_perm():
# Send contents of wire 4 to wire 0, of wire 2 to wire 1, etc.
qml.templates.Permute([4, 2, 0, 1, 3], wires=dev.wires)
return qml.expval(qml.PauliZ(0))


See “Usage Details” for further examples.

As a simple example, suppose we have a 4-qubit device with wires labeled by the integers [0, 1, 2, 3]. We apply a permutation to shuffle the order to [3, 2, 0, 1] (i.e., the qubit state that was previously on wire 3 is now on wire 0, the one from 2 is on wire 1, etc.).

dev = qml.device('default.qubit', wires=4)

@qml.qnode(dev)
def apply_perm():
qml.templates.Permute([3, 2, 0, 1], dev.wires)
return qml.expval(qml.PauliZ(0))

>>> apply_perm()
>>> print(apply_perm.draw(wire_order=[0,1,2,3]))
0: ─────────╭SWAP─────────┤ ⟨Z⟩
1: ──╭SWAP──│─────────────┤
2: ──╰SWAP──│──────╭SWAP──┤
3: ─────────╰SWAP──╰SWAP──┤


Permute can also be used with quantum tapes. For example, suppose we have a tape with 5 wires [0, 1, 2, 3, 4], and we’d like to reorder them so that wire 4 is moved to the location of wire 0, wire 2 is moved to the original location of wire 1, and so on.

import pennylane as qml

with qml.tape.QuantumTape() as tape:
qml.templates.Permute([4, 2, 0, 1, 3], wires=[0, 1, 2, 3, 4])

>>> tape_expanded = qml.tape.tape.expand_tape(tape)
>>> print(tape_expanded.draw(wire_order=qml.wires.Wires([0,1,2,3,4])))
0: ─────────╭SWAP────────────────┤
1: ──╭SWAP──│────────────────────┤
2: ──╰SWAP──│──────╭SWAP─────────┤
3: ─────────│──────│──────╭SWAP──┤
4: ─────────╰SWAP──╰SWAP──╰SWAP──┤


Permute can also be applied to wires with arbitrary labels, like so:

wire_labels = [3, 2, "a", 0, "c"]

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

@qml.qnode(dev)
def circuit():
qml.templates.Permute(["c", 3,"a",2,0], wires=wire_labels)
return qml.expval(qml.PauliZ("c"))


The permuted circuit is:

>>> circuit()
>>> print(circuit.draw(wire_order=wire_labels))
3: ──╭SWAP────────────────┤
2: ──│──────╭SWAP─────────┤
0: ──│──────│──────╭SWAP──┤
c: ──╰SWAP──╰SWAP──╰SWAP──┤


It is also possible to permute a subset of wires by specifying a subset of labels. For example,

wire_labels = [3, 2, "a", 0, "c"]

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

@qml.qnode(dev)
def circuit()
# Only permute the order of 3 of them
qml.templates.Permute(["c", 2, 0], wires=[2, 0, "c"])
return qml.expval(qml.PauliZ("c"))


will permute only the second, third, and fifth wires as follows:

>>> circuit()
>>> print(circuit.draw(wire_order=wire_labels))
3: ──╭SWAP────────────────┤
2: ──│──────╭SWAP─────────┤
0: ──│──────│──────╭SWAP──┤
c: ──╰SWAP──╰SWAP──╰SWAP──┤ ⟨Z⟩

 base_name Get base name of the operator. eigvals Eigenvalues of an instantiated operator. generator Generator of the operation. grad_method Gradient computation method. grad_recipe Gradient recipe for the parameter-shift method. 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 par_domain parameters Current parameter values. string_for_inverse wires Wires of this operator.
base_name

Get base name of the operator.

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

• 'A': analytic differentiation using the parameter-shift method.

• 'F': finite difference numerical differentiation.

• None: the operation may not be differentiated.

Default is 'F', or None if the Operation has zero parameters.

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

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 = -1
par_domain = 'A'
parameters

Current parameter values.

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. decomposition(*params, wires) Returns a template decomposing the operation into other quantum operations. 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. 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

static decomposition(*params, wires)

Returns a template decomposing the operation into other quantum operations.

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

multiplier, shift

Return type

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

queue()

Append the operator to the Operator queue.