qml.FermiC

class FermiC(orbital)

Bases: pennylane.fermi.fermionic.FermiWord

The fermionic creation operator \(a^{\dagger}\)

For instance, the operator qml.FermiC(2) denotes \(a^{\dagger}_2\). This operator applied to \(\ket{0000}\) gives \(\ket{0010}\).

Parameters

orbital (int) – the non-negative integer indicating the orbital the operator acts on.

Note

While the FermiC class represents a mathematical operator, it is not a PennyLane qubit Operator.

See also

FermiA

Example

To construct the operator \(a^{\dagger}_0\):

>>> FermiC(0)
a⁺(0)

This can be combined with the annihilation operator FermiA. For example, \(a^{\dagger}_0 a_1 a^{\dagger}_2 a_3\) can be constructed as:

>>> qml.FermiC(0) * qml.FermiA(1) * qml.FermiC(2) * qml.FermiA(3)
a⁺(0) a(1) a⁺(2) a(3)

Attributes

wires

Return wires in a FermiWord.

wires

Return wires in a FermiWord.

Methods

clear()
copy()
fromkeys([value])	Create a new dictionary with keys from iterable and values set to value.
get(key[, default])	Return the value for key if key is in the dictionary, else default.
items()
keys()
pop(k[,d])	If key is not found, default is returned if given, otherwise KeyError is raised
popitem()	Remove and return a (key, value) pair as a 2-tuple.
setdefault(key[, default])	Insert key with a value of default if key is not in the dictionary.
to_mat([n_orbitals])	Return the matrix representation.
to_string()	Return a compact string representation of a FermiWord.
update(item)	Restrict updating FermiWord after instantiation.
values()

clear() → None.  Remove all items from D.

copy() → a shallow copy of D

fromkeys(value=None, /)

Create a new dictionary with keys from iterable and values set to value.

get(key, default=None, /)

Return the value for key if key is in the dictionary, else default.

items() → a set-like object providing a view on D’s items

keys() → a set-like object providing a view on D’s keys

pop(k[, d]) → v, remove specified key and return the corresponding value.

If key is not found, default is returned if given, otherwise KeyError is raised

popitem()

Remove and return a (key, value) pair as a 2-tuple.

Pairs are returned in LIFO (last-in, first-out) order. Raises KeyError if the dict is empty.

setdefault(key, default=None, /)

Insert key with a value of default if key is not in the dictionary.

Return the value for key if key is in the dictionary, else default.

to_mat(n_orbitals=None)

Return the matrix representation.

Parameters

n_orbitals (int or None) – Number of orbitals. If not provided, it will be inferred from the largest orbital index in the Fermi operator.

Returns

Matrix representation of the FermiWord.

Return type

NumpyArray

Example

>>> w = FermiWord({(0, 0): '+', (1, 1): '-'})
>>> w.to_mat()
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, 1.+0.j, 0.+0.j, 0.+0.j],
      [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j])

to_string()

Return a compact string representation of a FermiWord. Each operator in the word is represented by the number of the wire it operates on, and a + or - to indicate either a creation or annihilation operator.

>>> w = FermiWord({(0, 0) : '+', (1, 1) : '-'})
>>> w.to_string()
a⁺(0) a(1)

update(item)

Restrict updating FermiWord after instantiation.

values() → an object providing a view on D’s values

code/api/pennylane.FermiC

 

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