qml.fermi.FermiWord

class FermiWord(operator)

Bases: dict

Immutable dictionary used to represent a Fermi word, a product of fermionic creation and annihilation operators, that can be constructed from a standard dictionary.

The keys of the dictionary are tuples of two integers. The first integer represents the position of the creation/annihilation operator in the Fermi word and the second integer represents the orbital it acts on. The values of the dictionary are one of '+' or '-' symbols that denote creation and annihilation operators, respectively. The operator \(a^{\dagger}_0 a_1\) can then be constructed as

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

Attributes

wires

Return wires in a FermiWord.

wires

Return wires in a FermiWord.

Methods

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.

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.

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