qml.pauli.pauli_word_to_matrix

pauli_word_to_matrix(pauli_word, wire_map=None)

Convert a Pauli word from a tensor to its matrix representation.

A Pauli word can be either:

• A single pauli operator (see PauliX for an example).

• A Prod instance containing Pauli operators.

• A SProd instance containing a Pauli operator.

• A Sum instance with only one term.

The matrix representation of a Pauli word has dimension \(2^n \times 2^n\), where \(n\) is the number of qubits provided in wire_map. For wires that the Pauli word does not act on, identities must be inserted into the tensor product at the correct positions.

Parameters

• pauli_word (Union[Observable, Prod, SProd, Sum]) – an observable, either a single-qubit observable representing a Pauli group element, or a tensor product of single-qubit observables.

• wire_map (dict[Union[str, int], int]) – dictionary containing all wire labels used in the Pauli word as keys, and unique integer labels as their values

Returns

The matrix representation of the multi-qubit Pauli over the specified wire map.

Return type

array[complex]

Raises

TypeError – if the input observable is not a proper Pauli word.

Example

>>> wire_map = {'a' : 0, 'b' : 1}
>>> pauli_word = qml.X('a') @ qml.Y('b')
>>> pauli_word_to_matrix(pauli_word, wire_map=wire_map)
array([[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.-1.j, 0.+0.j, 0.-0.j],
       [0.+1.j, 0.+0.j, 0.+0.j, 0.+0.j]])

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