peropq.pauli_bitstring
======================

.. py:module:: peropq.pauli_bitstring


Classes
-------

.. autoapisummary::

   peropq.pauli_bitstring.PauliString


Functions
---------

.. autoapisummary::

   peropq.pauli_bitstring.pauli_from_string
   peropq.pauli_bitstring._get_non_identity_indices
   peropq.pauli_bitstring._get_i_power
   peropq.pauli_bitstring._pauli_string_mult
   peropq.pauli_bitstring.bit_string_commutation


Module Contents
---------------

.. py:class:: PauliString(bit_string, coefficient = 1.0)

   Class representing efficiently Pauli matrices as bitstrings.


   .. py:attribute:: bit_string


   .. py:attribute:: coefficient


   .. py:method:: __mul__(other)

      Multiply PauliString with a complex number or PauliString.



   .. py:method:: __rmul__(other)

      Multiply PauliString with a complex number or PauliString.



   .. py:method:: __eq__(other)

      Equality for PauliStrings.

      Two PauliStrings are equal if their coefficients are equal and
      if their Paulis are equal on all qubits. The underlying qubit_pauli_maps
      may differ (in the number of Identities).



   .. py:method:: commutes_with(other)

      Return whether this PauliString commutes with given PauliString.

      :param other: The right side of the Commutator

      :return: True if PauliStrings commute, False otherwise



   .. py:method:: get_pauli(qubit)

      Return a string indicating the Pauli matrix associated with the input qubit.



   .. py:method:: normalized_trace()

      Returns `2^(-n)*Tr(self)`.

      The trace is just the coefficient times the product of the traces of the Paulis
      over all n qubits (including any identities on qubits not explicitly contained in the qubit_pauli_map). Since
      `Tr(Pauli.I) == 2`, and `Tr(Pauli.X) == Tr(Pauli.Y) == Tr(Pauli.Z) == 0`, the result will either be 0 (if any
      of the Paulis is not the Identity) or `self.coefficient` (if all paulis are the identity).



.. py:function:: pauli_from_string(string, length, start_qubit = 0, coefficient = 1.0)

   Get an instance of PauliString from a string.

   :param string: represents the pauli string
   :param length: legnth of the Pauli string (i.e. number of qubits)
   :param start_qubit: first qubit to place the Pauli on
   :param coefficent: of the Pauli string
   :returns: instace of PauliString corresponding to the input string.


.. py:function:: _get_non_identity_indices(bit_string)

   Get the non identity indices.


.. py:function:: _get_i_power(bit_string1, bit_string2)

   Get the right power for the multiplication, i.e. (1j)^power.


.. py:function:: _pauli_string_mult(pauli_string1, pauli_string2)

   Multiply two bitstrings.


.. py:function:: bit_string_commutation(bit_string1, bit_string2)

   Return whether two bitstrings representing pauli strings commute.

   :param bit_string1: first bit_string
   :param bit_string2: second bit_string
   :returns: True if the two bitstrings commute, False otherwise.