peropq.bch_optimized
====================

.. py:module:: peropq.bch_optimized


Classes
-------

.. autoapisummary::

   peropq.bch_optimized.NormTerm
   peropq.bch_optimized.VariationalNorm


Functions
---------

.. autoapisummary::

   peropq.bch_optimized._get_non_zero_trace_indices
   peropq.bch_optimized._loop_over_trace
   peropq.bch_optimized._is_pauli_string
   peropq.bch_optimized._is_norm_term
   peropq.bch_optimized.commutator


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

.. py:function:: _get_non_zero_trace_indices(bitstrings)

   Get all the the term indices which have non zero trace, i.e Tr(term[i]*term[j])!=0.

   Works directly at the bitstring level.
   :param bitstring: array containing bitstrings one which to compute the trace over.
   :returns: an array containing the qubit indices on which the Pauli string does not have identity.


.. py:function:: _loop_over_trace(trace_list, indices, theta, min_order, all_the_orders, all_the_indices, begin_list, end_list, all_the_coefficients)

   Just in timed compiled function which computes the norm once all the traces are calculated.

   :param trace_list: array containing all the non zero traces
   :param indices: array containing the indices corresponding to every trace
   :param theta: variational parameters
   :param min_order: minimum order to be taken into the calculation (i.e. 0 for uncontrained and 1 for contrained)
   :param all_the_orders: array containaing the order of every term included in the terms
   :param all_the_indices: indices of the theta parameters for all the terms in the trace
   :param begin_list: array containing the first index to take into account in the trace for the variational parameters
   :param end_list: array containing the last index to take into account in the trace for the variational parameters
   :param all_the_coefficients: coefficient of the NormTerms which need to be taken into account in the trace
   :returns: the perturbative norm


.. py:class:: NormTerm

   Class representing a term to be taken into account in the norm.

   :param pauli_string: of the term
   :param order: at which the term is relevant
   :param coefficient: in front of the Pauli string
   :param theta_indices: represents the indices of the variational parameter to be multiplied in front


   .. py:attribute:: pauli_string
      :type:  peropq.pauli_bitstring.PauliString


   .. py:attribute:: order
      :type:  int


   .. py:attribute:: coefficient
      :type:  complex


   .. py:attribute:: theta_indices
      :type:  list[tuple[int, int]]


.. py:function:: _is_pauli_string(to_test)

.. py:function:: _is_norm_term(to_test)

.. py:function:: commutator(aterm, other)

   Take the commutator between two NormTerm instances.


.. py:class:: VariationalNorm(variational_unitary, order, *, unconstrained = False)

   Class representing the perturbative norm with some variational parameters. It is used in the optimization process.


   .. py:attribute:: variational_unitary


   .. py:attribute:: order


   .. py:attribute:: terms
      :type:  dict[int, list[NormTerm]]


   .. py:attribute:: unconstrained


   .. py:attribute:: calculated_trace
      :value: False



   .. py:method:: compute_commutator_sum(term_list1, term_list2)

      Compute the commutator of two sums of Pauli strings: [term_list1[0]+term_list1[1]+term_list1[2]+...,term_list2[0]+term_list2[1]+term_list2[2]+...].

      :returns: a list of instances of NormTerm corresponding to the commutator.



   .. py:method:: add_term(new_term)

      Take into account a new term in the variational norm. This is currently implemented up to order 4.



   .. py:method:: get_commutators()

      Get the commutators required to calculate the perturbative variational norm.



   .. py:method:: get_traces()

      Calculate all the traces of commutator needed for the perturbative variational norm.



   .. py:method:: calculate_norm(theta)

      Calculate the norm for a given variational parameter theta.

      :param theta: variational parameter
      :returns: the norm