pygsti.algorithms.fiducialpairreduction.find_sufficient_fiducial_pairs_per_germ_global

pygsti.algorithms.fiducialpairreduction.find_sufficient_fiducial_pairs_per_germ_global#

find_sufficient_fiducial_pairs_per_germ_global(target_model, prep_fiducials, meas_fiducials, germ_vector_spanning_set=None, germs=None, prep_povm_tuples='first', mem_limit=None, inv_trace_tol=10, initial_seed_mode='greedy', evd_tol=1e-10, seed=None, verbosity=0, float_type=<class 'numpy.complex128'>, germ_set_spanning_kwargs=None, precomputed_jacobians=None)#

Finds a per-germ set of fiducial pairs that are amplificationally complete.

A “standard” set of GST circuits consists of all circuits of the form:

statePrep + prepFiducial + germPower + measureFiducial + measurement

This set is typically over-complete, and it is possible to restrict the (prepFiducial, measureFiducial) pairs to a subset of all the possible pairs given the separate prep_fiducials and meas_fiducials lists. This function attempts to find sets of fiducial pairs, one set per germ, that still amplify all of the model’s parameters (i.e. is “amplificationally complete”). For each germ, a fiducial pair set is found that amplifies all of the “parameters” (really linear combinations of them) that the particular germ amplifies.

To test whether a set of fiducial pairs satisfies this condition, the sum of projectors P_i = dot(J_i,J_i^T), where J_i is a matrix of the derivatives of each of the selected (prepFiducial+germ+effectFiducial) sequence probabilities with respect to the i-th amplified parameter.

Parameters:

  • target_model (Model) – The target model used to determine amplificational completeness.

  • prep_fiducials (list of Circuits) – Fiducial circuits used to construct an informationally complete effective preparation.

  • meas_fiducials (list of Circuits) – Fiducial circuits used to construct an informationally complete effective measurement.

  • germ_vector_spanning_set (dictionary of lists) – A dictionary with keys corresponding to germs and values corresponding to lists of parameter vectors (less spam parameters) for which we need sensitivity.

  • germs (list of circuits) – If passed in and germ_vector_spanning_set is None then we’ll use this in the calculation of the germ vector spanning set.

  • prep_povm_tuples (list or "first", optional) – A list of (prepLabel, povmLabel) tuples to consider when checking for completeness. Usually this should be left as the special (and default) value “first”, which considers the first prep and POVM contained in target_model.

  • verbosity (int, optional) – How much detail to print to stdout.

  • mem_limit (int, optional) – A memory limit in bytes.

  • inv_trace_tol (float, optional (default 10)) – A threshold tolerance value corresponding to the maximum reduction in sensitivity we are willing to tolerate relative to the complete set of fiducial pairs. Specifically the increase in the trace of the inverse/psuedoinverse of the directional derivative matrix for a germ’s specified amplified parameters that we are willing to tolerate.

  • initial_seed_mode (str, optional (default 'greedy')) – Specifies the manner in which an initial set of fiducial pairs is selected for a germ to seed the greedy search routine. Currently only supports ‘greedy’ wherein we start from scratch from an empty set of fiducial pairs and select them entirely greedily.

  • evd_tol (float, optional (default 1e-10)) – Threshold value for eigenvalues below which they are treated as zero. Used in the construction of compact eigenvalue decompositions (technically rank-decompositions) for directional derivative matrices.

  • seed (int, optional (default None)) – Seed for PRNGs. Not currently used.

  • float_type (numpy dtype, optional (default numpy.cdouble)) – Numpy data type to use for floating point arrays.

  • germ_set_spanning_kwargs (dict, optional (default None)) – A dictionary of optional kwargs for the function pygsti.algorithms.germselection.germ_set_spanning_vectors. See doctring for that function for more details. Only utilized if the germ_vector_spanning_set argument of this function is None.

  • precomputed_jacobians (dict, optional (default None)) – An optional dictionary of precomputed jacobian dictionaries for the germ fiducial pair set. The keys are germs and the values are the dictionaries corresponding that that germ-fiducial-pair set’s jacobian.

Returns:

A dictionary whose keys are the germ circuits and whose values are lists of (iRhoFid,iMeasFid) tuples of integers, each specifying the list of fiducial pairs for a particular germ (indices are into prep_fiducials and meas_fiducials).

Return type:

dict