pygsti.algorithms.fiducialpairreduction.find_sufficient_fiducial_pairs_per_germ_greedy

pygsti.algorithms.fiducialpairreduction.find_sufficient_fiducial_pairs_per_germ_greedy#

find_sufficient_fiducial_pairs_per_germ_greedy(target_model, prep_fiducials, meas_fiducials, germs, prep_povm_tuples='first', constrain_to_tp=True, inv_trace_tol=10, initial_seed_mode='random', evd_tol=1e-10, sensitivity_threshold=1e-10, seed=None, verbosity=0, check_complete_fid_set=True, mem_limit=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 germ eigenvalue (or more generally, amplified parameter), is computed. If the fiducial-pair set is sufficient, the rank of the resulting sum (an operator) will be equal to the total (maximal) number of parameters the germ can amplify.

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.

  • germs (list of Circuits) – The germ circuits that are repeated to amplify errors.

  • 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.

  • constrain_to_tp (bool, optional (default True)) – Whether or not to consider non-TP parameters the the germs amplify. If the fiducal pairs will be used in a GST estimation where the model is constrained to being trace-preserving (TP), this should be set to True.

  • inv_trace_tol (float, optional (default 10)) – Tolerance used to identify whether a candidate fiducial set has a feasible cost function value and for comparing among both complete and incomplete candidate sets. The cost function corresponds to trace(pinv(sum_i(dot(J_i,J_i^T)))), where the J_i’s are described above, which is related to a condition in optimal design theory called a-optimality. The tolerance is a relative tolerance compared to the complete fiducial set. This essentially measures the relative sensitivity loss we’re willing to accept as part of applying FPR.

  • initial_seed_mode (str, optional (default 'random')) – A string corresponding to the method used to seed an initial set of fiducial pairs in starting the greedy search routine. The default ‘random’ identifies the minimum number of fiducial pairs required for sensitivity to every parameter of a given germ and then randomly samples that number of fiducial pairs to use as an initial seed. Also supports the option ‘greedy’ in which case we start the greedy search from scratch using an empty seed set and select every fiducial pair greedily. Random is generally faster computationally, but greedy has been fount to often (but not always) find a smaller solution.

  • 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) of jacobians. If encountering an error related to failing Cholesky decompositions consider increasing the value of this tolerance.

  • sensitivity_threshold (float, optional (default 1e-10)) – Threshold used for determining is a fiducial pair is useless for measuring a given germ’s amplified parameters due to trivial sensitivity to the germ kite parameters (norm of jacobian w.r.t. the kite parameters is <sensitivity_threshold).

  • seed (int, optional) – The seed to use for generating random-pair-sets.

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

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

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