Driver functions for running Gate Set Tomography

The pygsti package provides multiple levels of abstraction over the core Gate Set Tomography (GST) algorithms. This tutorial will show you how to work with pyGSTi's top-level functions for performing GST with a minimial amount of effort. In order to run the GST protocol there are 3 essential ingredients: 1) data specifing the experimental outcomes, 2) a desired, or "target", Model, and 3) lists of Circuit objects, specifying the operation sequences to use at each successive step in the GST optimization. The GST overview tutorial, gave an end-to-end example of how to construct GST circuits, run GST, and generate a report. This tutorial focus on the second step in more detail; more information about circuit construction and report generation can be found in the GST circuits tutorial and report generation tutorial.

There are several different "driver routines" for running GST, and we'll cover in turn:

Each function returns a single pygsti.objects.Results object (see the Result object tutorial, which contains the single input DataSet and one or more estimates (pygsti.objects.Estimate objects).

Note: The abbreviation LSGST (lowercase in function names to follow Python naming conventions) stands for Long Sequence LinearOperator Set Tomography, and refers to the more powerful and flexible of GST that utilizes long sequences to find model estimates. LSGST can be compared to Linear GST, or LGST, which only uses short sequences and as a result provides much less accurate estimates.

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import pygsti


First, we set our desired target model to be the standard $I$, $X(\pi/2)$, $Y(\pi/2)$ model that we've been using in many of these tutorials, and use the standard fiducial and germ sequences needed to generate the GST operation sequences (see the standard module tutorial). We also specify a list of maximum lengths. We'll analyze the simulated data generated in the DataSet tutorial, so you'll need to run that tutorial if you haven't already.

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from pygsti.modelpacks import smq1Q_XYI
target_model = smq1Q_XYI.target_model()
prep_fiducials, meas_fiducials = smq1Q_XYI.prep_fiducials(), smq1Q_XYI.meas_fiducials()
germs = smq1Q_XYI.germs()

maxLengths = [1,2,4,8,16,32]

ds ="../tutorial_files/Example_Dataset.txt", cache=True)


This driver function finds what is logically a single GST estimate given a DataSet, a target Model, and other parameters. We say "logically" because the returned Results object may actually contain multiple related estimates in certain cases. Most important among the other parameters are the fiducial and germ sequences and list of maximum lengths needed to define a standard (prep_fiducial + germ^power + meas_fiducial) set of GST circuit lists.

In [ ]:
results = pygsti.do_long_sequence_gst(ds, target_model, prep_fiducials, meas_fiducials, germs, maxLengths)

A summary of what's inside a Results object is obtained by printing it (for more examples of how to use a Results object, see the Results tutorial).

In [ ]:

Beyond the minimum

The above example supplies the minimal amount of information required to run the long-sequence GST algorithm. do_long_sequence_gst can be used in a variety of contexts and accepts additional (optional) arguments that affect the way the algorithm is run. Here we make several remarks regarding alternate or more advanced usage of do_long_sequence_gst.

  • For many of the arguments, you can supply either a filename or a python object (e.g. dataset, target model, operation sequence lists), so if you find yourself loading things from files just to pass them in as arguments, you're probabaly working too hard.

  • Typically we want to apply certain constraints to a GST optimization. As mentioned in the model tutorial, the space over which a gate-set estimation is carried out is dictated by the parameterization of the target_model argument. For example, to constrain a GST estimate to be trace-preserving, one should call set_all_parameterizations("TP") on the target Model before calling do_long_sequence_gst. See the tutorial on explicit models for more information.

  • the gauge_opt_params argument specifies a dictionary of parameters ultimately to be passed to the gaugeopt_to_target function (which provides full documentation). By specifying an item_weights argument we can set the ratio of the state preparation and measurement (SPAM) weighting to the gate weighting when performing a gauge optimization. In the example below, the gate parameters are weighted 1000 times more relative to the SPAM parameters. Mathematically this corresponds to a multiplicative factor of 0.001 preceding the sum-of-squared-difference terms corresponding to SPAM elements in the model. Typically it is good to weight the gates parameters more heavily since GST amplifies gate parameter errors via long operation sequences but cannot amplify SPAM parameter errors. If unsure, 0.001 is a good value to start with. For more details on the arguments of gaugeopt_to_target, see the previous tutorial on low-level algorithms. For more infomation, see the gauge optimization tutorial.

The below call illustrates all three of these.

In [ ]:
mdl_target_TP = target_model.copy() #make a copy so we don't change target_model's parameterization, 
                                #  since this could be confusing later...
mdl_target_TP.set_all_parameterizations("TP") #constrain GST estimate to TP

results_TP = pygsti.do_long_sequence_gst("../tutorial_files/Example_Dataset.txt", mdl_target_TP,
                                         prep_fiducials, meas_fiducials, germs, maxLengths,
                                        gauge_opt_params={'item_weights': {'gates': 1.0, 'spam': 0.001}})


This function performs the same analysis as do_long_sequence_gst except it allows the user to fully specify the list of operation sequences as either a list of lists of Circuit objects or a list of or single CircuitStructure object(s). A CircuitStructure is preferable as it allows the structured plotting of the sequences in report figures. In this example, we'll just generate a standard set of structures, but with some of the sequences randomly dropped (see the tutorial on GST circuit reduction. Note that like do_long_sequence_gst, do_long_sequence_gst_base is able to take filenames as arguments and accepts a gauge_opt_params argument for customizing the gauge optimization that is performed.

In [ ]:
#Create the same sequences but drop 50% of them randomly for each repeated-germ block.
lsgst_structs =, prep_fiducials, meas_fiducials,
                                                       germs, maxLengths, keep_fraction=0.5, keep_seed=2018)
results_reduced = pygsti.do_long_sequence_gst_base(ds, target_model, lsgst_structs)


This function calls do_long_sequence_gst multiple times using typical variations in gauge optimization parameters and ExplicitOpModel parameterization (this doesn't work for other types Model objects, e.g. implicit models, which don't implement set_all_parameterizations). This function provides a clean and simple interface to performing a "usual" set of GST analyses on a set of data. As such, it takes a single DataSet, similar gate-sequence-specifying parameters to do_long_sequence_gst, and a new modes argument which is a comma-separated list of "canned" GST analysis types (e.g. "TP,CPTP" will compute a Trace-Preserving estimate and a Completely-Positive & Trace-Preserving estimate). The currently available modes are:

  • "full" : unconstrained gates (fully parameterized)
  • "TP" : TP-constrained gates and state preparations
  • "CPTP" : CPTP-constrained gates and TP-constrained state preparations
  • "H+S" : Only Hamiltonian and Pauli stochastic errors allowed (CPTP)
  • "S" : Only Pauli-stochastic errors allowed (CPTP)
  • "Target" : use the target (ideal) gates as the estimate

The gauge optimization(s) do_stdpractice_gst performs are controlled by its gauge_opt_suite and gaugeOptTarget arguments. The former is can be either a string, specifying a standard "suite" of gauge optimizations, or a dictionary of dictionaries similar to the gauge_opt_params argument of do_long_sequence_gst (see docstring). The gaugeOptTarget argument may be set to a Model that is used as the target for gauge optimization, overriding the (typically ideal) target gates given by the target_modelFilenameOrObj argument.

In [ ]:
results_stdprac = pygsti.do_stdpractice_gst(ds, target_model, prep_fiducials, meas_fiducials, germs, maxLengths,
                                        modes="TP,CPTP,Target") #uses the default suite of gauge-optimizations
In [ ]:
print("Estimates: ", ", ".join(results_stdprac.estimates.keys()))
print("TP Estimate's gauge optimized models: ", ", ".join(results_stdprac.estimates["TP"].goparameters.keys()))

Next, we'll perform the same analysis but with a non-default standard suite of gauge optimizations - this one toggles the SPAM penalty in addition to varying the spam weight (the default suite just varies the spam weight without any SPAM penalty). See the gauge optimization tutorial for more details on gauge optmization "suites".

In [ ]:
results_stdprac_nondefaultgo = pygsti.do_stdpractice_gst(
    ds, target_model, prep_fiducials, meas_fiducials, germs, maxLengths,
    modes="TP,CPTP,Target", gauge_opt_suite="varySpam")
In [ ]:
print("Estimates: ", ", ".join(results_stdprac_nondefaultgo.estimates.keys()))
print("TP Estimate's gauge optimized models: ", ", ".join(results_stdprac_nondefaultgo.estimates["TP"].goparameters.keys()))

Finally, we'll demonstrate how to specify a fully custom set of gauge optimization parameters and how to use a separately-specified target model for gauge optimization. You can get a more intuitive gauge-optimized Model when by placing as much expected noise as possible into the gauge-optimization target, as this essentially tells the algorithm "this is what I think the estimated model should look like". If you just use the perfect or ideal model for this (the default), then the gauge optimizer may make tradeoffs which don't reflect the expected physics (remember, all gauge-equivalent models product the same observables!). For example, it may spread error across all your gate operations when you expect just the 2-qubit operations are noisy.

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my_goparams = { 'item_weights': {'gates': 1.0, 'spam': 0.001} }
my_gaugeOptTarget = target_model.depolarize(op_noise=0.005, spam_noise=0.01) # a guess at what estimate should be
results_stdprac_customgo = pygsti.do_stdpractice_gst(
    ds, target_model, prep_fiducials, meas_fiducials, germs, maxLengths,
    modes="TP,CPTP,Target", gauge_opt_suite={ 'myGO': my_goparams }, gauge_opt_target=my_gaugeOptTarget)
In [ ]:
print("Estimates: ", ", ".join(results_stdprac_customgo.estimates.keys()))
print("TP Estimate's gauge optimized models: ", ", ".join(results_stdprac_customgo.estimates["TP"].goparameters.keys()))

To finish up, we'll pickle the results for processing in other tutorials.

In [ ]:
import pickle
pickle.dump(results, open('../tutorial_files/exampleResults.pkl',"wb"))
pickle.dump(results_TP, open('../tutorial_files/exampleResults_TP.pkl',"wb"))
pickle.dump(results_reduced, open('../tutorial_files/exampleResults_reduced.pkl',"wb"))
pickle.dump(results_stdprac, open('../tutorial_files/exampleResults_stdprac.pkl',"wb"))