# Model Testing¶

This tutorial covers different methods of comparing data to given (fixed) QIP models. This is distinct from model-based tomography, which finds the best-fitting model for a data set within a space of models set by a Model object's parameterization. You might use this as a tool alongside or separate from GST. Perhaps you suspect that a given noisy QIP model is compatible with your data - model testing is the way to find out. Because there is no optimization involved, model testing requires much less time than GST does, and doens't place any requirements on which circuits are used in performing the test (though some circuits will give a more precise result).

## Setup¶

First, after some usual imports, we'll create some test data based on a depolarized and rotated version of a standard 1-qubit model consisting of $I$ (the identity), $X(\pi/2)$ and $Y(\pi/2)$ gates. Here we just use a set of standard GST circuits.

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from __future__ import division, print_function

import pygsti
import numpy as np
import scipy
from scipy import stats
from pygsti.modelpacks import smq1Q_XYI

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datagen_model = smq1Q_XYI.target_model().depolarize(op_noise=0.05, spam_noise=0.1).rotate((0.05,0,0.03))
exp_design = smq1Q_XYI.get_gst_experiment_design(max_max_length=64)
ds = pygsti.construction.simulate_data(datagen_model, exp_design.all_circuits_needing_data,
num_samples=1000, sample_error='binomial', seed=100)
data = pygsti.protocols.ProtocolData(exp_design, ds)


## Step 1: Construct a test model¶

After we have some data, the first step is creating a model or models that we want to test. This just means creating a Model object containing the operations (including SPAM) found in the data set. We'll create several models that are meant to look like guesses (some including more types of noise) of the true underlying model.

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target_model = smq1Q_XYI.target_model()
test_model1 = target_model.copy()
test_model2 = target_model.depolarize(op_noise=0.07, spam_noise=0.07)
test_model3 = target_model.depolarize(op_noise=0.07, spam_noise=0.07).rotate( (0.02,0.02,0.02) )


## Step 2: Test it!¶

There are three different ways to test a model. Note that in each case the default behavior (and the only behavior demonstrated here) is to never gauge-optimize the test Model. (Whenever gauge-optimized versions of an Estimate are useful for comparisons with other estimates, copies of the test Model are used without actually performing any modification of the original Model.)

### Method1: the ModelTest protocol¶

The most straightforward way to perform model testing is using the ModelTest protocol. This is invoked similarly to other protocols: you create a protocol object and .run() it on a ProtocolData object. This returns a ModelEstimateResults object, similarly to the GateSetTomography and StandardGST protocols. The "estimateLabel" advanced option names the Estimate within the returned results, and can be particularly useful when testing multiple models.

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# creates a Results object with a "model1" estimate
results = pygsti.protocols.ModelTest(test_model1, name='model1').run(data)

# creates a Results object with a "model2" estimate
results2 = pygsti.protocols.ModelTest(test_model2, name='model2').run(data)

# creates a Results object with a "model3" estimate
results3 = pygsti.protocols.ModelTest(test_model3, name='model3').run(data)


Like any other set of ModelEstimateResults objects which share the same underlying ProtocolData object, we can collect all of these estimates into a single ModelEstimateResults object and easily make a report containing all three.

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results.add_estimates(results2)

pygsti.report.construct_standard_report(
results, title="Model Test Example Report", verbosity=1
).write_html("../tutorial_files/modeltest_report", auto_open=True, verbosity=1)


### Method 2: add_model_test¶

Alternatively, you can add a model-to-test to an existing ModelEstimateResults object. This is convenient when running GST via GateSetTomography or StandardGST has left you with a ModelEstimateResults object and you also want to see how well a hand-picked model fares. Since the results object already contains a ProtocolData, all you need to do is provide a Model. This is accomplished using the add_model_test method of a ModelEstimateResults object.

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#Create some GST results using standard practice GST
gst_results = pygsti.protocols.StandardGST().run(data)

#Create a report to see that we've added an estimate labeled "MyModel3"
pygsti.report.construct_standard_report(
gst_results, title="GST with Model Test Example Report 1", verbosity=1
).write_html("../tutorial_files/gstwithtest_report1", auto_open=True, verbosity=1)


### Method 3: modelToTest argument¶

Finally, yet another way to perform model testing alongside GST is by using the models_to_test argument of the StandardGST protocol. This essentially combines calls to StandardGST.run and ModelEstimateResults.add_model_test (demonstrated above) with the added control of being able to specify the ordering of the estimates via the modes argument. Two important remarks are in order:

1. You must specify the names (keys of the models_to_test argument) of your test models in the comma-delimited string that is the modes argument. Just giving a dictionary of Models as models_to_test will not automatically test those models in the returned ModelEstimateResults object.

2. You don't actually need to run any GST modes, and can use StandardGST in this way to in one call create a single ModelEstimateResults object containing multiple model tests, with estimate names that you specify. Thus, running StandardGST can replace running ModelTest multiple tiems (with "estimateLabel" advanced options) followed by collecting the estimates using ModelEstimateResults.add_estimates demonstrated under "Method 1" above.

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proto = pygsti.protocols.StandardGST(modes="TP,Test2,Test3,Target", # You MUST put Test2 and Test3 here...
models_to_test={'Test2': test_model2, 'Test3': test_model3})
gst_results = proto.run(data)

pygsti.report.construct_standard_report(
gst_results, title="GST with Model Test Example Report 2", verbosity=1
).write_html("../tutorial_files/gstwithtest_report2", auto_open=True, verbosity=1)


Thats it! Now that you know more about model-testing you may want to go back to the overview of pyGST protocls.

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