Making sense of the result

You have just ran the simples QAOA workflow and now it is time to make sense of what just happened.

from openqaoa import QAOA  

q = QAOA()
q.compile(qubo_problem)
q.optimize()

A QAOA workflow is composed by 4 parts. this example, we have used the default values:

• the circuit ansats a 1-layer qaoa, with the standard parametrisation and the x mixer
• the classical optimizer cobyla, as implemented by the folks at SciPy
• the device employed vectorized, a very fast numpy-based QAOA simulator developed by Entropica Labs
• the result of the algorithm

The result object

Result is a class attribute of the object q, and its chief role is that of keeping a record of the steps behind the workflow.

In particular, there are three main attributes of the result object:

The optimized result

Evaluating

q.result.optimized

yields

{'angles': [0.35361247886982217, 0.383757626934605],
 'cost': 14.175868570032316,
 'measurement_outcomes': array([ 0.01401859-0.05426676j,  0.01930903-0.05959513j,
         0.01930903-0.05959513j,  0.06267756+0.02087j   ,
         ...,
         0.05136043-0.02452211j,  0.1342158 -0.01110605j]),
 'job_id': 'db3e0180-9bd7-40c8-b1a4-91d6d08e1ec8',
 'eval_number': 32}

Let's unpack it:

• angles : these are the optimized \({\gamma, \beta}\). we have only 2, because when the number of layers is 1 (that is, p=1) and the parametrization is standard we obtain (that is, param_type=standard) we have just two parameters.
• cost : this is the cost value obtained when the angles are plugged into the cost function.
• measurement_outcomes : represent either the wavefunction or the measurement count for the optimized state. In this case we used a wavefunction simulator, and the measurement_outcomes corresponds to a \(2^n\) complex numbers.
• job_id : the job id representing the optimized measurement outcomes. This is the job id returned by the cloud provider, if a QOU was used.
• eval_number : identify the index of the optimized state with respect to all the intermediate results stored in the optimization loop

The intermediate result

Evaluating

q.result.intermediate

yields

{'angles': [[0.35, 0.35],
  ...,
 [0.3540879842708628, 0.38463733973636544]],
 'cost': [15.412157445012767,
 ...,
 14.176027938975054],
 'measurement_outcomes': [],
 'job_id': ['e65d41ee-1775-46b8-abcb-4764949da1ea',
  ...,
  '5c80c9f8-02d0-45be-8c50-bd4e93b54c3b']}

Let's unpack it:

• angles : these are the \({\gamma, \beta}\) belonging to the i-th intermediate result within the optimization loop
• cost : the list of costs recorded during the optimization
• measurement_outcomes : the (empty) list of measurement outcomes. Recording all the intermediate results is switched off by default
• job_id : the list of job_ids corresponding to each cost evaluation

Plotting the cost function

OpenQAOA features some helper function to extract some common plots

q.result.plot_cost()

Indeed, from the plot we can see that:

1. The lowest cost was around the value of 14,
2. The optimizer stopped after around 30 iterations