08 QAOA Optimization Results
This notebook demonstrates the accessible information post QAOA optimization with the results object. The user can access different aspects of the optimization run through the results object.
Let’s start with a few import statements
[1]:
import networkx as nx
import numpy as np
from openqaoa.problems import MinimumVertexCover, NumberPartition, Knapsack
import matplotlib.pyplot as plt
from pprint import pprint
from openqaoa.backends import create_device, DeviceLocal
Problem Statement
We begin by creating the problem statement (and its subsequent translation into QUBO) to be optimized using QAOA. As an example, we consider the Knapsack problem class for this tutorial. The user can pass the following parameters to define a Knapsack problem: - Item values - Item weights - Knapsack weight capacity - Penalty coefficient
For this notebook, however, we create a problem instance using the random_instance method of the class
[2]:
kp_prob = Knapsack.random_instance(n_items=5, quantum=True,seed=1234)
kp_qubo = kp_prob.qubo
pprint(kp_qubo.asdict())
{'constant': 216.5,
'metadata': {},
'n': 9,
'problem_instance': {'n_items': 5,
'penalty': 8,
'problem_type': 'knapsack',
'values': [4, 4, 4, 2, 1],
'weight_capacity': 13,
'weights': [4, 1, 2, 1, 2]},
'terms': [[0, 1],
[0, 2],
[0, 3],
[1, 2],
[1, 3],
[2, 3],
[4, 5],
[4, 6],
[4, 7],
[8, 4],
[5, 6],
[5, 7],
[8, 5],
[6, 7],
[8, 6],
[8, 7],
[0, 4],
[0, 5],
[0, 6],
[0, 7],
[0, 8],
[1, 4],
[1, 5],
[1, 6],
[1, 7],
[8, 1],
[2, 4],
[2, 5],
[2, 6],
[2, 7],
[8, 2],
[3, 4],
[3, 5],
[3, 6],
[3, 7],
[8, 3],
[0],
[1],
[2],
[3],
[4],
[5],
[6],
[7],
[8]],
'weights': [8.0,
16.0,
32.0,
32.0,
64.0,
128.0,
16.0,
32.0,
16.0,
32.0,
8.0,
4.0,
8.0,
8.0,
16.0,
8.0,
16.0,
4.0,
8.0,
4.0,
8.0,
32.0,
8.0,
16.0,
8.0,
16.0,
64.0,
16.0,
32.0,
16.0,
32.0,
128.0,
32.0,
64.0,
32.0,
64.0,
4.0,
8.0,
16.0,
32.0,
18.0,
6.0,
10.0,
5.0,
8.5]}
Optimization using OpenQAOA
We perform the usual steps of: - creating and configuring the QAOA model - compiling the model with the problem statement - optimizing the problem
[3]:
from openqaoa import QAOA
[4]:
q = QAOA()
q.set_circuit_properties(p=3, init_type='ramp')
q.compile(kp_qubo)
[5]:
q.optimize()
Access the results object
Once the optimization process terminates, the user has access to information on the optimization process. This can be accessed in the form of a Result object, by calling the .results attribute of the model post optimization.
[6]:
result = q.result
[7]:
result.most_probable_states
[7]:
{'solutions_bitstrings': ['000100000'], 'bitstring_energy': 200.0}
Re-run the problem with a different backend: Qiskit statevector_simulator
Using the qiskit statevector simulator as the backend, we repeat the optimization. One of the fields of the results object is the data stored on the measurement outcomes of the intermediate circuit executions during the optimization process. The user has access to either the intermediate statevectors if using a statevector_simulator backend, or counts_dictionaries if using shot-based simulators or real QPUs. The size of these dictionaries will be proportional to the n_shots used.
Since this feature may require storage of large data objects, this feature is turned OFF by default. The user can switch this ON by configuring the QAOA model by passing the optimization_progress boolean as True. Apart from the measurement_outcomes, the results object also stores the intermediate results (comprising of the angle log) and the optimized results.
[8]:
q_qiskit_sv = QAOA()
qiskit_dev = create_device(location='local',name='qiskit.statevector_simulator')
q_qiskit_sv.set_device(qiskit_dev)
[9]:
q_qiskit_sv.compile(kp_qubo)
[10]:
q_qiskit_sv.optimize()
[11]:
qiskit_results = q_qiskit_sv.result
[12]:
qiskit_results.most_probable_states
[12]:
{'solutions_bitstrings': ['000110000'], 'bitstring_energy': 4.0}
[13]:
qiskit_results.evals
[13]:
{'number_of_evals': 29, 'jac_evals': 0, 'qfim_evals': 0}
[14]:
qiskit_results.intermediate
[14]:
{'angles': [[0.35, 0.35],
[1.35, 0.35],
[1.35, 1.35],
[1.822370451816, -0.531400111329],
[1.586185225908, -0.090700055665],
[1.107374603994, 0.289726314092],
[0.874986723481, 0.197553254086],
[1.061288073991, 0.405920254349],
[1.356749567622, 0.27205918316],
[1.232062085808, 0.280892748626],
[1.067097208615, 0.241935295883],
[1.138417610573, 0.28613545869],
[1.085761155786, 0.312296678656],
[1.097653929758, 0.277493198488],
[1.114323922504, 0.293295925906],
[1.121078540299, 0.289370331086],
[1.114212406068, 0.301107629967],
[1.116886829692, 0.290347995138],
[1.112660388281, 0.292272524149],
[1.11071674546, 0.292080300711],
[1.112904142973, 0.290334669429],
[1.112590602338, 0.293246589977],
[1.112725510973, 0.291788605133],
[1.112902347789, 0.292305085495],
[1.112850690299, 0.292790626515],
[1.112940982498, 0.292064021179],
[1.112895403108, 0.29240484406],
[1.112952227072, 0.292308557835],
[1.112967290836, 0.292209698931]],
'cost': [215.55245864841,
208.588874735772,
221.582286182776,
212.62173527352,
215.216018459443,
179.815570626776,
313.36769175789,
211.934595122054,
218.217638222992,
219.781419765252,
198.565209954299,
247.560664098383,
197.159286442288,
207.518056913936,
128.097355833634,
188.036080217214,
293.554491742425,
154.509608519926,
107.576203467122,
108.893427313291,
156.196908347037,
126.258690107777,
112.040420605493,
107.514186284575,
112.440380627188,
108.475984285951,
107.746629951845,
107.504668550891,
107.631894060712],
'measurement_outcomes': [],
'job_id': ['12dad73d-50f7-42ff-be85-5b9d013e210e',
'1f47131e-7ab1-4af1-83ff-6a2c4c8e8424',
'620afba1-b65f-48cb-806a-f9fb26a6c347',
'9d637f51-f619-4251-9787-80cc720647ca',
'af4290ab-4ee8-4b5f-bb3f-f700df02976e',
'21e42777-b18e-495f-addd-63967c114873',
'f7d42e4a-52e1-4ec3-a160-4d5cc835e73d',
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'1f0dd9dc-5275-4671-8a43-67813de6bf54',
'31d6f2e6-018e-45bc-9af7-88f8202d23ce',
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'c7bf23f3-eb80-4944-865a-5f5d889c7f6b',
'5fc48189-ff9c-4d27-87db-36558992cac7',
'19bdb8cf-747a-471b-b366-a9ea98bd64d3',
'b69d322d-84ba-4930-bf8b-77c7411ede1d',
'7752ec27-3c09-41af-bc10-c9790a62becf',
'b3e5ec62-e1f3-46bf-9948-84337a2bdca0',
'9256efc8-716a-4cf0-865e-e77d70711ff9',
'ea4071e6-c452-4e92-bf23-a5f21c228ed7',
'911df042-75c4-4199-bdbb-5ee948899dda',
'763cc6b1-f1f5-4074-b68d-e3b7c73fa8de',
'7d92cabb-063a-449c-89d2-84ef977a9f43',
'13590efa-e3bd-4386-a704-403c356bf128',
'992165ff-296e-4548-9a04-5d46d3fac7f4',
'5f6cdbb7-bf2a-45d9-a7ba-4a52a6d02e6c']}
[15]:
qiskit_results.optimized
[15]:
{'angles': [1.112952227072, 0.292308557835],
'cost': 107.504668550891,
'measurement_outcomes': array([-2.45038508e-02-1.31208386e-02j, -7.82037753e-03+2.95082418e-03j,
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'job_id': '992165ff-296e-4548-9a04-5d46d3fac7f4',
'eval_number': 28}
Qiskit shot simulator
Changing the backend again from a statevector_simulator backend to a shot-based backend, we can observe that the measurement outcome field is now populated by the counts_dictionary for n_shots executions.
[16]:
q_qiskit_shot = QAOA()
qiskit_shot_dev = create_device(location='local',name='qiskit.shot_simulator')
q_qiskit_shot.set_device(qiskit_shot_dev)
[17]:
q_qiskit_shot.compile(kp_qubo)
[18]:
q_qiskit_shot.optimize()
[19]:
q_qiskit_shot.result.most_probable_states
[19]:
{'solutions_bitstrings': ['001010101'], 'bitstring_energy': -1.0}
[20]:
q_qiskit_shot.result.evals
[20]:
{'number_of_evals': 32, 'jac_evals': 0, 'qfim_evals': 0}
[21]:
q_qiskit_shot.result.intermediate
[21]:
{'angles': [[0.35, 0.35],
[1.35, 0.35],
[1.35, 1.35],
[2.324458067551, 0.125430468262],
[1.837229033775, 0.237715234131],
[1.101931527088, 0.318983347263],
[1.383636915456, 0.597726780786],
[1.440801226771, 0.264092274987],
[1.287975879197, 0.342302049713],
[1.253262993197, 0.394275750231],
[1.291178419716, 0.279884153768],
[1.264218964736, 0.362604057379],
[1.250153929013, 0.390509921819],
[1.267486781435, 0.416512512592],
[1.219002511228, 0.38802966579],
[1.256235030568, 0.404903004493],
[1.242598810677, 0.388521117358],
[1.254186882112, 0.383818849741],
[1.24986035388, 0.394405124343],
[1.248402501753, 0.389645514613],
[1.251078496133, 0.388789493702],
[1.252052813741, 0.388723315794],
[1.250302532733, 0.388196572866],
[1.249600564869, 0.387517665336],
[1.250073715081, 0.388627920825],
[1.249906622095, 0.389086721994],
[1.250289389061, 0.388742329651],
[1.249621135127, 0.388444645175],
[1.250237260217, 0.388809187572],
[1.249978733621, 0.388596639486],
[1.250089355751, 0.388580430095],
[1.250074486964, 0.388727917846]],
'cost': [240.6,
201.33,
210.38,
279.79,
235.58,
249.37,
245.42,
256.21,
188.7,
339.05,
201.58,
171.4,
99.62,
217.22,
150.74,
205.06,
124.83,
223.86,
376.61,
104.87,
96.39,
104.04,
85.05,
99.54,
67.43,
82.27,
152.7,
113.78,
112.77,
91.99,
103.77,
119.62],
'measurement_outcomes': [],
'job_id': ['d4a3a48f-5f58-4fff-952e-693a2b836e0a',
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'd903af21-d7cc-4c6c-9cf6-bd90466f2cc9',
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'59723079-acb4-4042-a940-b221f565188a',
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'2945a017-b154-48b6-84ff-359ad45c6933',
'5db56541-e674-4d8f-9a10-f3bff80dd67f',
'9831ed3b-2308-44e6-a0b8-a4b496c60dd6',
'80fc2ec8-b23f-4eae-a9c8-743445744b62',
'89418050-bf68-437b-906c-d1ce779c604d']}
[22]:
q_qiskit_shot.result.optimized
[22]:
{'angles': [1.250073715081, 0.388627920825],
'cost': 67.43,
'measurement_outcomes': {'000110110': 1,
'110011101': 1,
'010110010': 1,
'101000101': 1,
'100011101': 1,
'100111100': 1,
'011011001': 1,
'100101110': 1,
'001110000': 1,
'101000111': 1,
'101110110': 1,
'110100101': 1,
'111000101': 2,
'100110100': 3,
'101011111': 1,
'010110001': 3,
'110010001': 2,
'100110000': 3,
'101100100': 2,
'111010011': 1,
'000111000': 1,
'101010101': 1,
'001100110': 1,
'100101101': 1,
'100010111': 1,
'001010111': 1,
'110110000': 1,
'000111100': 1,
'011000110': 1,
'001010100': 2,
'010010111': 1,
'001010110': 2,
'010101001': 1,
'010110000': 1,
'000110111': 2,
'011000001': 1,
'111010111': 1,
'011010000': 1,
'110101110': 1,
'000010110': 1,
'001010101': 4,
'011001001': 1,
'010010101': 3,
'100111110': 1,
'110010110': 1,
'101110111': 1,
'010100101': 2,
'100010101': 1,
'000010101': 1,
'001100101': 3,
'010010100': 1,
'000110101': 2,
'000111101': 1,
'000111110': 1,
'001101100': 1,
'111010100': 1,
'110010101': 2,
'010100100': 1,
'000000011': 1,
'101001101': 1,
'111100001': 1,
'011100100': 2,
'111100000': 1,
'011100001': 1,
'011010101': 1,
'110111100': 1,
'010011111': 2,
'000110100': 1,
'111010110': 1,
'100110101': 1,
'101011001': 1,
'100010011': 1,
'011010100': 2,
'110010100': 1,
'101011101': 1},
'job_id': 'f34039f5-da2f-484e-8865-feb9a34eafe2',
'eval_number': 25}
[23]:
fig, ax = q_qiskit_shot.result.plot_cost()
[ ]: