Pular para o conteúdo principal

Exemplos de primitivas

Novo modelo de execução, agora em versão beta

A versão beta de um novo modelo de execução já está disponível. O modelo de execução direcionada oferece mais flexibilidade para personalizar seu fluxo de mitigação de erros. Consulte o guia Modelo de execução direcionada para mais informações.

Versões dos pacotes

O código nesta página foi desenvolvido usando os requisitos a seguir. Recomendamos usar essas versões ou mais recentes.

qiskit[all]~=2.3.0
qiskit-ibm-runtime~=0.43.1

Os exemplos nesta seção ilustram algumas formas comuns de usar primitivas. Antes de executar esses exemplos, siga as instruções em Instalar e configurar.

nota

Todos esses exemplos utilizam as primitivas do Qiskit Runtime, mas você pode usar as primitivas base no lugar delas.

Exemplos com o Estimator​

Calcule e interprete com eficiência os valores esperados dos operadores quânticos necessários para muitos algoritmos com o Estimator. Explore usos em modelagem molecular, aprendizado de máquina e problemas de otimização complexos.

Executar um único experimento​

Use o Estimator para determinar o valor esperado de um único par circuito-observável.

# Added by doQumentation — required packages for this notebook
!pip install -q numpy qiskit qiskit-ibm-runtime
import numpy as np
from qiskit.circuit.library import iqp
from qiskit.transpiler import generate_preset_pass_manager
from qiskit.quantum_info import SparsePauliOp, random_hermitian
from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2 as Estimator

n_qubits = 50

service = QiskitRuntimeService()
backend = service.least_busy(
    operational=True, simulator=False, min_num_qubits=n_qubits
)

mat = np.real(random_hermitian(n_qubits, seed=1234))
circuit = iqp(mat)
observable = SparsePauliOp("Z" * 50)

pm = generate_preset_pass_manager(backend=backend, optimization_level=1)
isa_circuit = pm.run(circuit)
isa_observable = observable.apply_layout(isa_circuit.layout)

estimator = Estimator(mode=backend)
job = estimator.run([(isa_circuit, isa_observable)])
result = job.result()

print(f" > Expectation value: {result[0].data.evs}")
print(f" > Metadata: {result[0].metadata}")
> Expectation value: -0.13582342954159593
 > Metadata: {'shots': 4096, 'target_precision': 0.015625, 'circuit_metadata': {}, 'resilience': {}, 'num_randomizations': 32}

Executar múltiplos experimentos em um único job​

Use o Estimator para determinar os valores esperados de múltiplos pares circuito-observável.

import numpy as np
from qiskit.circuit.library import iqp
from qiskit.transpiler import generate_preset_pass_manager
from qiskit.quantum_info import SparsePauliOp, random_hermitian
from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2 as Estimator

n_qubits = 50

service = QiskitRuntimeService()
backend = service.least_busy(
    operational=True, simulator=False, min_num_qubits=n_qubits
)

rng = np.random.default_rng()
mats = [np.real(random_hermitian(n_qubits, seed=rng)) for _ in range(3)]

pubs = []
circuits = [iqp(mat) for mat in mats]
observables = [
    SparsePauliOp("X" * 50),
    SparsePauliOp("Y" * 50),
    SparsePauliOp("Z" * 50),
]

# Get ISA circuits
pm = generate_preset_pass_manager(optimization_level=1, backend=backend)

for qc, obs in zip(circuits, observables):
    isa_circuit = pm.run(qc)
    isa_obs = obs.apply_layout(isa_circuit.layout)
    pubs.append((isa_circuit, isa_obs))

estimator = Estimator(backend)
job = estimator.run(pubs)
job_result = job.result()

for idx in range(len(pubs)):
    pub_result = job_result[idx]
    print(f">>> Expectation values for PUB {idx}: {pub_result.data.evs}")
    print(f">>> Standard errors for PUB {idx}: {pub_result.data.stds}")
>>> Expectation values for PUB 0: 0.4873096446700508
>>> Standard errors for PUB 0: 1.3528950031716114
>>> Expectation values for PUB 1: -0.00390625
>>> Standard errors for PUB 1: 0.015347884419435263
>>> Expectation values for PUB 2: -0.02001953125
>>> Standard errors for PUB 2: 0.013797455737635134

Executar circuitos parametrizados​

Use o Estimator para executar três experimentos em um único job, aproveitando valores de parâmetros para aumentar a reutilização dos circuitos.

import numpy as np

from qiskit.circuit import QuantumCircuit, Parameter
from qiskit.quantum_info import SparsePauliOp
from qiskit.transpiler import generate_preset_pass_manager
from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2 as Estimator

service = QiskitRuntimeService()
backend = service.least_busy(operational=True, simulator=False)

# Step 1: Map classical inputs to a quantum problem
theta = Parameter("θ")

chsh_circuit = QuantumCircuit(2)
chsh_circuit.h(0)
chsh_circuit.cx(0, 1)
chsh_circuit.ry(theta, 0)

number_of_phases = 21
phases = np.linspace(0, 2 * np.pi, number_of_phases)
individual_phases = [[ph] for ph in phases]

ZZ = SparsePauliOp.from_list([("ZZ", 1)])
ZX = SparsePauliOp.from_list([("ZX", 1)])
XZ = SparsePauliOp.from_list([("XZ", 1)])
XX = SparsePauliOp.from_list([("XX", 1)])
ops = [ZZ, ZX, XZ, XX]

# Step 2: Optimize problem for quantum execution.

pm = generate_preset_pass_manager(backend=backend, optimization_level=1)
chsh_isa_circuit = pm.run(chsh_circuit)
isa_observables = [
    operator.apply_layout(chsh_isa_circuit.layout) for operator in ops
]

# Step 3: Execute using Qiskit primitives.

# Reshape observable array for broadcasting
reshaped_ops = np.fromiter(isa_observables, dtype=object)
reshaped_ops = reshaped_ops.reshape((4, 1))

estimator = Estimator(backend, options={"default_shots": int(1e4)})
job = estimator.run([(chsh_isa_circuit, reshaped_ops, individual_phases)])
# Get results for the first (and only) PUB
pub_result = job.result()[0]
print(f">>> Expectation values: {pub_result.data.evs}")
print(f">>> Standard errors: {pub_result.data.stds}")
print(f">>> Metadata: {pub_result.metadata}")
>>> Expectation values: [[ 1.0455093   0.98152862  0.82113463  0.60354133  0.29572641  0.01149883
  -0.33110743 -0.60560522 -0.83322315 -0.96531231 -1.0257549  -0.95853095
  -0.81081517 -0.61091237 -0.30221293  0.0035381   0.31371176  0.61061753
   0.83646641  0.97091431  1.03135689]
 [ 0.03390682  0.31194271  0.620937    0.87391133  0.96973494  1.03872794
   0.94260949  0.82378821  0.56344283  0.28688115 -0.04570049 -0.37474403
  -0.64540887 -0.87803912 -0.97887504 -1.03577952 -0.97268336 -0.83970967
  -0.59705481 -0.29867482  0.0380346 ]
 [ 0.00265358 -0.32992806 -0.59646512 -0.80934096 -0.96737621 -1.00128302
  -0.94673728 -0.82703147 -0.59705481 -0.31341692 -0.00117937  0.29985419
   0.59469607  0.78486908  0.93346939  0.97622146  0.94732696  0.81199454
   0.60914332  0.28393273 -0.00678136]
 [ 0.99656555  0.93553328  0.78398456  0.55872536  0.29749546 -0.04511081
  -0.33523522 -0.62889773 -0.82201916 -0.95351864 -1.02634458 -0.96796589
  -0.82054495 -0.57553135 -0.30103356  0.00265358  0.3104685   0.59705481
   0.83322315  0.94437854  0.99214292]]
>>> Standard errors: [[0.014353   0.01441151 0.01620648 0.0195418  0.019762   0.01515649
  0.02102523 0.02112359 0.0148494  0.01119219 0.01576623 0.01245824
  0.01239832 0.01501273 0.01821305 0.01776286 0.01500156 0.01635231
  0.01577367 0.01315371 0.01089558]
 [0.01352805 0.01627835 0.01247646 0.01287866 0.01570182 0.01060924
  0.01590468 0.01620303 0.01530626 0.01619973 0.01918078 0.01379676
  0.01564971 0.01377673 0.01454324 0.01242184 0.01252201 0.01396738
  0.01326188 0.0145736  0.01795044]
 [0.02029376 0.01610892 0.0161542  0.0157785  0.01385665 0.01113743
  0.01375237 0.01380922 0.0145974  0.01759484 0.01594193 0.02111719
  0.01521368 0.01365888 0.01188512 0.01353009 0.01195674 0.01446547
  0.01660987 0.01511225 0.01880871]
 [0.01105161 0.01164476 0.01329858 0.01439545 0.01888747 0.01629201
  0.01405852 0.01406643 0.01088709 0.01275198 0.01281432 0.01333301
  0.01268483 0.01443594 0.01495655 0.01715532 0.01822699 0.01508936
  0.01435528 0.01340555 0.01295649]]
>>> Metadata: {'shots': 10016, 'target_precision': 0.01, 'circuit_metadata': {}, 'resilience': {}, 'num_randomizations': 32}

Usar sessões e opções avançadas​

Explore sessões e opções avançadas para otimizar o desempenho dos circuitos em QPUs.

cuidado

O bloco de código a seguir retornará um erro para usuários do Plano Open porque ele usa sessões. As cargas de trabalho do Plano Open só podem ser executadas no modo de job ou no modo de lote.

import numpy as np
from qiskit.circuit.library import iqp
from qiskit.transpiler import generate_preset_pass_manager
from qiskit.quantum_info import SparsePauliOp, random_hermitian
from qiskit_ibm_runtime import (
    QiskitRuntimeService,
    Session,
    EstimatorV2 as Estimator,
)

n_qubits = 50

service = QiskitRuntimeService()
backend = service.least_busy(
    operational=True, simulator=False, min_num_qubits=n_qubits
)

rng = np.random.default_rng(1234)
mat = np.real(random_hermitian(n_qubits, seed=rng))
circuit = iqp(mat)
mat = np.real(random_hermitian(n_qubits, seed=rng))
another_circuit = iqp(mat)
observable = SparsePauliOp("X" * 50)
another_observable = SparsePauliOp("Y" * 50)

pm = generate_preset_pass_manager(optimization_level=1, backend=backend)
isa_circuit = pm.run(circuit)
another_isa_circuit = pm.run(another_circuit)
isa_observable = observable.apply_layout(isa_circuit.layout)
another_isa_observable = another_observable.apply_layout(
    another_isa_circuit.layout
)

with Session(backend=backend) as session:
    estimator = Estimator(mode=session)

    estimator.options.resilience_level = 1

    job = estimator.run([(isa_circuit, isa_observable)])
    another_job = estimator.run(
        [(another_isa_circuit, another_isa_observable)]
    )
    result = job.result()
    another_result = another_job.result()

    # first job
    print(f" > Expectation value: {result[0].data.evs}")
    print(f" > Metadata: {result[0].metadata}")

    # second job
    print(f" > Another Expectation value: {another_result[0].data.evs}")
    print(f" > More Metadata: {another_result[0].metadata}")
> Expectation value: 0.08045977011494253
 > Metadata: {'shots': 4096, 'target_precision': 0.015625, 'circuit_metadata': {}, 'resilience': {}, 'num_randomizations': 32}
 > Another Expectation value: 0.02127659574468085
 > More Metadata: {'shots': 4096, 'target_precision': 0.015625, 'circuit_metadata': {}, 'resilience': {}, 'num_randomizations': 32}

Exemplos com o Sampler​

Gere distribuições completas de quase-probabilidade com mitigação de erros, amostradas a partir das saídas de circuitos quânticos. Aproveite as capacidades do Sampler para algoritmos de busca e classificação como o de Grover e o QVSM.

Executar um único experimento​

Use o Sampler para retornar os resultados de medição como bitstrings ou contagens de um único circuito.

import numpy as np
from qiskit.circuit.library import iqp
from qiskit.transpiler import generate_preset_pass_manager
from qiskit.quantum_info import random_hermitian
from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2 as Sampler

n_qubits = 127

service = QiskitRuntimeService()
backend = service.least_busy(
    operational=True, simulator=False, min_num_qubits=n_qubits
)

mat = np.real(random_hermitian(n_qubits, seed=1234))
circuit = iqp(mat)
circuit.measure_all()

pm = generate_preset_pass_manager(backend=backend, optimization_level=1)
isa_circuit = pm.run(circuit)

sampler = Sampler(backend)
job = sampler.run([isa_circuit])
result = job.result()

# Get results for the first (and only) PUB
pub_result = result[0]

print(f" > First ten results: {pub_result.data.meas.get_bitstrings()[:10]}")
> First ten results: ['0101110000110001001111000101001111000110110100011000100101011101110011010010010101000110000111101010101000001010000100100000100', '0100010101111101010000100010011100110001010000011000000010001100010111000011001010000100100000100000000010000000010010101011110', '1101010111111111100010000011101010101010100100011001000000001001110010001000000010000010000101000111000100010010000001111000010', '1001110001100001001101111010111100000100010110010001001100111000110010111000001010001000000000000000100101101001110010101000110', '0001000000011011000011000111001000000000100110110011111110110100110000101010100010000010101011011000101011101000100000110000011', '1011100010011111010000001110110000111101000001110010011001100011111010001100100000110001000010001010110011100010000111000111010', '1101110000011000001011011000001111001110010111111111100100010001110100000010000001011000110000000011010011110100101001101000010', '0110100000110011000011001000110110110001000100100001111010001101000001010111000000101010101000001110100100001010110001000100101', '1000011010011011001111010010100000001110010010100000011010000110011010100000111000010010100111000001100101100010110010101001010', '1011011100111001010010101001000111000001110011110011001111010100100011101111011101011000000111011010000011100011010000001000000']

Executar múltiplos experimentos em um único job​

Use o Sampler para retornar os resultados de medição como bitstrings ou contagens de múltiplos circuitos em um único job.

import numpy as np
from qiskit.circuit.library import iqp
from qiskit.transpiler import generate_preset_pass_manager
from qiskit.quantum_info import random_hermitian
from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2 as Sampler

n_qubits = 127

service = QiskitRuntimeService()
backend = service.least_busy(
    operational=True, simulator=False, min_num_qubits=n_qubits
)

rng = np.random.default_rng()
mats = [np.real(random_hermitian(n_qubits, seed=rng)) for _ in range(3)]
circuits = [iqp(mat) for mat in mats]
for circuit in circuits:
    circuit.measure_all()

pm = generate_preset_pass_manager(backend=backend, optimization_level=1)
isa_circuits = pm.run(circuits)

sampler = Sampler(mode=backend)
job = sampler.run(isa_circuits)
result = job.result()

for idx, pub_result in enumerate(result):
    print(
        f" > First ten results for pub {idx}: {pub_result.data.meas.get_bitstrings()[:10]}"
    )
> First ten results for pub 0: ['1000000101000100010111001010101010000001001010101011011001011110001000000110110101010000010000000000110001001000011111110000001', '1111101011011011110001011000001100001101100001000101111011101110000101111010001011111010001001000010111001110111000010001011010', '1100100101110010000110101011110010111001101010001101100010110100110110000110110010001110001000001010011100001000011011000111010', '1100010010000100100010110100011010011001010101101101101001100001001110011001011011111100011100100001000101010000111101110001101', '0011101011101100010011111001001110000101100110000110000001111000011010011110000110100000110011011000000010110001010000111000100', '0110101101110000010110100100010011000100100010000010010010110001111111110000101011000100010000000100100100110011010111101110111', '1101011000111100011000010110000010001100101011000001110010110001111101010101011110110010000100011101000001010110010101000000100', '0000101010010100000010111110111000001011000000001011000110100010110011111000110110010110011010111101001011000000001101001110110', '1100101000110001000011111110010001011000010110010101101000000101011110000100011011111011011010001001110011011101001101010100000', '0110011000101110101001010100110010101000010111100001000111011000110101011010010101110011001010101000001001001000110010100010101']
 > First ten results for pub 1: ['1100100001011010010100000110101010100111101100110000100001011000100010001101010101101110000011010010011000010000010001000001000', '1100000011000000100110011000000110010000011111000000001010000101000010011001000001010000001000001010001000110010111000010000000', '0010000111101000111010101010101001010000001110100001011011100011000111000000010101001000010101001100000010100010011000000000010', '0010100100001000011100001010011000001010000010001000000001011100001010001110010110111101101000001101010101000000000011000100110', '0101101000011110111000100010000000101110100001010101110010001100001100001000111111110101001010100110000000010011111111000000010', '0101010111000000001110100110100011010111000111110100010010010001011010001000101001100001100110001001001000010010000011100100000', '0110010000001110111010010100010010010011010010110101001110010010001001101010111000010000000100011001001000001111010001100010010', '1100001100101011011010000110111110001101010100010100101100111000010000101101101010111011111011101100000000110000100101001000101', '0000111100001000000101101001010111110100011011011101101111000000001010001001100010110000100000000001010100110001001100110010000', '0100100001001011110000110001100001111011111100000001010111011011100010110111101110101111101010100101000000110111000110000000000']
 > First ten results for pub 2: ['1000010100111010101010111110101000110101010001111110011110011001010100001100100000000001000111111011001101100001001110011101100', '1110100000111000000000110110010100000011110000011110000110100010000100001100010101101001100100010111000010100101011000001000000', '1000010111011000000001110111010101000111111010010011110100001010000000111111100100001111111101010100001001011100111101010000010', '0000111011110110010011100111001010001000011010010110010010101000101110011100000010000101011000101001001001000100111101010100100', '0100000100111101110000101111011000100111101011101110100001000001000010101111100100000111010001101001100001100011011110101101100', '0100001000110101010010010100100110000100001010100001110001110101010011000111100111001001100000010100110111010111010100010100100', '0011111000010001101100000110111001000000100111110100001100001100010010010101011000000111011011111010100010000100100000100000000', '1000010010101100110110110110100010100000111001101011110100001000011000001000000110010001001011100100000000100000000000000000000', '0001011100010011111110011110000001000000010100111111000000101010000011011110110000110001010010000010010001000101110001111100010', '1111010100011100010010010110000101110000010001100101011111001100010111100001011001000001011010111011100001000001100000000000110']

Executar circuitos parametrizados​

Execute vários experimentos em um único job, aproveitando valores de parâmetros para aumentar a reutilização dos circuitos.

import numpy as np
from qiskit.circuit.library import real_amplitudes
from qiskit.transpiler import generate_preset_pass_manager
from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2 as Sampler

n_qubits = 127

service = QiskitRuntimeService()
backend = service.least_busy(
    operational=True, simulator=False, min_num_qubits=n_qubits
)

# Step 1: Map classical inputs to a quantum problem
circuit = real_amplitudes(num_qubits=n_qubits, reps=2)
circuit.measure_all()

# Define three sets of parameters for the circuit
rng = np.random.default_rng(1234)
parameter_values = [
    rng.uniform(-np.pi, np.pi, size=circuit.num_parameters) for _ in range(3)
]

# Step 2: Optimize problem for quantum execution.

pm = generate_preset_pass_manager(backend=backend, optimization_level=1)
isa_circuit = pm.run(circuit)

# Step 3: Execute using Qiskit primitives.
sampler = Sampler(backend)
job = sampler.run([(isa_circuit, parameter_values)])
result = job.result()
# Get results for the first (and only) PUB
pub_result = result[0]
# Get counts from the classical register "meas".
print(
    f" >> First ten results for the meas output register: {pub_result.data.meas.get_bitstrings()[:10]}"
)
>> First ten results for the meas output register: ['1100011011100001011000001001000001111110000001011100011110011100111110000111000100011100001111100010010111110001001111011000101', '1100011101010101010000100110110110010001100101011101001011101010111110000111110100000011111010101101011101101101001111011110011', '0000000011000011001101001000111110001100010010011011001111000101000000001111111101101011100111010110111101010111011001010001011', '0101010001101110100010001100111001011101101100001000100001011101110100001000011011001011110101000110010001001010011011100011101', '0110101110000010110000001000010101100010010001001001101000010100110001011111110001000001100110010001011111001010011001001000101', '0111011111110111010111100110101000010100101000001010001001011111010010100111110110000011100001100000110000111000011011100000000', '0110100111001000100100110110010001011110000000110111000011110000100111001000100110011100100001100000101111111100010111100111001', '0101101111010110000000001000010110100101001100001101110010101111010110001010000111010010001111000000011001001001111100111010110', '0100000110010101111011110111000010001101011110010000110010001111001101010010000011111100100101101000010000111100111010000000110', '0011110110011011000110000100100110111000000010010101111011111000111001100011110100001100010100100001110101110100011100110001100']

Usar sessões e opções avançadas​

Explore sessões e opções avançadas para otimizar o desempenho dos circuitos em QPUs.

cuidado

O bloco de código a seguir retornará um erro para usuários do Plano Open porque ele usa sessões. As cargas de trabalho do Plano Open só podem ser executadas no modo de job ou no modo de lote.

import numpy as np
from qiskit.circuit.library import iqp
from qiskit.quantum_info import random_hermitian
from qiskit.transpiler import generate_preset_pass_manager
from qiskit_ibm_runtime import Session, SamplerV2 as Sampler
from qiskit_ibm_runtime import QiskitRuntimeService

n_qubits = 127

service = QiskitRuntimeService()
backend = service.least_busy(
    operational=True, simulator=False, min_num_qubits=n_qubits
)

rng = np.random.default_rng(1234)
mat = np.real(random_hermitian(n_qubits, seed=rng))
circuit = iqp(mat)
circuit.measure_all()
mat = np.real(random_hermitian(n_qubits, seed=rng))
another_circuit = iqp(mat)
another_circuit.measure_all()

pm = generate_preset_pass_manager(backend=backend, optimization_level=1)
isa_circuit = pm.run(circuit)
another_isa_circuit = pm.run(another_circuit)

with Session(backend=backend) as session:
    sampler = Sampler(mode=session)
    job = sampler.run([isa_circuit])
    another_job = sampler.run([another_isa_circuit])
    result = job.result()
    another_result = another_job.result()

# first job

print(
    f" > The first ten measurement results of job 1: {result[0].data.meas.get_bitstrings()[:10]}"
)
> The first ten measurement results of job 1: ['1101100010101100001001110000100011110011000010110000010000001011000110000110010100011000101111011110010101101001000101010100010', '0010100100011100001011111101001010010000010010000100000011001010001110101011010000100011001010000101110101110110010000110001110', '1011000110110011011010001111001011111000011111111010010010011000000110000001000101001111001000010110000000011101010000111101101', '0101000010000101001011111010110011101000100101010011001000010000011010000010101000000001000100010100011100101001000101001011000', '1101010101011100000001100110111001000100110011110001110011000000110100011011100000010000001100001101011000000001010101001101001', '1111100011111010000000100011100110101000010101100100000110000110001011100000000101010110011110010010000100011110000010101010100', '1011011100110001000110100100110010101101110010100010011100001000001100010101101110010101100000001110000000111001001000000100010', '0100011011110111010010111011101010111010010011011110011001000010101110100100111010110001101100110001010100000101001000000111001', '0001110001110000001011101101010001001110000010100001000101100100110111001011100000101010011100011001110011100100000000010110001', '1010110110111000001100011100000100101000000001111110110010000110011100100100100010000101111110100110010010010101001011001000011']
# second job
print(
    " > The first ten measurement results of job 2:",
    another_result[0].data.meas.get_bitstrings()[:10],
)
> The first ten measurement results of job 2: ['0100010001111001111010000100101010011010000100010110100100010010010110001010101010000000110000010000001100100011000110101000001', '1101000100010000011100110101001110101100001000000000101001110110110010110110010010011100010000010001011000011100100000100000000', '1111101010100011010100000100010101111110011000000000010000010000101001010001100000100000100010000001100111000000111000111010000', '0101111100000110010101101100101110101011010100001001110101100010111100110011100001110101000000001000000000101000100000001000000', '1101001000000000011000010100111110101111001001110011100001100100100100000011110001001000001000010101111100001001110010110011100', '1100001000110110000111110110010010000100001000001001100011110001111100100101110010010111010010101100001010101011100100001010010', '0001001100010000000101101101101111000011101100101000111010000000000010010111011000100000011010100000100011100010110010010000001', '1010101100000000011000111101000011100101000110110000111111000001100010001110000101111111110110000000000000001000000010001110000', '1111111001001001001100010000101110110100001011011100010001100000100001010100111011000110100011110000001010101000010000000011000', '1011011010101100010101100001001000000010110001101000100001111010000100011100000000100111001001000001001001101000001000100000000']

Próximos passos​

Recomendações