Saltar al contenido principal

Ejemplos de primitivas

Nuevo modelo de ejecución, ahora en versión beta

La versión beta de un nuevo modelo de ejecución ya está disponible. El modelo de ejecución dirigida ofrece mayor flexibilidad para personalizar tu flujo de mitigación de errores. Consulta la guía del Modelo de ejecución dirigida para más información.

Versiones de paquetes

El código de esta página fue desarrollado con los siguientes requisitos. Recomendamos usar estas versiones o más recientes.

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

Los ejemplos de esta sección ilustran algunas formas comunes de usar primitivas. Antes de ejecutar estos ejemplos, sigue las instrucciones de Instalar y configurar.

nota

Todos estos ejemplos usan las primitivas de Qiskit Runtime, aunque también podrías usar las primitivas base.

Ejemplos de Estimator​

Calcula e interpreta de manera eficiente los valores esperados de los operadores cuánticos requeridos por muchos algoritmos con Estimator. Explora sus usos en modelado molecular, aprendizaje automático y problemas de optimización complejos.

Ejecutar un único experimento​

Usa Estimator para determinar el valor esperado de un único par circuito-observable.

# 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}

Ejecutar múltiples experimentos en un único trabajo​

Usa Estimator para determinar los valores esperados de múltiples pares circuito-observable.

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

Ejecutar circuitos parametrizados​

Usa Estimator para ejecutar tres experimentos en un único trabajo, aprovechando valores de parámetros para aumentar la reutilización de 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 sesiones y opciones avanzadas​

Explora sesiones y opciones avanzadas para optimizar el rendimiento de los circuitos en QPUs.

precaución

El siguiente bloque de código devolverá un error para los usuarios del Plan Abierto porque usa sesiones. Las cargas de trabajo del Plan Abierto solo pueden ejecutarse en modo trabajo o en modo por lotes.

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}

Ejemplos de Sampler​

Genera distribuciones de cuasiprobabilidad con mitigación de errores completa, muestreadas a partir de las salidas de circuitos cuánticos. Aprovecha las capacidades de Sampler para algoritmos de búsqueda y clasificación como Grover y QVSM.

Ejecutar un único experimento​

Usa Sampler para devolver el resultado de la medición como cadenas de bits o conteos de un 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']

Ejecutar múltiples experimentos en un único trabajo​

Usa Sampler para devolver el resultado de la medición como cadenas de bits o conteos de múltiples circuitos en un único trabajo.

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']

Ejecutar circuitos parametrizados​

Ejecuta varios experimentos en un único trabajo, aprovechando valores de parámetros para aumentar la reutilización de 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 sesiones y opciones avanzadas​

Explora sesiones y opciones avanzadas para optimizar el rendimiento de los circuitos en QPUs.

precaución

El siguiente bloque de código devolverá un error para los usuarios del Plan Abierto porque usa sesiones. Las cargas de trabajo del Plan Abierto solo pueden ejecutarse en modo trabajo o en modo por lotes.

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']

Pasos siguientes​

Recomendaciones