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Mga halimbawa ng Primitives

Bagong execution model, nasa beta release na

Available na ang beta release ng bagong execution model. Ang directed execution model ay nagbibigay ng mas maraming flexibility sa pag-customize ng iyong error mitigation workflow. Tingnan ang gabay na Directed execution model para sa karagdagang impormasyon.

Package versions

The code on this page was developed using the following requirements. We recommend using these versions or newer.

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

Ang mga halimbawa sa seksyong ito ay nagpapakita ng ilang karaniwang paraan ng paggamit ng primitives. Bago patakbuhin ang mga halimbawang ito, sundin ang mga tagubilin sa Install and set up.

tala

Lahat ng halimbawang ito ay gumagamit ng primitives mula sa Qiskit Runtime, pero maaari ka ring gumamit ng base primitives.

Mga halimbawa ng Estimator​

Mahusay na kalkulahin at bigyang-kahulugan ang mga expectation value ng quantum operators na kailangan ng maraming algorithm gamit ang Estimator. Tuklasin ang mga gamit nito sa molecular modeling, machine learning, at mga kumplikadong optimization problem.

Magpatakbo ng isang eksperimento​

Gamitin ang Estimator para matukoy ang expectation value ng isang circuit-observable pair.

# 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}

Magpatakbo ng maraming eksperimento sa iisang job​

Gamitin ang Estimator para matukoy ang mga expectation value ng maraming circuit-observable pair.

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

Magpatakbo ng mga parameterized circuit​

Gamitin ang Estimator para magpatakbo ng tatlong eksperimento sa iisang job, na ginagamit ang mga parameter value para mapataas ang reusability ng circuit.

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}

Gumamit ng sessions at advanced options​

Tuklasin ang mga session at advanced options para ma-optimize ang performance ng circuit sa mga QPU.

babala

Ang sumusunod na code block ay magbabalik ng error para sa mga gumagamit ng Open Plan dahil gumagamit ito ng sessions. Ang mga workload sa Open Plan ay maaari lang tumakbo sa job mode o batch mode.

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}

Mga halimbawa ng Sampler​

Gumawa ng mga kumpletong error-mitigated quasi-probability distribution na sinample mula sa mga output ng quantum circuit. Gamitin ang kakayahan ng Sampler para sa mga search at classification algorithm tulad ng Grover's at QVSM.

Magpatakbo ng isang eksperimento​

Gamitin ang Sampler para ibalik ang resulta ng pagsukat bilang mga bitstring o bilang counts mula sa isang circuit.

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']

Magpatakbo ng maraming eksperimento sa isang trabaho​

Gamitin ang Sampler para ibalik ang resulta ng pagsukat bilang mga bitstring o counts mula sa maraming circuit sa iisang trabaho.

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']

Magpatakbo ng mga parameterized circuit​

Magpatakbo ng ilang eksperimento sa iisang trabaho, gamit ang mga parameter value para mapataas ang reusability ng circuit.

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']

Gumamit ng mga session at advanced na opsyon​

I-explore ang mga session at advanced na opsyon para i-optimize ang performance ng circuit sa mga QPU.

babala

Ang sumusunod na code block ay magbabalik ng error para sa mga gumagamit ng Open Plan, dahil gumagamit ito ng mga session. Ang mga workload sa Open Plan ay maaari lamang tumakbo sa job mode o batch mode.

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']

Mga susunod na hakbang​

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