양자 알고리즘: 변분 양자 알고리즘

# % pip install 'qiskit[visualization]' qiskit-ibm-runtime

import numpy as np
from qiskit.circuit import ParameterVector, QuantumCircuit
from qiskit.primitives import StatevectorEstimator, StatevectorSampler
from qiskit.quantum_info import SparsePauliOp
from scipy.optimize import minimize

op = SparsePauliOp("Z")
op.to_matrix()

# compute eigenvalues with numpy
result = np.linalg.eigh(op.to_matrix())
print("Eigenvalues:", result.eigenvalues)

# define a variational form
param = ParameterVector("a", 3)
qc = QuantumCircuit(1, 1)
qc.u(param[0], param[1], param[2], 0)
qc_estimator = qc.copy()
qc.measure(0, 0)
qc.draw("mpl")

sampler = StatevectorSampler()
estimator = StatevectorEstimator()

# compute counts of bitstrings with random parameter values by Sampler
result = sampler.run([(qc, [1, 2, 3])]).result()
counts = result[0].data.c.get_counts()
counts

# compute the expectation value of Z based on the counts
(counts.get("0", 0) - counts.get("1", 0)) / sum(counts.values())

result = estimator.run([(qc_estimator, op, [1, 2, 3])]).result()
result[0].data.evs

# define a cost function to look for the minimum eigenvalue of Z
def cost(x):
    result = sampler.run([(qc, x)]).result()
    counts = result[0].data.c.get_counts()
    expval = (counts.get("0", 0) - counts.get("1", 0)) / sum(counts.values())
    # the following line shows the trajectory of the optimization
    print(expval, counts)
    return expval

# minimize the cost function with scipy's minimize
min_result = minimize(cost, [0, 0, 0], method="COBYLA", tol=1e-8)
min_result

# check counts of bitstrings with the optimal parameters
result = sampler.run([(qc, min_result.x)]).result()
result[0].data.c.get_counts()

z2 = SparsePauliOp("ZZ")
print(z2)
print(z2.to_matrix())

# compute eigenvalues with numpy

# define a variational form
# qc = ...

# compute counts of bitstrings with a random parameter values by Sampler
# result = sampler.run(...)
# result

# compute the expectation value of ZZ based on the counts

# verify the expectation value of ZZ with Estimator

# define a cost function to look for the minimum eigenvalue of ZZ
# def cost(x):
#    expval = ...
#    return expval

# minimize the cost function with scipy's minimize
# min_result = minimize(cost, [...], method="COBYLA", tol=1e-8)
# min_result

# check counts of bitstrings with the optimal parameter values
# result = sampler.run(qc, min_result.x).result()
# result

z2 = SparsePauliOp("ZZ")
print(z2)
print(z2.to_matrix())

# define a variational form
param = ParameterVector("a", 6)
qc = QuantumCircuit(2, 2)
qc.u(param[0], param[1], param[2], 0)
qc.u(param[3], param[4], param[5], 1)
qc_estimator = qc.copy()
qc.measure([0, 1], [0, 1])
qc.draw("mpl")

sampler = StatevectorSampler()
estimator = StatevectorEstimator()

# compute counts of bitstrings with random parameter values by Sampler
result = sampler.run([(qc, [1, 2, 3, 4, 5, 6])]).result()
counts = result[0].data.c.get_counts()
counts

# compute the expectation value of ZZ based on the counts
(
    counts.get("00", 0)
    - counts.get("01", 0)
    - counts.get("10", 0)
    + counts.get("11", 0)
) / sum(counts.values())

# verify the expectation value of ZZ with Estimator
result = estimator.run([(qc_estimator, z2, [1, 2, 3, 4, 5, 6])]).result()
result[0].data.evs

# define a cost function to look for the minimum eigenvalue of ZZ
def cost(x):
    result = sampler.run([(qc, x)]).result()
    counts = result[0].data.c.get_counts()
    expval = (
        counts.get("00", 0)
        - counts.get("01", 0)
        - counts.get("10", 0)
        + counts.get("11", 0)
    ) / sum(counts.values())
    print(expval, counts)
    return expval

# minimize the cost function with scipy's minimize
min_result = minimize(cost, [0, 0, 0, 0, 0, 0], method="COBYLA", tol=1e-8)
min_result

# check counts of bitstrings with the optimal parameters
result = sampler.run([(qc, min_result.x)]).result()
result[0].data.c.get_counts()

import matplotlib
import matplotlib.pyplot as plt
import numpy as np
import rustworkx as rx
from rustworkx.visualization import mpl_draw

n = 5

graph = rx.PyGraph()
graph.add_nodes_from(range(1, n + 1))
edge_list = [
    (0, 1, 1.0),
    (0, 2, 1.0),
    (1, 2, 1.0),
    (1, 3, 1.0),
    (2, 4, 1.0),
    (3, 4, 1.0),
]
graph.add_edges_from(edge_list)
pos = rx.spring_layout(graph, seed=2)
mpl_draw(graph, node_size=600, pos=pos, with_labels=True, labels=str)

def build_max_cut_operator(graph: rx.PyGraph) -> tuple[SparsePauliOp, float]:
    sp_list = []
    constant = 0
    for s, t in graph.edge_list():
        w = graph.get_edge_data(s, t)
        sp_list.append(("ZZ", [s, t], w / 2))
        constant -= 1 / 2
    return SparsePauliOp.from_sparse_list(
        sp_list, num_qubits=graph.num_nodes()
    ), constant

cost_hamiltonian, constant = build_max_cut_operator(graph)
print("Cost Function Hamiltonian:", cost_hamiltonian)
print("Constant:", constant)

from qiskit.circuit.library import QAOAAnsatz

circuit = QAOAAnsatz(cost_operator=cost_hamiltonian, reps=1)
circuit.measure_all()
circuit.draw("mpl")

circuit.decompose(reps=3).draw("mpl", fold=-1)

circuit.parameters

from qiskit_ibm_runtime import QiskitRuntimeService
from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager

# Use a quantum device
service = QiskitRuntimeService()
backend = service.least_busy(min_num_qubits=127)
# backend = service.backend("ibm_kingston")

# You can test your programs locally with a fake backend (local testing mode)
# backend = FakeBrisbane()

print(backend)

# Create pass manager for transpilation
pm = generate_preset_pass_manager(optimization_level=3, backend=backend)

candidate_circuit = pm.run(circuit)
candidate_circuit.draw("mpl", fold=False, idle_wires=False)

initial_gamma = np.pi
initial_beta = np.pi / 2
init_params = [initial_gamma, initial_beta]

def cost_func_estimator(params, ansatz, hamiltonian, estimator):
    # transform the observable defined on virtual qubits to
    # an observable defined on all physical qubits
    isa_hamiltonian = hamiltonian.apply_layout(ansatz.layout)

    pub = (ansatz, isa_hamiltonian, params)
    job = estimator.run([pub])

    results = job.result()[0]
    cost = results.data.evs

    objective_func_vals.append(cost)

    return cost

from qiskit_ibm_runtime import Session, EstimatorV2
from scipy.optimize import minimize

objective_func_vals = []  # Global variable
with Session(backend=backend) as session:
    # If using qiskit-ibm-runtime<0.24.0, change `mode=` to `session=`
    estimator = EstimatorV2(mode=session)
    estimator.options.default_shots = 1000

    # Set simple error suppression/mitigation options
    estimator.options.dynamical_decoupling.enable = True
    estimator.options.dynamical_decoupling.sequence_type = "XY4"
    estimator.options.twirling.enable_gates = True
    estimator.options.twirling.num_randomizations = "auto"

    result = minimize(
        cost_func_estimator,
        init_params,
        args=(candidate_circuit, cost_hamiltonian, estimator),
        method="COBYLA",
        tol=1e-2,
    )
    print(result)

plt.figure(figsize=(12, 6))
plt.plot(objective_func_vals)
plt.xlabel("Iteration")
plt.ylabel("Cost")
plt.show()

optimized_circuit = candidate_circuit.assign_parameters(result.x)
optimized_circuit.draw("mpl", fold=False, idle_wires=False)

from qiskit_ibm_runtime import SamplerV2

# If using qiskit-ibm-runtime<0.24.0, change `mode=` to `backend=`
sampler = SamplerV2(mode=backend)

# Set simple error suppression/mitigation options
sampler.options.dynamical_decoupling.enable = True
sampler.options.dynamical_decoupling.sequence_type = "XY4"
sampler.options.twirling.enable_gates = True
sampler.options.twirling.num_randomizations = "auto"

pub = (optimized_circuit,)
job = sampler.run([pub], shots=int(1e4))
counts_int = job.result()[0].data.meas.get_int_counts()
counts_bin = job.result()[0].data.meas.get_counts()
shots = sum(counts_int.values())
final_distribution_int = {key: val / shots for key, val in counts_int.items()}
final_distribution_bin = {key: val / shots for key, val in counts_bin.items()}
print(final_distribution_int)

# auxiliary functions to sample most likely bitstring
def to_bitstring(integer, num_bits):
    result = np.binary_repr(integer, width=num_bits)
    return [int(digit) for digit in result]


keys = list(final_distribution_int.keys())
values = list(final_distribution_int.values())
most_likely = keys[np.argmax(np.abs(values))]
most_likely_bitstring = to_bitstring(most_likely, len(graph))
most_likely_bitstring.reverse()

print("Result bitstring:", most_likely_bitstring)

import matplotlib.pyplot as plt

matplotlib.rcParams.update({"font.size": 10})
final_bits = final_distribution_bin
values = np.abs(list(final_bits.values()))
top_4_values = sorted(values, reverse=True)[:4]
positions = []
for value in top_4_values:
    positions.append(np.where(values == value)[0])
fig = plt.figure(figsize=(11, 6))
ax = fig.add_subplot(1, 1, 1)
plt.xticks(rotation=45)
plt.title("Result Distribution")
plt.xlabel("Bitstrings (reversed)")
plt.ylabel("Probability")
ax.bar(list(final_bits.keys()), list(final_bits.values()), color="tab:grey")
for p in positions:
    ax.get_children()[p[0].item()].set_color("tab:purple")
plt.show()

colors = ["tab:grey" if i == 0 else "tab:purple" for i in most_likely_bitstring]
mpl_draw(graph, node_size=600, pos=pos, with_labels=True, labels=str, node_color=colors)

from typing import Sequence


def evaluate_sample(x: Sequence[int], graph: rx.PyGraph) -> float:
    assert len(x) == len(
        list(graph.nodes())
    ), "The length of x must coincide with the number of nodes in the graph."
    return sum(
        x[u] * (1 - x[v]) + x[v] * (1 - x[u]) for u, v in list(graph.edge_list())
    )


cut_value = evaluate_sample(most_likely_bitstring, graph)
print("The value of the cut is:", cut_value)

# Check Qiskit version
import qiskit

qiskit.__version__