No differenceson declared inputs.

from qiskit import QuantumCircuit, transpile
from qiskit_aer import AerSimulator
import networkx as nx

def maxcut_obj(x, G):
    """
    Given a bitstring as a solution, this function returns
    the number of edges shared between the two partitions
    of the graph.

    Args:
        x: str
           solution bitstring

        G: networkx graph

    Returns:
        obj: float
             Objective
    """
    obj = 0
    for i, j in G.edges():
        if x[i] != x[j]:
            obj -= 1

    return obj


def compute_expectation(counts, G):

    """
    Computes expectation value based on measurement results

    Args:
        counts: dict
                key as bitstring, val as count

        G: networkx graph

    Returns:
        avg: float
             expectation value
    """

    avg = 0
    sum_count = 0
    for bitstring, count in counts.items():

        obj = maxcut_obj(bitstring[::-1], G)
        avg += obj * count
        sum_count += count

    return avg/sum_count


# We will also bring the different circuit components that
# build the qaoa circuit under a single function
def create_qaoa_circ(G, theta):

    """
    Creates a parametrized qaoa circuit

    Args:
        G: networkx graph
        theta: list
               unitary parameters

    Returns:
        qc: qiskit circuit
    """

    nqubits = len(G.nodes())
    p = len(theta)//2  # number of alternating unitaries
    qc = QuantumCircuit(nqubits)

    beta = theta[:p]
    gamma = theta[p:]

    # initial_state
    for i in range(0, nqubits):
        qc.h(i)

    for irep in range(0, p):

        # problem unitary
        for pair in list(G.edges()):
            qc.rzz(2 * gamma[irep], pair[0], pair[1])

        # mixer unitary
        for i in range(0, nqubits):
            qc.rx(2 * beta[irep], i)

    qc.measure_all()

    return qc

# Finally we write a function that executes the circuit on the chosen backend
def get_expectation(G, shots=512):

    """
    Runs parametrized circuit

    Args:
        G: networkx graph
        shots: int,
           Number of measurement shots per circuit execution
    """

    backend = AerSimulator()

    def execute_circ(theta):

        qc = create_qaoa_circ(G, theta)
        # Qiskit 2.x backends no longer transpile implicitly in run()
        tqc = transpile(qc, backend, optimization_level=0)
        counts = backend.run(tqc, shots=shots, seed_simulator=10
                             ).result().get_counts()

        return compute_expectation(counts, G)

    return execute_circ

from qiskit import QuantumCircuit, transpile
from qiskit_aer import AerSimulator
import networkx as nx

def maxcut_obj(x, G):
    """
    Given a bitstring as a solution, this function returns
    the number of edges shared between the two partitions
    of the graph.

    Args:
        x: str
           solution bitstring

        G: networkx graph

    Returns:
        obj: float
             Objective
    """
    obj = 0
    for i, j in G.edges():
        if x[i] != x[j]:
            obj -= 1

    return obj


def compute_expectation(counts, G):

    """
    Computes expectation value based on measurement results

    Args:
        counts: dict
                key as bitstring, val as count

        G: networkx graph

    Returns:
        avg: float
             expectation value
    """

    avg = 0
    sum_count = 0
    for bitstring, count in counts.items():

        obj = maxcut_obj(bitstring[::-1], G)
        avg += obj * count
        sum_count += count

    return avg/sum_count


# We will also bring the different circuit components that
# build the qaoa circuit under a single function
def create_qaoa_circ(G, theta):

    """
    Creates a parametrized qaoa circuit

    Args:
        G: networkx graph
        theta: list
               unitary parameters

    Returns:
        qc: qiskit circuit
    """

    nqubits = len(G.nodes())
    p = len(theta)//2  # number of alternating unitaries
    qc = QuantumCircuit(nqubits)

    beta = theta[:p]
    gamma = theta[p:]

    # initial_state
    for i in range(0, nqubits):
        qc.h(i)

    for irep in range(0, p):

        # problem unitary
        for pair in list(G.edges()):
            qc.rzz(2 * gamma[irep], pair[0], pair[1])

        # mixer unitary
        for i in range(0, nqubits):
            qc.rx(2 * beta[irep], i)

    qc.measure_all()

    return qc

# Finally we write a function that executes the circuit on the chosen backend
def get_expectation(G, shots=512):

    """
    Runs parametrized circuit

    Args:
        G: networkx graph
        shots: int,
           Number of measurement shots per circuit execution
    """

    backend = AerSimulator()

    def execute_circ(theta):

        qc = create_qaoa_circ(G, theta)
        # Qiskit 2.x backends no longer transpile implicitly in run()
        tqc = transpile(qc, backend, optimization_level=0)
        counts = backend.run(tqc, shots=shots, seed_simulator=10
                             ).result().get_counts()

        return compute_expectation(counts, G)

    return execute_circ

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    {
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    {
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        "cycle5/p1-b/shots-512",
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        "ring7_isolated8/p1-b/shots-512",
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    },
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  "evidence_summary": "consistent",
  "findings": [],
  "limitations": [
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    "Numerical agreement uses floating-point arithmetic with absolute tolerance 1e-10.",
    "No optimizer convergence, hardware, noise, dynamic-circuit or whole-program claim.",
    "The reference is a preservation baseline, not scientific truth.",
    "Candidate code ran locally as trusted, inspected code; virtual environments isolate versions, not hostile code.",
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