QAOA Example

import matplotlib.pyplot as plt
import networkx as nx
import numpy as np
from iqm.qiskit_iqm import IQMFakeAdonis
from qiskit import QuantumCircuit, transpile
from qiskit.circuit import Parameter
from qiskit.primitives import BackendEstimatorV2 as BackendEstimator
from qiskit.quantum_info import PauliList, SparsePauliOp
from qiskit_aer import AerSimulator
from scipy.optimize import minimize

import QCut as ck
from QCut import cut

/home/nivalajo/work/QCut/.venv/lib/python3.12/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm

edges = [(0, 1), (1, 2), (2, 0), (2, 3), (2, 4), (3, 4)]
G = nx.Graph(edges)
nx.draw(G, with_labels=True, alpha=0.8, node_size=500)

reformattedHamiltonian = {
    "paulis": PauliList(["IIIZZ", "IIZIZ", "IIZZI", "IZZII", "ZIZII", "ZZIII"]),
    "coefs": [1.0, 1.0, 1.0, 1.0, 1.0, 1.0],
    "const": 0.0,
}

nqubits = 5

observables = SparsePauliOp(
    reformattedHamiltonian["paulis"], reformattedHamiltonian["coefs"]
)

def create_cut_qaoa_circ(n_layers):
    beta = [Parameter(f"beta_{i}") for i in range(n_layers)]
    gamma = [Parameter(f"gamma_{i}") for i in range(n_layers)]

    # create actual circuit object
    qc = QuantumCircuit(nqubits)
    # entagling layer
    for i in range(nqubits):
        qc.h(i)
    for layer_index in range(n_layers):
        # cost layer
        count = 0
        for i, j in G.edges():
            qc.rzz(2 * gamma[layer_index], i, j)
            if count == 2:
                qc.append(cut(), [max(i, j)])
            count += 1
        # mixing layer
        for i in range(nqubits):
            qc.rx(2 * beta[layer_index], i)
    return qc


def create_qaoa_circ(n_layers):

    beta = [Parameter(f"beta_{i}") for i in range(n_layers)]
    gamma = [Parameter(f"gamma_{i}") for i in range(n_layers)]

    # create actual circuit object
    qc = QuantumCircuit(nqubits)
    # entagling layer
    for i in range(nqubits):
        qc.h(i)
    for layer_index in range(n_layers):
        # cost layer
        for i, j in G.edges():
            qc.rzz(2 * gamma[layer_index], i, j)
        # mixing layer
        for i in range(nqubits):
            qc.rx(2 * beta[layer_index], i)
    return qc

qc = create_qaoa_circ(1)

qc.draw("mpl")

qca = create_cut_qaoa_circ(1)

qca.draw("mpl")

backend = IQMFakeAdonis()
sim = AerSimulator()

cut_circuit = ck.get_locations_and_subcircuits(qca)

transpiled = ck.transpile_circuits(cut_circuit, backend, optimization_level=3)

cut_experiment = ck.get_experiment_circuits(transpiled, observables)


tr_qc = transpile(qc, backend, optimization_level=3)
tr_obs = observables.apply_layout(tr_qc.layout)

def get_expectation_backend(circuit, hamiltonian, observables, backend):
    exps_uncut = np.empty(0)

    def execute_circ(theta):

        params = {}
        n_layers = len(theta) // 2  # number of alternating unitaries
        for i in range(n_layers):
            params[f"beta_{i}"] = theta[i]
            params[f"gamma_{i}"] = theta[i + n_layers]

        p_circuit = circuit.assign_parameters(params, inplace=False)

        fake_estimator = BackendEstimator(backend=backend)

        exps = [
            e.data.evs
            for e in fake_estimator.run(
                [(x) for x in zip([p_circuit] * len([observables]), [observables])]
            ).result()
        ]

        f = hamiltonian["const"] + sum(exps)

        global exps_uncut
        exps_uncut = np.append(exps_uncut, f)

        return f

    return execute_circ, exps_uncut


def get_expectation_cut(cut_experiment, hamiltonian, observables, backend):
    exps_cut = np.empty(0)  # store expectation value from each optimization step

    # execute circuit and calculate expectation value
    def execute_circ(theta):

        params = {}
        n_layers = len(theta) // 2  # number of alternating unitaries
        for i in range(n_layers):
            params[f"beta_{i}"] = theta[i]
            params[f"gamma_{i}"] = theta[i + n_layers]

        p_cut_experiment = cut_experiment.assign_parameters(params, inplace=False)

        # run the experiments, apply the {0,1} -> [-1,1] post-processing function
        results = ck.run_experiments(p_cut_experiment, shots=2**12, backend=backend)

        reconstructed_expval = ck.estimate_expectation_values(results)

        f = hamiltonian["const"] + float(reconstructed_expval)
        global exps_cut
        exps_cut = np.append(exps_cut, f)
        return f

    return execute_circ, exps_cut

initial_params = [np.pi, -np.pi]

expectation, exps_uncut = get_expectation_backend(
    tr_qc, reformattedHamiltonian, tr_obs, sim
)
# minimize uncut qaoa cost using COBYLA
res_uncut = minimize(
    expectation, initial_params, method="COBYLA", options={"maxiter": 100}
)
res_uncut

 message: Return from COBYLA because the trust region radius reaches its lower bound.
 success: True
  status: 0
     fun: -1.775390625
       x: [ 3.417e+00 -1.948e+00]
    nfev: 30
   maxcv: 0.0

expectation_cut, exps_cut = get_expectation_cut(
    cut_experiment, reformattedHamiltonian, observables, sim
)
# minimize uncut qaoa cost using COBYLA
res_cut = minimize(
    expectation_cut, initial_params, method="COBYLA", options={"maxiter": 100}
)
res_cut

 message: Return from COBYLA because the trust region radius reaches its lower bound.
 success: True
  status: 0
     fun: -1.8179985284805298
       x: [ 4.408e+00 -2.774e+00]
    nfev: 34
   maxcv: 0.0

x = range(len(exps_cut))
x1 = range(len(exps_uncut))
plt.plot(x, exps_cut, label="QCut")
plt.plot(x1, exps_uncut, label="uncut")
plt.axhline(y=-2, color="r", linestyle="--", label="Actual minimum")
plt.xlabel("Optimization round")
plt.ylabel("Cost")
plt.title("cut vs uncut Max-Cut QAOA cost on IQMFakeAdonis")
plt.legend()
plt.grid(True)

uncut_solution_circuit = create_qaoa_circ(1).assign_parameters(
    {
        "beta_0": res_uncut.x[0],
        "gamma_0": res_uncut.x[1],
    }
)

uncut_solution_circuit.measure_all()

uncut_solution_circuit.draw("mpl")

cut_solution_circuit = create_cut_qaoa_circ(1).assign_parameters(
    {
        "beta_0": res_uncut.x[0],
        "gamma_0": res_uncut.x[1],
    }
)

cut_solution_circuit.draw("mpl")

uncut_counts = sim.run(uncut_solution_circuit, shots=2**12).result().get_counts()

top_uncut_counts = dict(sorted(uncut_counts.items(), key=lambda item: item[1], reverse=True)[:20])

cut_dist = ck.run(cut_solution_circuit, shots=2**12, backend=sim, qubits=[0, 1, 2, 3, 4])

cut_counts = cut_dist.top(20)

from qiskit.visualization import plot_histogram
plot_histogram([top_uncut_counts, cut_counts], legend=["uncut", "cut"], figsize=(10, 6), sort="desc")

Only solution states have a high probability in both the cut and uncut cases