QCut to Three Parts

import QCut as ck
from QCut import cut, cutGate
from qiskit import QuantumCircuit, transpile
from qiskit.circuit.library import CXGate
from qiskit.quantum_info import SparsePauliOp
from qiskit.circuit.library import CXGate
from qiskit_aer import AerSimulator
from qiskit.primitives import Estimator, BackendEstimator
from iqm.qiskit_iqm import IQMFakeAdonis

#define initial circuit

circuit = QuantumCircuit(4)
circuit.h(0)
circuit.cx(0,1)
circuit.cx(1,2)
circuit.cx(2,3)

circuit.draw("mpl")

#insert cuts

cut_circuit = QuantumCircuit(4)
cut_circuit.h(0)
cut_circuit.cx(0,1)
cut_circuit.append(cut, [1])
cut_circuit.cx(1,2)
cut_circuit.append(cut, [2])
cut_circuit.cx(2,3)

cut_circuit.draw("mpl")

# Now one can continue as in othrer examples