# References for two-local forms in QISKIT

I am using 'Two local' form of QISKIT as a waveform ansatz in VQE to compute ground state. QISKIT documentation does not provide references to all the entangling options. Is there any other place where I can find references for different entangling structure: 'Full', 'Linear', 'Circular' etc?

here you go, for references check: https://github.com/Qiskit/qiskit-terra/issues/8219

from qiskit.circuit.library import TwoLocal
from qiskit import QuantumCircuit
qubit_num = 3
two_full = TwoLocal(qubit_num, ['ry','rz'], 'cz', 'full', reps=2, insert_barriers=True)
two_linear = TwoLocal(qubit_num, ['ry','rz'], 'cz', 'linear', reps=2, insert_barriers=True)
two_circular = TwoLocal(qubit_num, ['ry','rz'], 'cz', 'circular', reps=2, insert_barriers=True)
two_sca = TwoLocal(qubit_num, ['ry','rz'], 'cz', 'sca', reps=2, insert_barriers=True)

print("two_full: ")
display(two_full.decompose().draw('mpl'))
print("two_linear: ")
display(two_linear.decompose().draw('mpl'))
print("two_circular: ")
display(two_circular.decompose().draw('mpl'))
print("two_sca: ")
display(two_sca.decompose().draw('mpl'))



'full' entanglement is each qubit is entangled with all the others:

'linear' entanglement is qubit $$i$$ entangled with qubit $$i + 1$$,for all $$i \in \{0, 1, ... , n - 2\}$$, where $$n$$ is the total number of qubits:

'circular' entanglement is linear entanglement but with an additional entanglement of the first and last qubit before the linear part:

'sca' (shifted-circular-alternating) entanglement is a generalized and modified version of the proposed circuit 14 in Sim et al..It consists of circular entanglement where the 'long' entanglement connecting the first with the last qubit is shifted by one each block. Furthermore the role of control and target qubits are swapped every block (therefore alternating):

• Sorry, if the question was not clear, I was looking for the reference articles for different wavefunction ansatz. They only have references for 'sca'. Looking at other articles in the arxiv, it seems these are all variations of Hardware-Efficient Ansatz (HEA) first introduced in this paper: nature.com/articles/nature23879. But I could not be sure if this the correct paper to refer to. Jun 22 at 3:59
• @Anyon I think only code owner knows the correct reference, I will help you open an issue on qiskit-terra about it,
– poig
Jun 22 at 4:19
• thanks, appreciate your help and effort. Jun 22 at 4:39
• – poig
Jun 22 at 4:45
• @Anyon seems like code owner had respawned the question.
– poig
Jun 22 at 17:16