Investigation of Entanglement Through Circuit Geometry.

Quantum entanglement is a fundamental phenomenon that enables the connection of a large

number of qubits and serves as the backbone for quantum computing and quantum information

processing. Along with the coupling strength, the interaction between the qubits depends upon the

circuit geometry. This work deals with the longe range qubit-qubit interactions by analyzing

different structures of qubit lattices. Long-range cross-Kerr effercts are calculated to quantify the

correlations between the qubits[1]. We extend our work with calculations of correlations between

qubits using Mermin inequalities, providing deeper insights into the nature of quantum

entanglement[2,3]. The findings can help optimize quantum gate designs and improve error correction

protocols.