Entangled state engineering in the 4-coupled qubits system

Abstract

This article studies the behavior of the avoided level crossing in the 4-coupled qubit to each other and mainly focuses on how to engineer it. This phenomenon occurs due to the two transitions out of the ground state in a two-coupled qubit, contributing to the entangled states. This essential and unique behavior can be engineered in a quantum circuit. For this reason, a quantum circuit containing 4 qubits is designed, and its quantum Hamiltonian and dynamic equation of the motion are theoretically derived. Analysis of the entanglement between each coupled qubit using the entanglement metric reveals that the strength of the qubit-qubit coupling factor and the qubit's non-linearity play an essential role in engineering the photonic mode entanglement. The results show that the avoided level crossing appears in the photonic mode entanglement. In other words, two or more transitions from the ground state to the multiple excited states for each bias current. However, the interesting point is that the avoided level crossing just occurs for the qubits connected capacitively to the driven field (the first qubit in this work), not for all.