this study significantly emphasizes on the entanglement engineering using a transmon qubit. A transmon qubit is created with two superconducting islands coupled with two Josephson Junction embedded into a transmission line. The transmon qubit energies are manipulated through its coupling to the transmission line. The key factor here is the coupling factor between transmission line and qubit by which the quantum features of the system such as transmon decay rate, energy dispersion, and related coherence time are controlled. To complete knowledge about the design, the system is quantum mechanically analyzed and the related Hamiltonian is derived. Accordingly, the dynamics equation of motions is derived and so the energy dispersion and the coupled system coherence time are investigated. The system engineering should be established in such a way that satisfies the energy dispersion and the coherence time. However, to analyze the entanglement between modes, it needs to calculate the number of photons of the transmission lines and the transmon qubit, and also the phase sensitive cross-correlation. The important section of this study emphasizes on engineering the coupling between the transmon qubit and transmission line to enhance the entanglement. The results show that around the Josephson Junction location where the more coupling is established the more entanglement between modes is created.
We present a framework for implementing two-qubit entangling operations between distant superconducting qubits using a space-time modulated Josephson junction (JJ) metasurface. By modulating the surface in both space and time, we engineer sidebands with controllable wavevectors that selectively couple target qubits. The metasurface acts as a reconfigurable coupling medium, where the interaction strength is determined by engineered transmission coefficients
Tμ(kμ⋅r)rather than by exponentially decaying near-field coupling, thus reducing the dependence on physical proximity. We investigated the implementation of two-qubit interactions via iSWAP gates driven resonantly through the metasurface and controlled phase gates via geometric phase accumulation. Simulations show entangling fidelity exceeding 98% maintained over centimeter-scale separations.