Diagonalizing the Hamiltonian of capacitively coupled superconducting phase qubits

Coupling qubits together towards large-scale integration is a key point for realizing a quantum computer. We study the capacitively coupled superconducting phase qubits using two diagonalization methods, which are very efficient to obtain the wave functions and energies of the bound states of such two-qubit system. The first diagonalization method is based on two-dimensional cubic approximation for the coupled system with wave functions of the eigenstates for harmonic oscillators as the bases of diagonalization, and also reveals the physics underlying it. The other one utilizes the Fast Fourier Transform to perform diagonalization with plane waves as the bases, and it can be easily extended to other problems with even high dimension.