Tight binding as a numerical tool for diagonalizing superconducting-circuit Hamiltonians

We adopt solid-state tight-binding techniques for the spectral analysis of superconducting circuits with more than four degrees of freedom. Such circuits are typically beyond the reach of standard exact diagonalization techniques, owing to the exponential increase in Hilbert space dimension. We demonstrate that for many circuits of interest (including flux qubit, zero-pi circuit and current-mirror circuit) tight-binding states are better suited for approximating the low-energy excitations than charge-basis states. Their use can dramatically lower the Hilbert space dimension required for convergence to the true spectrum which opens up the way for studying circuits with more than 20 nodes.