  We introduce an efficient tensor network toolbox to compute the low-energy
excitations of large-scale superconducting quantum circuits up to a desired
accuracy. We benchmark this algorithm on the fluxonium qubit, a superconducting
quantum circuit based on a Josephson junction array with over a hundred
junctions. As an example of the possibilities offered by this numerical tool,
we compute the pure-dephasing coherence time of the fluxonium qubit due to
charge noise and coherent quantum phase slips, taking into account the array
degrees of freedom corresponding to a Hilbert space as large as$~15^{180}$. Our
algorithm is applicable to the wide variety of circuit-QED systems and may be a
useful tool for scaling up superconducting-qubit technologies.
