Black-box superconducting circuit quantization
  We present a semi-classical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multi-mode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D-transmon system, and quantitative agreement with measurements is found. 
Simon E. Nigg, Hanhee Paik, Brian Vlastakis, Gerhard Kirchmair, Shyam   Shankar, Luigi Frunzio, Michel Devoret, Robert Schoe...
cond-mat.mes-hall quant-ph