title: A graph-theoretical representation of multiphoton resonance processes in superconducting quantum circuits.
abstract: We propose a graph-theoretical formalism to study generic circuit quantum electrodynamics systems consisting of a two level qubit coupled with a single-mode resonator in arbitrary coupling strength regimes beyond rotating-wave approximation. We define colored-weighted graphs, and introduce different products between them to investigate the dynamics of superconducting qubits in transverse, longitudinal, and bidirectional coupling schemes. The intuitive and predictive picture provided by this method, and the simplicity of the mathematical construction, are demonstrated with some numerical studies of the multiphoton resonance processes and quantum interference phenomena for the superconducting qubit systems driven by intense ac fields.
authors.affiliation: Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA.
authors.forename: Hossein Z
authors.initials: HZ
authors.lastname: Jooya
authors.affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843, USA.
authors.forename: Kamran
authors.initials: K
authors.lastname: Reihani
authors.affiliation: Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, USA.|Center for Quantum Science and Engineering, Department of Physics, National Taiwan University, Taipei 10617, Taiwan.
authors.forename: Shih-I
authors.initials: SI
authors.lastname: Chu