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@ARTICLE{Solgun:276257,
      author       = {Solgun, F. and DiVincenzo, David},
      title        = {{M}ultiport {I}mpedance {Q}uantization},
      journal      = {Annals of physics},
      volume       = {361},
      issn         = {0003-4916},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier},
      reportid     = {FZJ-2015-06720},
      pages        = {605-669},
      year         = {2015},
      abstract     = {With the increase of complexity and coherence of
                      superconducting systems made using the principles of circuit
                      quantum electrodynamics, more accurate methods are needed
                      for the characterization, analysis and optimization of these
                      quantum processors. Here we introduce a new method of
                      modelling that can be applied to superconducting structures
                      involving multiple Josephson junctions, high-Q
                      superconducting cavities, external ports, and voltage
                      sources. Our technique, an extension of our previous work on
                      single-port structures [1], permits the derivation of system
                      Hamiltonians that are capable of representing every feature
                      of the physical system over a wide frequency band and the
                      computation of T1 times for qubits. We begin with a black
                      box model of the linear and passive part of the system. Its
                      response is given by its multiport impedance function
                      Zsim(w), which can be obtained using a finite-element
                      electormagnetics simulator. The ports of this black box are
                      defined by the terminal pairs of Josephson junctions,
                      voltage sources, and 50 Ohm connectors to high-frequency
                      lines. We fit Zsim(w) to a positive-real (PR) multiport
                      impedance matrix Z(s), a function of the complex Laplace
                      variable s. We then use state-space techniques to synthesize
                      a finite electric circuit admitting exactly the same
                      impedance Z(s) across its ports; the PR property ensures the
                      existence of this finite physical circuit. We compare the
                      performance of state-space algorithms to classical frequency
                      domain methods, justifying their superiority in numerical
                      stability. The Hamiltonian of the multiport model circuit is
                      obtained by using existing lumped element circuit
                      quantization formalisms [2, 3]. Due to the presence of ideal
                      transformers in the model circuit, these quantization
                      methods must be extended, requiring the introduction of an
                      extension of the Kirchhoff voltage and current laws.},
      cin          = {PGI-2 / IAS-3},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106 / I:(DE-Juel1)IAS-3-20090406},
      pnm          = {144 - Controlling Collective States (POF3-144)},
      pid          = {G:(DE-HGF)POF3-144},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {1505.04116},
      howpublished = {arXiv:1505.04116},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1505.04116;\%\%$},
      UT           = {WOS:000360418800037},
      doi          = {10.1016/j.aop.2015.07.005},
      url          = {https://juser.fz-juelich.de/record/276257},
}