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@ARTICLE{Ansari:902779,
      author       = {Ansari, Mohammad},
      title        = {{S}uperconducting qubits beyond the dispersive regime},
      journal      = {Physical review / B},
      volume       = {100},
      number       = {2},
      issn         = {1098-0121},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2021-04550},
      pages        = {024509},
      year         = {2019},
      abstract     = {Superconducting circuits consisting of a few low-anharmonic
                      transmons coupled to readout and bus resonators can perform
                      basic quantum computations. Since the number of qubits in
                      such circuits is limited to not more than a few tens, the
                      qubits can be designed to operate within the dispersive
                      regime where frequency detunings are much stronger than
                      coupling strengths. However, scaling up the number of qubits
                      will bring the circuit out of the regime, and this
                      invalidates current theories. We develop a formalism that
                      allows to consistently diagonalize the superconducting
                      circuit Hamiltonian beyond the dispersive regime. This will
                      allow to study qubit-qubit interaction unperturbatively,
                      therefore, our formalism remains valid and accurate at small
                      or even negligible frequency detuning; thus, our formalism
                      serves as a theoretical ground for designing qubit
                      characteristics for scaling up the number of qubits in
                      superconducting circuits. We study the most important
                      circuits with single- and two-qubit gates, i.e., a single
                      transmon coupled to a resonator and two transmons sharing a
                      bus resonator. Surprisingly, our formalism allows to
                      determine the circuit characteristics, such as dressed
                      frequencies and Kerr couplings, in closed-form formulas that
                      not only reproduce perturbative results, but also
                      extrapolate beyond the dispersive regime and can ultimately
                      reproduce (and even modify) the Jaynes-Cumming results at
                      resonant frequencies.},
      cin          = {PGI-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5224 - Quantum Networking (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5224},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000476685600003},
      doi          = {10.1103/PhysRevB.100.024509},
      url          = {https://juser.fz-juelich.de/record/902779},
}