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@ARTICLE{GonzlezRosado:890328,
      author       = {González Rosado, L. and Hassler, F. and Catelani, G.},
      title        = {{L}ong-range exchange interaction between spin qubits
                      mediated by a superconducting link at finite magnetic field},
      journal      = {Physical review / B},
      volume       = {103},
      number       = {3},
      issn         = {2469-9950},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2021-00894},
      pages        = {035430},
      year         = {2021},
      abstract     = {Solid-state spin qubits are promising candidates for the
                      realization of a quantum computer due to their long
                      coherence times and easy electrical manipulation. However,
                      spin-spin interactions, which are needed for entangling
                      gates, have only limited range as they generally rely on
                      tunneling between neighboring quantum dots. This severely
                      constrains scalability. Proposals to extend the interaction
                      range generally focus on coherent electron transport between
                      dots or on extending the coupling range. Here, we study a
                      setup in which such an extension is obtained by using a
                      superconductor as a quantum mediator. Because of its gap,
                      the superconductor effectively acts as a long tunnel
                      barrier. We analyze the impact of spin-orbit (SO) coupling,
                      external magnetic fields, and the geometry of the
                      superconductor. We show that while spin-nonconserving
                      tunneling between the dots and the superconductor due to SO
                      coupling does not affect the exchange interaction, strong SO
                      scattering in the superconducting bulk is detrimental.
                      Moreover, we find that the addition of an external magnetic
                      field decreases the strength of the exchange interaction.
                      Fortunately, the geometry of the superconducting link offers
                      a lot of room to optimize the interaction range, with gains
                      of over an order of magnitude from a two-dimensional (2D)
                      film to a quasi-1D strip. We estimate that for
                      superconductors with weak SO coupling (e.g., aluminum),
                      exchange rates of up to 100 MHz over a micron-scale range
                      can be achieved with this setup in the presence of magnetic
                      fields of the order of 100 mT.},
      cin          = {PGI-11},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-11-20170113},
      pnm          = {522 - Quantum Computing (POF4-522) / DFG project 387689860
                      - Langreichweitige Kopplung von Spin Quantenbits in
                      Supraleiter-Halbleiter Heterostukturen},
      pid          = {G:(DE-HGF)POF4-522 / G:(GEPRIS)387689860},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000612137100003},
      doi          = {10.1103/PhysRevB.103.035430},
      url          = {https://juser.fz-juelich.de/record/890328},
}