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@ARTICLE{Vuillot:1026360,
      author       = {Vuillot, Christophe and Ciani, Alessandro and Terhal,
                      Barbara M.},
      title        = {{H}omological {Q}uantum {R}otor {C}odes: {L}ogical {Q}ubits
                      from {T}orsion},
      journal      = {Communications in mathematical physics},
      volume       = {405},
      number       = {2},
      issn         = {0010-3616},
      address      = {Heidelberg},
      publisher    = {Springer},
      reportid     = {FZJ-2024-03391},
      pages        = {53},
      year         = {2024},
      abstract     = {We formally define homological quantum rotor codes which
                      use multiple quantum rotors to encode logical information.
                      These codes generalize homological or CSS quantum codes for
                      qubits or qudits, as well as linear oscillator codes which
                      encode logical oscillators. Unlike for qubits or
                      oscillators, homological quantum rotor codes allow one to
                      encode both logical rotors and logical qudits in the same
                      block of code, depending on the homology of the underlying
                      chain complex. In particular, a code based on the chain
                      complex obtained from tessellating the real projective plane
                      or a Möbius strip encodes a qubit. We discuss the distance
                      scaling for such codes which can be more subtle than in the
                      qubit case due to the concept of logical operator spreading
                      by continuous stabilizer phase-shifts. We give constructions
                      of homological quantum rotor codes based on 2D and 3D
                      manifolds as well as products of chain complexes.
                      Superconducting devices being composed of islands with
                      integer Cooper pair charges could form a natural hardware
                      platform for realizing these codes: we show that the 0-
                      qubit as well as Kitaev’s current-mirror qubit—also
                      known as the Möbius strip qubit—are indeed small examples
                      of such codes and discuss possible extensions.},
      cin          = {PGI-12},
      ddc          = {510},
      cid          = {I:(DE-Juel1)PGI-12-20200716},
      pnm          = {5214 - Quantum State Preparation and Control (POF4-521)},
      pid          = {G:(DE-HGF)POF4-5214},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001165283300005},
      doi          = {10.1007/s00220-023-04905-4},
      url          = {https://juser.fz-juelich.de/record/1026360},
}