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@ARTICLE{Heuen:1005616,
      author       = {Heußen, Sascha and Postler, Lukas and Rispler, Manuel and
                      Pogorelov, Ivan and Marciniak, Christian D. and Monz, Thomas
                      and Schindler, Philipp and Müller, Markus},
      title        = {{S}trategies for a practical advantage of fault-tolerant
                      circuit design in noisy trapped-ion quantum computers},
      journal      = {Physical review / A},
      volume       = {107},
      number       = {4},
      issn         = {2469-9926},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2023-01565},
      pages        = {042422},
      year         = {2023},
      abstract     = {Fault-tolerant quantum error correction provides a strategy
                      to protect information processed by aquantum computer
                      against noise which would otherwise corrupt the data. A
                      fault-tolerant universalquantum computer must implement a
                      universal gate set on the logical level in order to perform
                      arbi-trary calculations to in principle unlimited precision.
                      In this manuscript, we characterize the recentdemonstration
                      of a fault-tolerant universal gate set in a trapped-ion
                      quantum computer [Postler etal. Nature 605.7911 (2022)] and
                      identify aspects to improve the design of experimental
                      setups toreach an advantage of logical over physical qubit
                      operation. We show that various criteria to assessthe
                      break-even point for fault-tolerant quantum operations are
                      within reach for the ion trap quan-tum computing
                      architecture under consideration. Furthermore, we analyze
                      the influence of crosstalkin entangling gates for logical
                      state preparation circuits. These circuits can be designed
                      to respectfault tolerance for specific microscopic noise
                      models. We find that an experimentally-informed
                      de-polarizing noise model captures the essential noise
                      dynamics of the fault-tolerant experiment thatwe consider,
                      and crosstalk is negligible in the currently accessible
                      regime of physical error rates. Fordeterministic Pauli state
                      preparation, we provide a fault-tolerant unitary logical
                      qubit initializationcircuit, which can be realized without
                      in-sequence measurement and feed-forward of classical
                      infor-mation. Additionally, we show that non-deterministic
                      state preparation schemes, i.e. repeat untilsuccess, for
                      logical Pauli and magic states perform with higher logical
                      fidelity over their deterministiccounterparts for the
                      current and anticipated future regime of physical error
                      rates. Our results offerguidance on improvements of physical
                      qubit operations and validate the
                      experimentally-informednoise model as a tool to predict
                      logical failure rates in quantum computing architectures
                      based ontrapped ions.},
      cin          = {PGI-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5221},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000976385800005},
      doi          = {10.1103/PhysRevA.107.042422},
      url          = {https://juser.fz-juelich.de/record/1005616},
}