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@ARTICLE{Zen:1038567,
      author       = {Zen, Remmy and Olle, Jan and Colmenarez, Luis and Puviani,
                      Matteo and Müller, Markus and Marquardt, Florian},
      title        = {{Q}uantum {C}ircuit {D}iscovery for {F}ault-{T}olerant
                      {L}ogical {S}tate {P}reparation with {R}einforcement
                      {L}earning},
      reportid     = {FZJ-2025-01550, arXiv:2402.17761},
      year         = {2025},
      note         = {34 pages, 20 figures},
      abstract     = {The realization of large-scale quantum computers requires
                      not only quantum error correction (QEC) but also
                      fault-tolerant operations to handle errors that propagate
                      into harmful errors. Recently, flag-based protocols have
                      been introduced that use ancillary qubits to flag harmful
                      errors. However, there is no clear recipe for finding a
                      fault-tolerant quantum circuit with flag-based protocols,
                      especially when we consider hardware constraints, such as
                      qubit connectivity and available gate set. In this work, we
                      propose and explore reinforcement learning (RL) to
                      automatically discover compact and hardware-adapted
                      fault-tolerant quantum circuits. We show that in the task of
                      fault-tolerant logical state preparation, RL discovers
                      circuits with fewer gates and ancillary qubits than
                      published results without and with hardware constraints of
                      up to 15 physical qubits. Furthermore, RL allows for
                      straightforward exploration of different qubit
                      connectivities and the use of transfer learning to
                      accelerate the discovery. More generally, our work opens the
                      door towards the use of RL for the discovery of
                      fault-tolerant quantum circuits for addressing tasks beyond
                      state preparation, including magic state preparation,
                      logical gate synthesis, or syndrome measurement.},
      cin          = {PGI-2},
      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)25},
      eprint       = {2402.17761},
      howpublished = {arXiv:2402.17761},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2402.17761;\%\%$},
      url          = {https://juser.fz-juelich.de/record/1038567},
}