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@ARTICLE{RodriguezBlanco:902776,
      author       = {Rodriguez-Blanco, Andrea and Bermudez, Alejandro and
                      Müller, Markus and Shahandeh, Farid},
      title        = {{E}fficient and {R}obust {C}ertification of {G}enuine
                      {M}ultipartite {E}ntanglement in {N}oisy {Q}uantum {E}rror
                      {C}orrection {C}ircuits},
      journal      = {PRX quantum},
      volume       = {2},
      number       = {2},
      issn         = {2691-3399},
      address      = {College Park, MD},
      publisher    = {American Physical Society},
      reportid     = {FZJ-2021-04547},
      pages        = {020304},
      year         = {2021},
      abstract     = {Ensuring the correct functioning of quantum error
                      correction (QEC) circuits is crucial to achieve fault
                      tolerance in realistic quantum processors subjected to
                      noise. The first checkpoint for a fully operational QEC
                      circuit is to create genuine multipartite entanglement (GME)
                      across all subsystems of physical qubits. We introduce a
                      conditional witnessing technique to certify GME that is
                      efficient in the number of subsystems and, importantly,
                      robust against experimental noise and imperfections.
                      Specifically, we prove that the detection of entanglement in
                      a linear number of bipartitions by a number of measurements
                      that also scales linearly, suffices to certify GME.
                      Moreover, our method goes beyond the standard procedure of
                      separating the state from the convex hull of biseparable
                      states, yielding an improved finesse and robustness compared
                      to previous techniques. We apply our method to the noisy
                      readout of stabilizer operators of the distance-three
                      topological color code and its flag-based fault-tolerant
                      version. In particular, we subject the circuits to
                      combinations of three types of noise, namely, uniform
                      depolarizing noise, two-qubit gate depolarizing noise, and
                      bit-flip measurement noise. We numerically compare our
                      method with the standard, yet generally inefficient,
                      fidelity test and to a pair of efficient witnesses,
                      verifying the increased robustness of our method. Last but
                      not least, we provide the full translation of our analysis
                      to a trapped-ion native gate set that makes it suitable for
                      experimental applications.},
      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:000674698700001},
      doi          = {10.1103/PRXQuantum.2.020304},
      url          = {https://juser.fz-juelich.de/record/902776},
}