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@ARTICLE{Guedes:1023042,
      author       = {Guedes, Thiago L. M. and Winter, Don and Müller, Markus},
      title        = {{Q}uantum cellular automata for quantum error correction
                      and density classification},
      publisher    = {arXiv},
      reportid     = {FZJ-2024-01623},
      year         = {2023},
      abstract     = {Quantum cellular automata are alternative quantum-computing
                      paradigms to quantum Turing machines and quantum circuits.
                      Their working mechanisms are inherently automated, therefore
                      measurement free, and they act in a translation invariant
                      manner on all cells/qudits of a register, generating a
                      global rule that updates cell states locally, i.e., based
                      solely on the states of their neighbors. Although desirable
                      features in many applications, it is generally not clear to
                      which extent these fully automated discrete-time local
                      updates can generate and sustain long-range order in the
                      (noisy) systems they act upon. In special, whether and how
                      quantum cellular automata can perform quantum error
                      correction remain open questions. We close this conceptual
                      gap by proposing quantum cellular automata with
                      quantum-error-correction capabilities. We design and
                      investigate two (quasi-)one dimensional quantum cellular
                      automata based on known classical cellular-automata rules
                      with density-classification capabilities, namely the local
                      majority voting and the two-line voting. We investigate the
                      performances of those quantum cellular automata as
                      quantum-memory components by simulating the number of update
                      steps required for the logical information they act upon to
                      be afflicted by a logical bit flip. The proposed designs
                      pave a way to further explore the potential of new types of
                      quantum cellular automata with built-in quantum error
                      correction capabilities.},
      keywords     = {Quantum Physics (quant-ph) (Other) / FOS: Physical sciences
                      (Other)},
      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},
      doi          = {10.48550/ARXIV.2309.03608},
      url          = {https://juser.fz-juelich.de/record/1023042},
}