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@ARTICLE{Old:1048966,
      author       = {Old, Josias and Bechar, Juval and Müller, Markus and
                      Heußen, Sascha},
      title        = {{A}ddressable fault-tolerant universal quantum gate
                      operations for high-rate lift-connected surface codes},
      reportid     = {FZJ-2025-05063, arXiv:2511.10191},
      year         = {2025},
      note         = {13 pages, 12 Figures},
      abstract     = {Quantum low-density parity check (qLDPC) codes are among
                      the leading candidates to realize error-corrected quantum
                      memories with low qubit overhead. Potentially high encoding
                      rates and large distance relative to their block size make
                      them appealing for practical suppression of noise in
                      near-term quantum computers. In addition to increased
                      qubit-connectivity requirements compared to more
                      conventional topological quantum error correcting codes,
                      qLDPC codes remain notoriously hard to compute with. In this
                      work, we introduce a construction to implement all Clifford
                      quantum gate operations on the recently introduced
                      lift-connected surface (LCS) codes (Old et al. 2024). These
                      codes can be implemented in a 3D-local architecture and
                      achieve asymptotic scaling $[[n, \mathcal{O}(n^{1/3}),
                      \mathcal{O}(n^{1/3})]]$. In particular, LCS codes realize
                      favorable instances with small numbers of qubits: For the
                      $[[15,3,3]]$ LCS code, we provide deterministic
                      fault-tolerant (FT) circuits of the logical gate set
                      $\{\overline{H}_i, \overline{S}_i, \overline{C_i X_j}\}_{i,j
                      \in (0,1,2)}$ based on flag qubits. By adding a procedure
                      for FT magic state preparation, we show quantitatively how
                      to realize an FT universal gate set in $d=3$ LCS codes.
                      Numerical simulations indicate that our gate constructions
                      can attain pseudothresholds in the range $p_{\mathrm{th}}
                      \approx 4.8\cdot 10^{-3}-1.2\cdot 10^{-2}$ for circuit-level
                      noise. The schemes use a moderate number of qubits and are
                      therefore feasible for near-term experiments, facilitating
                      progress for fault-tolerant error corrected logic in
                      high-rate qLPDC codes.},
      cin          = {PGI-2},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522) / BMBF 13N16073 - MUNIQC-Atoms -
                      Neutralatom-basierter Quantencomputer-Demonstrator
                      (BMBF-13N16073) / EXC 2004:  Matter and Light for Quantum
                      Computing (ML4Q) (390534769)},
      pid          = {G:(DE-HGF)POF4-5221 / G:(DE-Juel1)BMBF-13N16073 /
                      G:(BMBF)390534769},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2511.10191},
      howpublished = {arXiv:2511.10191},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2511.10191;\%\%$},
      doi          = {10.34734/FZJ-2025-05063},
      url          = {https://juser.fz-juelich.de/record/1048966},
}