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001048966 005__ 20251211202155.0
001048966 0247_ $$2arXiv$$aarXiv:2511.10191
001048966 0247_ $$2datacite_doi$$a10.34734/FZJ-2025-05063
001048966 037__ $$aFZJ-2025-05063
001048966 088__ $$2arXiv$$aarXiv:2511.10191
001048966 1001_ $$0P:(DE-Juel1)192118$$aOld, Josias$$b0$$eCorresponding author$$ufzj
001048966 245__ $$aAddressable fault-tolerant universal quantum gate operations for high-rate lift-connected surface codes
001048966 260__ $$c2025
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001048966 500__ $$a13 pages, 12 Figures
001048966 520__ $$aQuantum 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.
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001048966 536__ $$0G:(BMBF)390534769$$aEXC 2004:  Matter and Light for Quantum Computing (ML4Q) (390534769)$$c390534769$$x2
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001048966 7001_ $$0P:(DE-Juel1)201506$$aBechar, Juval$$b1
001048966 7001_ $$0P:(DE-Juel1)179396$$aMüller, Markus$$b2$$ufzj
001048966 7001_ $$0P:(DE-Juel1)184903$$aHeußen, Sascha$$b3
001048966 8564_ $$uhttps://arxiv.org/abs/2511.10191
001048966 8564_ $$uhttps://juser.fz-juelich.de/record/1048966/files/old2025addressable.pdf$$yOpenAccess
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001048966 9141_ $$y2025
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