2025/11/13 by Old, Josias, Bechar, Juval, Müller, Markus +1
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2511.10191
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, O(n1/3), O(n1/3)]]. 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 \Hi, Hi, Ci Xj\i,j ∈ (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 pth ≈ 4.8⋅ 10-3-1.2⋅ 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.