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Paper 1
Fast surgery for quantum LDPC codes
Nouédyn Baspin, Lucas Berent, Lawrence Z. Cohen
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.04521
- arXiv
- 2510.04521
Quantum LDPC codes promise significant reductions in physical qubit overhead compared with topological codes. However, many existing constructions for performing logical operations come with distance-dependent temporal overheads. We introduce a scheme for performing generalized surgery on quantum LDPC codes using a constant number of rounds of syndrome measurement. The merged code in our scheme is constructed by taking the total complex of the base code and a suitably chosen homomorphic chain complex. We demonstrate the applicability of our scheme on an example multi-cycle code and assess the performance under a phenomenological noise model, showing that fast surgery performs comparably to standard generalized surgery with multiple rounds. Our results pave the way towards fault-tolerant quantum computing with LDPC codes with both low spatial and temporal overheads.
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Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements
Ryota Nakai, Hayato Goto
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.04526
- arXiv
- 2510.04526
Quantum error-correcting codes (QECCs) require high encoding rate in addition to high threshold unless a sufficiently large number of physical qubits are available. The many-hypercube (MHC) codes defined as the concatenation of the [[6,4,2]] quantum error-detecting code have been proposed as high-performance and high-encoding-rate QECCs. However, the concatenated codes have a disadvantage that the syndrome weight grows exponentially with respect to the concatenation level. To address this issue, here we propose subsystem quantum codes based on the MHC codes. In particular, we study the smallest subsystem MHC codes, namely, subsystem codes derived from the concatenated [[4,2,2]] error-detecting codes. The resulting codes have a constant syndrome-measurement weight of 4, while keeping high encoding rates. We build the block-MAP and neural-network decoders and show that they demonstrate superior performance to the bounded-distance decoder.
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