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Paper 1
Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes
A. Bolt, D. Poulin, T. M. Stace
- Year
- 2018
- Journal
- arXiv preprint
- DOI
- arXiv:1810.11572
- arXiv
- 1810.11572
Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error correcting codes into larger fault-tolerant networks. Here we present an efficient heuristic decoding scheme for foliated quantum codes, based on message passing between primal and dual code 'sheets'. We test this decoder on two different families of sparse quantum error correcting code: turbo codes and bicycle codes, and show reasonably high numerical performance thresholds. We also present a construction schedule for building such code states.
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Tradeoffs on the volume of fault-tolerant circuits
Anirudh Krishna, Gilles Zémor
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.03057
- arXiv
- 2510.03057
Dating back to the seminal work of von Neumann [von Neumann, Automata Studies, 1956], it is known that error correcting codes can overcome faulty circuit components to enable robust computation. Choosing an appropriate code is non-trivial as it must balance several requirements. Increasing the rate of the code reduces the relative number of redundant bits used in the fault-tolerant circuit, while increasing the distance of the code ensures robustness against faults. If the rate and distance were the only concerns, we could use asymptotically optimal codes as is done in communication settings. However, choosing a code for computation is challenging due to an additional requirement: The code needs to facilitate accessibility of encoded information to enable computation on encoded data. This seems to conflict with having large rate and distance. We prove that this is indeed the case, namely that a code family cannot simultaneously have constant rate, growing distance and short-depth gadgets to perform encoded CNOT gates. As a consequence, achieving good rate and distance may necessarily entail accepting very deep circuits, an undesirable trade-off in certain architectures and applications.
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