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Paper 1
An Error Correctable Implication Algebra for a System of Qubits
Morrison Turnansky
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2511.14797
- arXiv
- 2511.14797
We present the Lukasiewicz logic as a viable system for an implication algebra on a system of qubits. Our results show that the three valued Lukasiewicz logic can be embedded in the stabilized space of an arbitrary quantum error correcting stabilizer code. We then fully characterize the non trivial errors that may occur up to group isomorphism. Lastly, we demonstrate by explicit algorithmic example, how any algorithm consistent with the Lukasiewicz logic can immediately run on a quantum system and utilize the indeterminate state.
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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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