GB codes are expressed as cyclic submodules of R_ℓ² to derive necessary and sufficient conditions for block-separable automorphisms and fold-transversal gates, with the new MCR family demonstrated to generate the 2-qubit Clifford group for k=2 codes up to distance 13.
arXiv preprint arXiv:2603.05082 , year=
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
fields
quant-ph 6years
2026 6roles
background 1polarities
background 1representative citing papers
Full extractors for HGP codes are built to enable logical processing via PBC without compilation overhead, with sizes 50-80% of base codes and low error rates in simulations.
Concatenating quantum Reed-Solomon codes over the gross code via Galois qudits reaches teraquop regime at uniform 10^{-3} noise with reduced overhead.
A forced-gap post-selection strategy using repeated Relay-BP decoder runs improves logical error rates by over 4x on 72- and 144-qubit bivariate bicycle codes at fixed post-selection rate.
Compactification of a single higher-dimensional hypergraph-product fracton model yields a broad family of translation-invariant quantum LDPC codes that includes fracton models and all A2BGA codes such as BB codes.
A trapped-ion architecture based on LDPC codes and cat-state factories achieves 110 logical qubits and one million T gates per day using 2514 physical qubits, with estimates for Heisenberg model simulation on 100 sites in one month using 10000 qubits.
citing papers explorer
-
Generalized Bicycle Codes as Cyclic Submodules and their Automorphism Structure
GB codes are expressed as cyclic submodules of R_ℓ² to derive necessary and sufficient conditions for block-separable automorphisms and fold-transversal gates, with the new MCR family demonstrated to generate the 2-qubit Clifford group for k=2 codes up to distance 13.
-
Full Extractors for Logical Processing in Hypergraph Product Codes
Full extractors for HGP codes are built to enable logical processing via PBC without compilation overhead, with sizes 50-80% of base codes and low error rates in simulations.
-
Concatenating Algebraic Codes over High-Rate Quantum LDPC Codes
Concatenating quantum Reed-Solomon codes over the gross code via Galois qudits reaches teraquop regime at uniform 10^{-3} noise with reduced overhead.
-
Forced Gap Post-Selection for Quantum LDPC Codes and their Operations
A forced-gap post-selection strategy using repeated Relay-BP decoder runs improves logical error rates by over 4x on 72- and 144-qubit bivariate bicycle codes at fixed post-selection rate.
-
Translation-invariant quantum low-density parity-check codes from compactified fracton models
Compactification of a single higher-dimensional hypergraph-product fracton model yields a broad family of translation-invariant quantum LDPC codes that includes fracton models and all A2BGA codes such as BB codes.
-
Fault-Tolerant Quantum Computing with Trapped Ions: The Walking Cat Architecture
A trapped-ion architecture based on LDPC codes and cat-state factories achieves 110 logical qubits and one million T gates per day using 2514 physical qubits, with estimates for Heisenberg model simulation on 100 sites in one month using 10000 qubits.