Towards Block-Level Fault-Tolerant Quantum Simulation on Small High-Rate Non-CSS Codes
Abstract
Small high-rate non-CSS stabilizer codes provide compact platforms for encoded quantum computation, but mixed-Pauli checks and limited native transversal logical gates complicate fault-tolerant dynamics. Block-level constructions offer an alternative by mapping an entire logical block to a physical circuit rather than compiling separately protected logical gates. We investigate this approach using the high-rate [[8,3,3]] non-CSS code and logical Trotter circuits as a testbed. We construct flagged syndrome-extraction circuits and establish a circuit-level memory pseudo-threshold near 1.5×10−3. We then apply our symplectic-transvection construction, which maps a logical Trotter circuit to a physical circuit with the same block pattern for any stabilizer code. Although this mapping preserves the intended unitary algebraically, encoded Trotter circuits exhibit asymmetry between logical-X and logical-Z failure channels. Single-fault analysis identifies the mechanism: a fault on the shared parity ancilla can propagate through the uncomputation network into an undetectable logical operator, reducing the effective circuit distance in the affected sector. We evaluate flag-conditioned recovery, biased-noise decoding, CliNR resource verification, flag postselection, and asymmetric gate-noise models. These methods suppress propagated faults but do not simultaneously suppress both logical sectors in the realistic configurations studied. A diagnostic protected limit removing the identified malignant first-order locations restores pseudo-threshold behavior in both sectors, approaching memory performance. These results demonstrate the potential of block-level logical constructions for non-CSS codes without rich native transversal gate sets and the joint protection of the parity network, analog rotation, and recovery required to preserve fault-tolerant distance.
Related
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BibTeX
@misc{chen2026towards,
title = {{Towards Block-Level Fault-Tolerant Quantum Simulation on Small High-Rate Non-CSS Codes}},
author = {Zhuangzhuang Chen and Narayanan Rengaswamy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16159},
eprint = {2609.16159},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16159},
}
RIS
TY - UNPB
TI - Towards Block-Level Fault-Tolerant Quantum Simulation on Small High-Rate Non-CSS Codes
AU - Zhuangzhuang Chen
AU - Narayanan Rengaswamy
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.16159
UR - https://arxiv.org/abs/2609.16159
AB - Small high-rate non-CSS stabilizer codes provide compact platforms for encoded quantum computation, but mixed-Pauli checks and limited native transversal logical gates complicate fault-tolerant dynamics. Block-level constructions offer an alternative by mapping an entire logical block to a physical circuit rather than compiling separately protected logical gates. We investigate this approach using the high-rate [[8,3,3]] non-CSS code and logical Trotter circuits as a testbed. We construct flagged syndrome-extraction circuits and establish a circuit-level memory pseudo-threshold near 1.5×10^−3. We then apply our symplectic-transvection construction, which maps a logical Trotter circuit to a physical circuit with the same block pattern for any stabilizer code. Although this mapping preserves the intended unitary algebraically, encoded Trotter circuits exhibit asymmetry between logical-X and logical-Z failure channels. Single-fault analysis identifies the mechanism: a fault on the shared parity ancilla can propagate through the uncomputation network into an undetectable logical operator, reducing the effective circuit distance in the affected sector. We evaluate flag-conditioned recovery, biased-noise decoding, CliNR resource verification, flag postselection, and asymmetric gate-noise models. These methods suppress propagated faults but do not simultaneously suppress both logical sectors in the realistic configurations studied. A diagnostic protected limit removing the identified malignant first-order locations restores pseudo-threshold behavior in both sectors, approaching memory performance. These results demonstrate the potential of block-level logical constructions for non-CSS codes without rich native transversal gate sets and the joint protection of the parity network, analog rotation, and recovery required to preserve fault-tolerant distance.
ER -