High-Rate Quantum Codes with Proven Distance and Low-Weight Measurements
Abstract
We study a family of quantum subsystem codes defined on rectangular coordinate grids of any dimension, with even side lengths of at least four. The directly measured operators act along coordinate lines. For every member of the family, we derive the number of protected logical qubits and prove its dressed distance without a numerical search. To illustrate the resulting design choices, we impose a budget of at most 10,000 data qubits and determine the complete tradeoff between encoding rate and measurement weight within this family at distances 16, 32, and 64. At distance 16, one code protects 4,096 logical qubits among 10,000 data qubits using weight-ten measurements. At distances 32 and 64, codes with 7,776 and 9,216 data qubits protect 1,024 and 256 logical qubits, respectively, using weight-six measurements. We include and explain Lean code snippets throughout the paper to guide readers through the formal verification of our subsystem-code construction and its dressed and bare distances.
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BibTeX
@misc{bharti2026highrate,
title = {{High-Rate Quantum Codes with Proven Distance and Low-Weight Measurements}},
author = {Kishor Bharti and Tobias Haug and Runzhou Tao and Kevin Ye},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02621},
eprint = {2610.02621},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02621},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - High-Rate Quantum Codes with Proven Distance and Low-Weight Measurements
AU - Kishor Bharti
AU - Tobias Haug
AU - Runzhou Tao
AU - Kevin Ye
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02621
UR - https://arxiv.org/abs/2610.02621
AB - We study a family of quantum subsystem codes defined on rectangular coordinate grids of any dimension, with even side lengths of at least four. The directly measured operators act along coordinate lines. For every member of the family, we derive the number of protected logical qubits and prove its dressed distance without a numerical search. To illustrate the resulting design choices, we impose a budget of at most 10,000 data qubits and determine the complete tradeoff between encoding rate and measurement weight within this family at distances 16, 32, and 64. At distance 16, one code protects 4,096 logical qubits among 10,000 data qubits using weight-ten measurements. At distances 32 and 64, codes with 7,776 and 9,216 data qubits protect 1,024 and 256 logical qubits, respectively, using weight-six measurements. We include and explain Lean code snippets throughout the paper to guide readers through the formal verification of our subsystem-code construction and its dressed and bare distances.
ER -