Optimizing Encoder Circuits of Entanglement-Assisted Quantum LDPC Codes via Beam Search
Abstract
In encoder circuits built on the stabilizer formalism, the dominant contribution to circuit complexity comes from the use of controlled (CNOT) gates, making CNOT-count reduction a central circuit-design objective. Entanglement-assisted (EA) quantum QC-LDPC codes offer strong error-correction capabilities with structured parity-check matrices, but their practical use depends on efficient encoder circuits and the availability of pre-shared Bell pairs (ebits). In this paper, we adopt a prior entanglement-assisted QC-LDPC (EAQC) encoder construction. We formulate the encoder optimization as a search over GF(2) row operations that decompose the binary matrix derived from its CNOT sub-sequence. We solve this problem using a beam search algorithm guided by a Hamming-distance heuristic. For the tested EA quantum QC-LDPC code families, the proposed method achieves CNOT-count reductions of 7.3-34.0% relative to the baseline EAQC encoder. The optimized circuits also outperform the Patel-Markov-Hayes and greedy cost-minimization baselines, and are verified by stabilizer-tableau simulation. These results show that substantial encoder simplification is possible for structured EA QC-LDPC codes.
Versions
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BibTeX
@misc{sodhani2026optimizing,
title = {{Optimizing Encoder Circuits of Entanglement-Assisted Quantum LDPC Codes via Beam Search}},
author = {Aditya Sodhani and Pavan Kumar and Shayan Srinivasa Garani and Keshab K. Parhi},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.11468},
eprint = {2606.11468},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.11468},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Optimizing Encoder Circuits of Entanglement-Assisted Quantum LDPC Codes via Beam Search
AU - Aditya Sodhani
AU - Pavan Kumar
AU - Shayan Srinivasa Garani
AU - Keshab K. Parhi
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2606.11468
UR - https://arxiv.org/abs/2606.11468
AB - In encoder circuits built on the stabilizer formalism, the dominant contribution to circuit complexity comes from the use of controlled (CNOT) gates, making CNOT-count reduction a central circuit-design objective. Entanglement-assisted (EA) quantum QC-LDPC codes offer strong error-correction capabilities with structured parity-check matrices, but their practical use depends on efficient encoder circuits and the availability of pre-shared Bell pairs (ebits). In this paper, we adopt a prior entanglement-assisted QC-LDPC (EAQC) encoder construction. We formulate the encoder optimization as a search over GF(2) row operations that decompose the binary matrix derived from its CNOT sub-sequence. We solve this problem using a beam search algorithm guided by a Hamming-distance heuristic. For the tested EA quantum QC-LDPC code families, the proposed method achieves CNOT-count reductions of 7.3-34.0% relative to the baseline EAQC encoder. The optimized circuits also outperform the Patel-Markov-Hayes and greedy cost-minimization baselines, and are verified by stabilizer-tableau simulation. These results show that substantial encoder simplification is possible for structured EA QC-LDPC codes.
ER -