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arXiv:2606.11468 · IEEE Transactions on Circuits & Systems II Express Briefs

Optimizing Encoder Circuits of Entanglement-Assisted Quantum LDPC Codes via Beam Search

Aditya Sodhani, Pavan Kumar, Shayan Srinivasa Garani, Keshab K. Parhi

quant-phcs.ITSubmitted Jun 9, 2026• Announced Jun 11, 2026• 0 citations

v1 · Jun 9, 2026 v2 · Aug 28, 2026

Abstract

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 all encoder implementations based on the stabilizer formalism, the dominant contribution to this complexity comes from the use of controlled gates. In this paper, we adopt the Sharma-Kumar-Garani (SKG) 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 SKG baseline encoder. The optimized circuits also yield lower CNOT counts than Patel-Markov-Hayes synthesis on all tested instances and are verified by stabilizer-tableau simulation. These results show that substantial encoder simplification is possible for structured EA QC-LDPC codes.

Journal reference: IEEE Trans. Circuits and Systems II: Express Briefs, 73, 2026
DOI: 10.1109/TCSII.2026.3734949

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