Problem
Research questions and friction points this paper is trying to address.
entanglement-assisted quantum codes
QC-LDPC codes
encoder optimization
CNOT complexity
quantum error correction
Optimizing Encoder Circuits of Entanglement-Assisted Quantum LDPC Codes via Beam Search
🤖 AI Summary
This work addresses the excessive number of CNOT gates in encoders for entanglement-assisted (EA) quantum QC-LDPC codes by formulating encoder optimization as a row-operation search problem over GF(2), building upon the Sharma–Kumar–Garani (SKG) construction. The authors propose, for the first time, an optimization algorithm that integrates beam search with a Hamming-distance-based heuristic. By decomposing binary matrices derived from CNOT subsequences, the method significantly reduces gate count while preserving the structured nature of the encoder. Evaluated across multiple families of EA quantum QC-LDPC codes, the approach achieves a 7.3%–34.0% reduction in CNOT gate count compared to the SKG baseline and outperforms the Patel–Markov–Hayes synthesis method. Correctness of the optimized encoders is verified through stabilizer table simulations.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
beam search
entanglement-assisted quantum LDPC codes
CNOT optimization
GF(2) row operations
quantum encoder synthesis
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