Quantum low-density parity-check (QLDPC) codes are the leading candidate for performing error correction in scalable fault-tolerant quantum computing systems. This invention presents a method for designing quasi-cyclic lifted-product QLDPC codes to enhance error correction performance in quantum systems, such as quantum computing, communication, and storage. This design makes it possible to create LP-QLDPC codes that ensure a minimum distance strictly greater than that of the lowest-weight stabilizer generators, which achieves superior error correction. By focusing on quasi-cyclic base codes, specifically type-I protographs, the method establishes necessary conditions for code construction based on row and column indices of the base code. This method results in QLDPC codes with certain minimum distance guarantees and degeneracy. Background: Quantum computing is a rapidly growing field that can be used for more applications than classical computers, but it is prone to errors due to quantum decoherence and other noise sources. Error correction is crucial for the development of practical quantum computers. Error correction codes in quantum systems can be thought of as “safety nets” that catch and correct errors, allowing quantum systems to work accurately even in noisy environments where mistakes can easily happen. QLDPC codes are a leading candidate for error correction because of their efficiency and scalability. Traditional QLDPC decoders, however, face limitations in correcting errors quickly and effectively, especially when multiple types of errors occur. Traditional QLDPC code designs often fail to guarantee sufficient minimum distance, leading to increased vulnerability to errors. This method addresses these limitations by developing quasi-cyclic lifted-product QLDPC codes with specific structural constraints, achieving codes with guaranteed minimum distances and degeneracy properties that enhance error-correction capabilities. This construction method enhances fault tolerance in quantum systems, allowing for more stable and efficient quantum information processing and communication. Applications:
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