Introduction to quantum LDPC codes – constructions, decoding and logical gates

Anqi Gong

PhD student of ETH in the QIT Group

Abstract

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Quantum low-density parity-check (qLDPC) codes have recently attracted significant interest due to their high encoding rates and good distance properties, while still requiring only low-weight stabilizer measurements. In this introductory talk, I will present leading constructions for qLDPC codes, such as the hypergraph-product and lift-product methods, and briefly discuss how the resulting codes can be realized on actual quantum hardware. 
 
I will then introduce two basic decoding techniques—belief propagation (BP) and BP combined with ordered statistics decoding (OSD)—and explain how these can be adapted to the more realistic circuit-level noise model. Numerical studies suggest that qLDPC codes are promising candidates for robust quantum memory. However, implementing fault-tolerant logical gates on these codes remains a major challenge, with all current approaches incurring notable time overhead.
 
Nevertheless, I will discuss two important techniques—automorphism-based gates and surgery-type gates—for realizing Clifford operations. When combined with magic state distillation and injection for non-Clifford gates, these approaches open a path toward universal quantum computation using qLDPC codes.