Bibliographic Information: Hong, Y. (2024). Single-shot preparation of hypergraph product codes via dimension jump. arXiv preprint arXiv:2410.05171v1.
Research Objective: This paper introduces a new method for preparing the codespace of constant-rate hypergraph product (HGP) codes, aiming to overcome the limitations of traditional transversal initialization techniques that require multiple rounds of syndrome measurements and are susceptible to errors.
Methodology: The authors propose a two-stage protocol. The first stage involves transversally initializing a "thickened" code, created by the homological product of the target HGP code and a classical repetition code. This thickened code possesses soundness, enabling single-shot preparation. The second stage involves measuring a subset of qubits to collapse the thickened code onto the desired HGP code, followed by a novel decoding algorithm that corrects for errors introduced during the collapse.
Key Findings: The proposed protocol achieves single-shot preparation of constant-rate HGP codes in constant depth, requiring only O(√n) spatial overhead. The protocol is shown to be robust against adversarial noise, ensuring fault tolerance during the initialization process.
Main Conclusions: This work provides a significant advancement in fault-tolerant quantum computing by enabling efficient and reliable preparation of HGP codes, a promising family of quantum error-correcting codes. The single-shot nature of the protocol reduces the temporal bottleneck associated with traditional initialization methods, paving the way for faster and more robust quantum computation.
Significance: This research contributes significantly to the field of quantum error correction by addressing a critical challenge in utilizing HGP codes for fault-tolerant quantum computing. The proposed protocol and its analysis provide valuable insights for practical implementation of these codes in future quantum computers.
Limitations and Future Research: While the protocol demonstrates significant advantages, the authors acknowledge the need for further exploration of alternative classical codes beyond repetition codes to potentially reduce the spatial overhead. Investigating the performance of the protocol under more realistic noise models and with practical decoders is also suggested for future research.
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