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  • Writer's pictureMin-Hsiu Hsieh

Quantum Error Correction

One of the most important discoveries in quantum information science was the existence of QECCs in 1995. Up to that point, there was a widespread belief that environmental noise would doom any chance of building large scale quantum computers or quantum communication protocols. The discovery of the first QECC defied these expectations, and was quickly followed by the development of the theory of stabiliser codes, thereby drawing on the well-studied theory of classical error correction. However, the connection between classical codes and quantum codes was not universal. Rather, only a subset of classical codes that satisfied a certain constraint could be used to construct quantum codes.

My PhD thesis proposed a methodology to generalize the stabilizer codes. With my supervisors Todd Brun and Igor Devetak, we found that, with the assistance of prior shared entanglement, every classical linear code could be used to construct a corresponding quantum code. The result was published in [Science 314:436–439 (2006)], and became a book chapter in "Quantum Error Correction" published by Cambridge University Press in 2013. My subsequent research into QECCs has been widely cited in papers published in Physical Review Letters, IEEE Transactions on Information Theory, and by distinguished researchers.

  • Entanglement-assisted Coding Theory. PhD Thesis, University of Southern California 2008. [arXiv:0807.2080]

Book Chapter
  • Todd Brun and Min-Hsiu Hsieh. Entanglement-assisted quantum error-correcting codes.Quantum Error Correction, in D. Lidar and T. Brun (eds.), Cambridge University Press (ISBN: 9780521897877), 2013.

  1. Jihao Fan, Min-Hsiu Hsieh, Hanwu Chen, Younghui Li, He Chen. Construction and Performance of Quantum Burst Error Correction Codes for Correlated Errors.  2018 IEEE International Symposium on Information Theory (ISIT), Vail, 2018, pp. 2336-2340

  2. Jihao Fan, Yonghui Li, Min-Hsiu Hsieh, Hanwu Chen. On Quantum Tensor Product Codes. Quantum Information and Computation, vol. 17, no. 13&14, pp. 1105–1122 (2017). 

  3. Ching-Yi Lai, Min-Hsiu Hsieh, Francis Lu. On the MacWilliams Identity for Classical and Quantum Convolutional Codes. IEEE Transactions on Communications, vol. 64, no. 8, pp. 3148–3159 (2016).

  4. Todd Brun, Igor Devetak, and Min-Hsiu Hsieh. Catalytic quantum error correction. IEEE Transactions on Information Theory, vol. 60, no. 6, pp. 3073–3089 (2014).

  5. Mark Wilde, Min-Hsiu Hsieh, and Zunaira Baber. Entanglement-assisted quantum turbo codes. IEEE Transactions on Information Theory, vol. 60, no. 2, pp. 1203–1222 (2014).

  6. Sheng-Mei Zhao, Yu Xiao, Yan Zhu, Xiu-Li Zhu, and Min-Hsiu Hsieh. New class of quantum codes constructed from cyclic difference set. International Journal of Quantum Information, vol. 10, no. 1, p. 1250015 ( 2012). 

  7. Min-Hsiu Hsieh, Wen-Tai Yen, and Li-Yi Hsu. High performance entanglement-assisted quantum LDPC codes need little entanglement. IEEE Transactions on Information Theory, vol. 57, no. 3, pp. 1761–1769 (2011).

  8. Min-Hsiu Hsieh and François Le Gall. NP-hardness of decoding quantum error-correction codes. Physical Review A, vol. 83, no. 5, p. 052331 (2011).

  9. Min-Hsiu Hsieh, Todd Brun, and Igor Devetak. Entanglement-assisted quantum quasicyclic low-density parity-check codes. Physical Review A, vol. 79, no. 3, p. 032340 (2009).

  10. Isaac Kremsky, Min-Hsiu Hsieh, and Todd Brun. Classical enhancement of quantum-error-correcting codes. Physical Review A, vol. 78, no. 1, p. 012341 (2008).

  11. Min-Hsiu Hsieh, Igor Devetak, and Todd Brun. General entanglement-assisted quantum error-correcting codes. Physical Review A, vol. 76, no. 6, p. 062313 (2007).

  12. Todd Brun, Igor Devetak, and Min-Hsiu Hsieh. Correcting quantum errors with entanglement. Science, vol. 314, no. 5798, pp. 436–439 (2006).

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