A Holographic Quantum Code

Grant Elliot

Abstract


Abstract: It was shown by [2] how bulk operators in the AdS/CFT correspondence can be represented on the boundary analogously to the way logical qubits are represented in an encoded subspace in quantum error correction. Then in [1]  holographic tensor networks that serve as toy models of the bulk boundary. This paper reviews some of the developments of [1] and [2]. Then it is demonstrated explicitly how to construct perfect tensors, which are essential to the tensor networks mentioned in [2]. Lastly a new example of a holographic quantum error-correcting code based on an eight index perfect tensor is presented.

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References


F. Pastawski, B. Yoshida, D. Harlow, and J. Preskill, Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence, JHEP 06 (2015) 149

A. Almheiri, X. Dong, and D. Harlow, Bulk Locality and Quantum Error Correction in AdS/CFT, JHEP 04 (2015) 163.20

W. Helwig and W. Cui, arXiv:1306.2536.

I. Reed and G. Solomon, “Polynomial codes over certain finite fields,” Journal of the Society for Industrial and Applied Mathematics, vol. 8, no. 2, pp. 300–304, 1960

J. H. Van Lint T. A. Springer "Generalized Reed-Solomon Codes and Algebraic-Geometry" IEEE Trans. Inform. Theoryvol. 33 pp. 305-309 May 1987




DOI: http://dx.doi.org/10.32473/ufjur.v20i2.106167

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ISSN: 2683-0668

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