Tensor-Network Codes
Farrelly T, Harris RJ, McMahon N, Stace TM (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 127
Journal Issue: 4
DOI: 10.1103/PhysRevLett.127.040507
Abstract
We introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. These codes can correspond to any geometry, but, as a special case, we generalize holographic codes beyond those constructed from perfect or block-perfect isometries, and we give an example that corresponds to neither. Using the tensor-network decoder, we find a threshold of 18.8% for this code under depolarizing noise. We show that, for holographic codes, the exact tensor-network decoder (with no bond-dimension truncation) has polynomial complexity in the number of physical qubits, even for locally correlated noise, making this the first efficient decoder for holographic codes against Pauli noise and, also, a rare example of a decoder that is both efficient and exact.
Authors with CRIS profile
Involved external institutions
Australia (AU)How to cite
APA:
Farrelly, T., Harris, R.J., McMahon, N., & Stace, T.M. (2021). Tensor-Network Codes. Physical Review Letters, 127(4). https://doi.org/10.1103/PhysRevLett.127.040507
MLA:
Farrelly, Terry, et al. "Tensor-Network Codes." Physical Review Letters 127.4 (2021).
BibTeX: Download