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Quantum Machine Learning
Quantum Error Correction Fault Tolerance
Haar random codes attain the quantum Hamming bound, approximately
arXiv
Authors: Fermi Ma, Xinyu Tan, John Wright
Year
2025
Paper ID
51618
Status
Preprint
Abstract Read
~2 min
Abstract Words
115
Citations
N/A
Abstract
We study the error correcting properties of Haar random codes, in which a K-dimensional code space boldsymbol{C} subseteq mathbb{C}N is chosen at random from the Haar distribution. Our main result is that Haar random codes can approximately correct errors up to the quantum Hamming bound, meaning that a set of m Pauli errors can be approximately corrected so long as mK ll N. This is the strongest bound known for any family of quantum error correcting codes (QECs), and continues a line of work showing that approximate QECs can significantly outperform exact QECs [LNCY97, CGS05, BGG24]. Our proof relies on a recent matrix concentration result of Bandeira, Boedihardjo, and van Handel.
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- This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
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- We study the error correcting properties of Haar random codes, in which a K-dimensional code space boldsymbolC subseteq mathbbC^N is chosen at random from the Haar distribution.
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