Posted

Fermi Ma, Xinyu Tan, John Wright (Oct 09 2025).
Abstract: We study the error correcting properties of Haar random codes, in which a KK-dimensional code space CCN\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 mm Pauli errors can be approximately corrected so long as mKNmK \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.

Order by:

Want to join this discussion?

Join our community today and start discussing with our members by participating in exciting events, competitions, and challenges. Sign up now to engage with quantum experts!