Author(s): Ryota Nakai and Hayato Goto Quantum error-correcting codes (QECCs) require high encoding rates in addition to high thresholds unless a sufficiently large number of physical qubits are available. Many-hypercube (MHC) codes, defined as concatenations of the [ [ 6 , 4 , 2 ] ] quantum error-detecting code, have been proposed as high-perfo… [Phys. Rev. Applied 25, 014032] Published Tue Jan 13, 2026