Building better quantum error-correcting codes with finite-field algebra

A systematic method for designing quantum error-correcting codes combines finite-field algebra with a two-stage lifting procedure to guarantee good structural properties — no short cycles, no harmful logical errors — without relying on randomness. The resulting 10,240-qubit code hits a frame error rate of 10⁻⁷ at a depolarizing noise level of 5.8%, close to the theoretical limit. For fault-tolerant quantum computing, having explicit, algebraically verified codes with predictable finite-size performance matters more than asymptotic promises.