Towards “Good-Enough” Quantum Low-Density Parity-Check Codes
The accumulation of errors in quantum computers obstructs the execution of powerful algorithms. Hence,
current quantum computers require Quantum Error Correction (QEC) in order to be functional and reliable
even in the presence of such errors, something known as Fault-Tolerant Quantum Computation (FTQC).
Conventional strategies for protecting and correcting against qubit errors, such as Surface Codes, suffer
from large overheads in the number of physical qubits that are used to encode logical information. In other
words, practical implementation of quantum error-correcting codes requires a better ratio between the
number of logical and physical qubits, something known as a high encoding rate. Quantum Tanner Codes
have been shown to be optimal in the asymptotic limit due to their rich structure, providing a potential
solution to this conundrum. However, “good-enough” finite explicit constructions have not been found so
far. In this work, we reformulate Tanner codes as unconventional lattice gauge theories describing spin
many-body systems. Preliminary results indicate the potential for an unusually robust relative of
topologically ordered matter as a key element for the outstanding capabilities of this family of codes.