Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code

Understand

Classically simulating the dynamics of anyonic excitations in two-dimensional quantum systems is likely intractable in general because such dynamics are sufficient to implement universal quantum computation.

• However, processes of interest for the study of quantum error correction in anyon systems are typically drawn from a restricted class that displays significant structure over a wide range of system parameters.
• We exploit this structure to classically simulate, and thereby demonstrate the success of, an error-correction protocol for a quantum memory based on the universal Fibonacci anyon model.
• We numerically simulate a phenomenological model of the system and noise processes on lattice sizes of up to 128x128 sites, and find a lower bound on the error-correction threshold of approximately 0.125 errors per edge, which is comparable to those previously known for abelian and (non-universal) nonabelian anyon models.