Research Progress

Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry

Source Jan 03,2023

Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. They may potentially be used for fault-tolerant quantum computation. 

In a recent study, we calculated optimal error thresholds for quantum error correcting codes based on fracton models. By mapping the error-correction process for bit-flip and phase-flip noises into novel statistical models with Ising variables and random multi-body couplings, we obtained models that exhibit an unconventional subsystem symmetry instead of a more usual global symmetry. We performed large-scale parallel tempering Monte Carlo simulations to obtain disorder-temperature phase diagrams, which were then used to predict optimal error thresholds for the corresponding fracton code. Remarkably, we found that the X-cube fracton code displays a minimum error threshold (7.5%) that is much higher than 3D topological codes such as the toric code (3.3%), or the color code (1.9%). This result, together with the predicted absence of glass order at the Nishimori line, shows great potential for fracton phases to be used as quantum memory platforms. 

This result was recently published in Physical Review Letters ( and featured as the cover of that issue ( The work was jointly completed by Prof. Hao Song (ITP-CAS), Dr. Janik Schonmeier-Kromer (University of Munich), Dr. Ke Liu (University of Munich), Dr. Oscar Viyuela (MIT & Harvard), Prof. Lode Pollet (University of Munich), and Prof. M. A. Martin-Delgado (Complutense University of Madrid).



Institute of Theoretical Physics, CAS