Quantum Error Corrections and Z(2) Lattice Models

To construct a quantum computer which may be superior to conventional supercomputers, fault-tolerant architecture is essential. Here we look at the basics of Quantum Error Corrections (QEC) via the case of topological quantum memory with a simple Pauli error (Dennis et al.), and introduce the concept of threshold probability in QEC. Dennis et al. showed that this threshold probability can be studied through a phase diagram of a mapped statistical mechanics model. Following this, in arXiv:2402.14004 we find a statistical mechanics model mapping of the surface/toric code with realistic circuit-level noise and syndrome noise: the Random-Coupled Plaquette Gauge Model (or Z(2) x Z(2) lattice gauge theory in 3-dimension). We perform Monte Carlo simulation of the mapped model with a parallel tempering metropolis algorithm and study the phase diagram. Here, we report the numerical results.