Southwest Quantum Information and Technology

Three-dimensional color code thresholds via statistical-mechanical mapping

Presenting Author: Aleksander Kubica, IQIM, Caltech
Contributing Author(s): Michael Beverland, Fernando Brandao, John Preskill and Krysta Svore

The color code is an example of a topological quantum error-correcting code which recently has gained a lot of attention due to achieving universality without magic-state distillation in three dimensions. Also, the color code illustrates a new and exciting idea of single-shot error correction which might drastically reduce time overhead of quantum computation. In this work we find fundamental bounds on the error-correcting capabilities of the three-dimensional color code, namely the threshold for optimal error correction of bit-flip/phase-flip noise with perfect measurements on the body-centered cubic lattice. In particular, the threshold associated with string-like (one- dimensional) and sheet-like (two-dimensional) logical operators is p_1 ≃ 1.9% and p_2 ≃ 27.5%, respectively. The aforementioned results were obtained by exploiting a connection between error correction and statistical mechanics. We performed parallel tempering Monte Carlo simulations of two previously unexplored three-dimensional statistical-mechanical models: the 4-body and the 6- body random coupling Ising models. We find their phase diagrams in terms of disorder strength and temperature. Our results put constraints on the practical use of the color code from the viewpoint of efficient decoders and bounding overhead.

(Session 9a : Friday from 4:15pm - 4:45pm)