All Abstracts | Poster Abstracts | Talk Abstracts

Subsystem and stabilizer quantum codes with spatially local generators

Sergey Bravyi, IBM Watson Research Center

(Session 2 : Thursday from 5:15pm-6:00pm)

Abstract. Fault-tolerant quantum computation based on 2D topological quantum codes has received a considerable attention lately since it can be implemented on quantum machines with a geometrically local architecture. To better understand the potential of topological codes we derive upper bounds on the parameters of quantum codes that stem from the spatial locality constraint and find families of codes that achieve these bounds. Our analysis applies to both subspace and subsystem quantum codes. We also discuss topological subsystem codes (TSCs) proposed recently by Bombin. These codes require only the measurement of two-qubit nearest-neighbor operators for error correction. We demonstrate that TSCs can be viewed as generalizations of Kitaev's honeycomb model to 3-valent hypergraphs. This new connection provides a systematic way of constructing TSCs and analyzing their properties. Furthermore, we propose and implement some candidate decoding algorithms for one particular TSC assuming perfect error correction. Our Monte Carlo simulations indicate that this code, which we call the five-squares code, has a threshold against depolarizing noise of at least 2%.