Topological approach toward quantum codes with realistic physical constraints

TL;DR

This paper explores fundamental limits of quantum error-correcting codes with physical constraints, focusing on code distances and self-correcting memories using topological methods on lattice-supported stabilizer codes.

Contribution

It introduces a topological framework to analyze quantum codes with local interactions, providing new insights into their fundamental limits under physical constraints.

Findings

Upper bounds on code distances for local quantum codes

Feasibility analysis of self-correcting quantum memories

Topological perspective reveals new constraints on quantum code design

Abstract

The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum error-correcting codes with geometrically local generators, (b) the feasibility of a self-correcting quantum memory. To investigate these problems, we study stabilizer codes supported by local interaction terms with translation and scale symmetries on a $D$-dimensional lattice. Our analysis uses the notion of topology emerging in geometric shapes of logical operators, which sheds a surprising new light on theory of quantum codes with physical constraints.