Symplectic Isometries of Stabilizer Codes

TL;DR

This paper investigates the equivalence of quantum stabilizer codes through symplectic isometries, establishing connections with local Clifford operators and the LU-LC Conjecture.

Contribution

It introduces the notions of monomial and symplectic equivalence for stabilizer codes and explores their relationship, linking monomial maps to local Clifford operators.

Findings

Monomial maps correspond to local Clifford operators.

The paper clarifies the difference between monomial and symplectic equivalences.

Connections are made with the LU-LC Conjecture.

Abstract

In this paper we study the equivalence of quantum stabilizer codes via symplectic isometries of stabilizer codes. We define monomially and symplectically equivalent stabilizer codes and determine how different the two notions can be. Further, we show that to monomial maps correspond local Clifford operators. We relate the latter with the LU-LC Conjecture.