Stabilizer codes for Open Quantum Systems

Reliable models of a large variety of open quantum systems can be described by Lindblad master equation. An important property of some open quantum systems is the existence of decoherence-free subspaces. In this paper, we develop tools for constructing stabilizer codes over open quantum systems governed by Lindblad master equation. We apply the developed stabilizer code formalism to the area of quantum metrology. In particular, a strategy to attain the Heisenberg limit scaling is proposed.