Decoherence-free Subspaces

Decoherence-free Subspaces

A decoherence-free subspace (DFS) is a subspace of a system's Hilbert space that is invariant to non-unitary dynamics. Alternatively stated, they are a small section of the system Hilbert space where the system is decoupled from the environment and thus its evolution is completely unitary. DFSs can also be characterized as a special class of quantum error correcting codes. In this representation they are passive error-preventing codes since these subspaces are encoded with information that (possibly) won't require any active stabilization methods. These subspaces prevent destructive environmental interactions by isolating quantum information. As such, they are an important subject in quantum computing, where (coherent) control of quantum systems is the desired goal. Decoherence creates problems in this regard by causing loss of coherence between the quantum states of a system and therefore the decay of their interference terms, thus leading to loss of information from the (open) quantum system to the surrounding environment. Since quantum computers cannot be isolated from their environment (i.e. we cannot have a truly isolated quantum system in the real world) and information can be lost, the study of DFSs is important for the implementation of quantum computers into the real world.