  Quantum spin liquids and anyons, used to be subjects of condensed matter
physics, now are realized in various platforms of qubits, offering
unprecedented opportunities to investigate fundamental physics of many-body
quantum entangled states. Qubits are inevitably exposed to environment effects
such as decoherence and dissipation, which are believed to be detrimental to
many-body entanglement. Here, we argue that unlike the common belief
decoherence and dissipation can give rise to novel topological phenomena in
quantum spin liquids. We study open quantum systems of the Kitaev spin liquid
and the toric code via the Lindblad master equation approach. By using exact
solutions and numerical approaches, we show the dynamical occurrence of anyon
condensation by decoherence and dissipation, which results in a topological
transition from the initial state spin liquid to the steady state spin liquid.
The mechanism of the anyon condensation transition by the Lindblad dynamics is
elucidated. We also provide an insight into the relationship between the Kitaev
spin liquid and the toric code in the picture of anyon condensation. Our work
suggests open quantum systems to be a new venue for topological phenomena of
quantum spin liquids and anyons.
