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Quantum spin liquids and anyons, used to be subjects of condensed matterphysics, now are realized in various platforms of qubits, offeringunprecedented opportunities to investigate fundamental physics of many-bodyquantum entangled states. Qubits are inevitably exposed to environment effectssuch as decoherence and dissipation, which are believed to be detrimental tomany-body entanglement. Here, we argue that unlike the common beliefdecoherence and dissipation can give rise to novel topological phenomena inquantum spin liquids. We study open quantum systems of the Kitaev spin liquidand the toric code via the Lindblad master equation approach. By using exactsolutions and numerical approaches, we show the dynamical occurrence of anyoncondensation by decoherence and dissipation, which results in a topologicaltransition from the initial state spin liquid to the steady state spin liquid.The mechanism of the anyon condensation transition by the Lindblad dynamics iselucidated. We also provide an insight into the relationship between the Kitaevspin liquid and the toric code in the picture of anyon condensation. Our worksuggests open quantum systems to be a new venue for topological phenomena ofquantum spin liquids and anyons.

Mixed-State Quantum Spin Liquids and Dynamical Anyon Condensations in Kitaev Lindbladians