Abstract: Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians. We provide significant analytical and numerical insights into the power of dissipation for preparing the ground state of non-commuting Hamiltonians. For quasi-free dissipative dynamics, which includes certain 1D spin systems with boundary dissipation, we prove an explicit and sharp bound on the mixing time, which scales polynomially in system size. Our results reveal a new connection between the mixing time in trace distance and spectral properties of a non-Hermitian Hamiltonian, and highlight the role of the coherent term in the dissipative dynamics that is often not amenable to previous analysis. We also prove rapid mixing for certain weakly interacting spin and fermionic models in arbitrary dimensions, extending recent results for high-temperature quantum Gibbs samplers to the zero-temperature regime. Our theoretical approaches are applicable to systems with singular stationary states, and are thus expected to have more general applications.
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