  Lindblad dynamics and other open-system dynamics provide a promising path
towards efficient Gibbs sampling on quantum computers. In these proposals, the
Lindbladian is obtained via an algorithmic construction akin to designing an
artificial thermostat in classical Monte Carlo or molecular dynamics methods,
rather than treated as an approximation to weakly coupled system-bath unitary
dynamics. Recently, Chen, Kastoryano, and Gily\'en (arXiv:2311.09207)
introduced the first efficiently implementable Lindbladian satisfying the
Kubo--Martin--Schwinger (KMS) detailed balance condition, which ensures that
the Gibbs state is a fixed point of the dynamics and is applicable to
non-commuting Hamiltonians. This Gibbs sampler uses a continuously
parameterized set of jump operators, and the energy resolution required for
implementing each jump operator depends only logarithmically on the precision
and the mixing time. In this work, we build upon the structural
characterization of KMS detailed balanced Lindbladians by Fagnola and
Umanit\`a, and develop a family of efficient quantum Gibbs samplers that only
use a discrete set of jump operators (the number can be as few as one). Our
methodology simplifies the implementation and the analysis of Lindbladian-based
quantum Gibbs samplers, and encompasses the construction of Chen, Kastoryano,
and Gily\'en as a special instance.
