Proves quasi-optimal preparation of MCMI-clustering quantum Gibbs states of commuting Hamiltonians via Davies evolution in quantum Wasserstein distance of order one.
As we will consecutively reduce the ‘extensive’ dimensions until we reach zero subtracting ℓ in every step by 2( k + c), we further require ℓ > 2D(k + c)
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Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics
Proves quasi-optimal preparation of MCMI-clustering quantum Gibbs states of commuting Hamiltonians via Davies evolution in quantum Wasserstein distance of order one.