Lindblad engineering for quantum Gibbs state preparationunder the eigenstate thermalization hypothesis

Building upon recent progress in Lindblad engineering for quantum Gibbs statepreparation algorithms, we propose a simplified protocol that is shown to be efficientunder the eigenstate thermalization hypothesis (ETH). The ETH reduces circuit overheadof the Lindblad simulation algorithm and ensures a fast convergence toward the targetGibbs state.

Moreover, we show that the realized Lindblad dynamics exhibits resilienceagainst depolarizing noise, opening up the path to a first demonstration on quantumcomputers. We complement our claims with numerical studies of the algorithm'sconvergence in various regimes of the mixed-field Ising model. In line with ourpredictions, we observe a mixing time scaling polynomially with system size when theETH is satisfied.

In addition, we assess the impact of algorithmic and hardware-inducederrors on the algorithm's performance by carrying out quantum circuit simulations ofour Lindblad simulation protocol with realistic noise models. This work bridges the gapbetween recent theoretical advances in Gibbs state preparation algorithms and theireventual quantum hardware implementation.