Lindblad engineering for quantum Gibbs state preparation under the eigenstate thermalization hypothesis

TL;DR

This paper introduces a simplified Lindblad engineering protocol for quantum Gibbs state preparation that is efficient under the eigenstate thermalization hypothesis, demonstrating fast convergence, noise resilience, and polynomial mixing time scaling.

Contribution

The authors propose a new Lindblad-based algorithm for Gibbs state preparation that leverages ETH to reduce complexity and enhance robustness, bridging theory and quantum hardware implementation.

Findings

Efficient convergence to Gibbs states under ETH

Polynomial mixing time scaling with system size

Resilience to stochastic noise in Lindblad dynamics

Abstract

Building upon recent progress in Lindblad engineering for quantum Gibbs state preparation algorithms, we propose a simplified protocol that is shown to be efficient under the eigenstate thermalization hypothesis (ETH). The ETH reduces circuit overheads of the Lindblad simulation algorithm and ensures a fast convergence toward the target Gibbs state. Moreover, we show that the realized Lindblad dynamics exhibits an inherent resilience against stochastic noise, opening up the path to a first demonstration on quantum computers. We complement our claims with numerical studies of the algorithm's convergence in various regimes of the mixed-field Ising model. In line with our predictions, we observe a mixing time scaling polynomially with system size when the ETH is satisfied. In addition, we assess the impact of algorithmic and hardware-induced errors on the algorithm's performance by carrying out quantum circuit simulations of our Lindblad simulation protocol with a local depolarizing noise model. This work bridges the gap between recent theoretical advances in dissipative Gibbs state preparation algorithms and their eventual quantum hardware implementation.