IQI Weekly Seminar

Abstract: We consider quantum Gibbs states with Hamiltonians on arbitrary graphs (i.e., including infinite dimensional systems or long-range interacting systems). The simulation of such states is known to be usually NP-hard to due to exponentially increasing parameters. However, when we restrict ourselves to high-temperature regime, various problems become significantly simple. In this regime, any kinds of non-local structures are believed to disappear, and it is a crucial problem how to characterize the absence of non-local structures in the quantum Gibbs state. In the present talk, we prove the following fundamental properties above a certain threshold temperature: i) existence of the fully-polynomial-time-approximation scheme to simulate thermodynamic properties, ii) quantum approximate Markov chain, iii) Ensemble equivalence between the canonical and the micro-canonical distributions for long-range interacting systems.