High-Temperature Gibbs States Are Unentangled and Efficiently Preparable

The paper titled "High-Temperature Gibbs States are Unentangled and Efficiently Preparable" by Ainesh Bakshi and colleagues presents significant findings regarding thermal states of local Hamiltonians. The authors demonstrate that above a certain constant temperature, specifically for a local Hamiltonian on a graph with degree \( \mathfrak{d} \), the Gibbs state becomes separable. This means that for inverse temperatures \( \beta < 1/(c\mathfrak{d}) \), where \( c \) is a constant, the Gibbs state can be represented as a classical distribution over product states. This finding challenges the traditional understanding of short-range quantum correlations in Gibbs states. Furthermore, the authors establish that it is possible to efficiently sample from this distribution, allowing for the preparation of a state that is close to the Gibbs state using a depth-one quantum circuit and polynomial classical overhead, specifically for \( \beta < 1/(c\mathfrak{d}^3) \). The results indicate that the preparation of Gibbs states does not offer super-polynomial quantum speedups at temperatures above a fixed constant, which has implications for quantum computing and thermal state manipulation.

- The Gibbs states of local Hamiltonians are separable above a constant temperature.

- Efficient sampling from the distribution over product states is possible.

- The findings challenge existing beliefs about quantum correlations in Gibbs states.

- Preparation of Gibbs states does not yield super-polynomial speedups at high temperatures.