Neural Network Ansatz for Finite Temperature

Neural-network Quantum States [1] are an efficient ansatz for approximating the ground and excited-states of highly entangled systems in 1 and 2 dimensional quantum systems at zero temperature. Some extensions to systems coupled to thermal baths have been recently proposed, but they are either limited to classical systems, to shallow networks encoding a Neural Density Matrix or they require 3 different sampling procedures [2].

In this talk we will present a novel approach targeting such systems based on an efficient encoding of the full density matrix. This ansatz is general and can be combined with networks of arbitrary depth, which is necessary to describe highly entangled states. The effectiveness of the technique will be demonstrated by benchmarking it against the Transverse-Field Ising model.

[1] G. Carleo and M. Troyer, Science 355, 602 (2017).

[2] Y. Nomura, N. Yoshioka, and F. Nori, Phys. Rev. Lett. 127, (2021).