Finite temperature quantum condensations in the space of states: a new perspective for quantum annealing

TL;DR

This paper extends the concept of quantum phase transitions to finite temperatures using free energies, illustrating their application in quantum annealing and demonstrating universal features across different models.

Contribution

It introduces a finite temperature framework for quantum condensations and shows how these can be used to develop effective quantum annealers.

Findings

Finite temperature quantum phase transitions can be characterized by free energies.

The phase diagrams of different models exhibit universal features.

Finite temperature condensation QPTs enable quantum annealing with high success probability.

Abstract

In nature, everything occurs at finite temperature and quantum phase transitions (QPTs) cannot be an exception. Nevertheless, they are still mainly discussed and formulated at zero temperature. We show that the condensation QPTs recently introduced at zero temperature can naturally be extended to finite temperature just by replacing ground state energies with corresponding free energies. We illustrate this criterion in the paradigmatic Grover model and in a system of free fermions in a one-dimensional inhomogeneous lattice. In agreement with expected universal features, the two systems show structurally similar phase diagrams. Last, we explain how finite temperature condensation QPTs can be used to construct quantum annealers having, at finite temperature, output-probability exponentially close to 1 in the system size. As examples we consider again the Grover model and the fermionic system, the latter being well within the reach of present heterostructure technology.