The preparation of thermal states of matter is a crucial task in quantum simulation, finding applications ranging from quantum chemistry to optimization.
In this work, EQUALITY partners from Inria and collaborators prove that a recently introduced, efficiently implementable dissipative evolution thermalizes to the Gibbs state in time scaling polynomially with system size at high enough temperatures, and for any Hamiltonian that satisfies a Lieb-Robinson bound, such as local Hamiltonians on a lattice. Furthermore, they show the efficient adiabatic preparation of the associated purifications or ``thermofield double'' states.
To the best of our knowledge, these are the first results rigorously establishing the efficient preparation of high-temperature Gibbs states and their purifications.
On a technical level, for high temperatures, their proof makes use of the mapping of the generator of the evolution into a Hamiltonian, and then analysing it as perturbation of the Hamiltonian corresponding to infinite temperature. Their results show that a family of quasi-local dissipative evolutions efficiently prepares a large class of quantum many-body states of interest and has the potential to mirror the success of classical Monte Carlo methods for quantum many-body systems.
Read the paper by clicking on the link below.
