Description
Preparing Thermal States on a Quantum Computer by Dissipation
How hard is it to prepare the thermal (Gibbs) state of a quantum many-body Hamiltonian? For very small temperatures (scaling as an inverse polynomial in the system size) the problem is QMA-hard, but almost nothing is known in the important case of constant temperatures.
In this talk I’ll present recent results relating the time of preparation of thermal states by local quantum dissipative processes (i.e. master equations) with the static properties of the state. In particular connecting to whether the thermal state has a finite correlation length (i.e. exponentially decaying correlations).
Our goal is to generalize to the quantum case a sequence of beautiful works -- by Stroock, Zergalinski, Martinelli and others -- in mathematical physics and statistical mechanics showing the equivalence of mixing in time (fast convergence of the Glauber dynamics) to mixing in space (finite correlation length in the Gibbs state) for classical models.
The talk will be based on on-going joint work with Michael Kastoryano.