**Speaker:** Angelo Lucia (Universidad Complutense de Madrid)

**Title:** Spectral gap estimates for quantum Markov semigroups

**Abstract: **Obtaining lower bounds to the spectral gap of a quantum Markov semigroup (QMS) is a way to estimate the time it takes to reach its equilibrium state. This has many applications, from disproving self-correction of quantum memories to obtaining efficient sampling of Gibbs states. In this talk, I will present some recent results for estimating the spectral gap of QMS which are primitive and detailed balanced with respect to a Gibbs state of a local, commuting Hamiltonian, a case which includes the Davies semigroup. I will do this by relating the generator of the QMS to a certain self-adjoint operator, which we named the canonical purified Hamiltonian associated to the Gibbs state. I will show how a certain decay condition on the Gibbs state implies a spectral gap estimate for this Hamiltonian, and via a simpler sufficient condition obtain various examples in which the decay is verified.

**About the seminar:** Weekly seminar hosted by the Quantum Working Group. Topics include quantum information theory and related topics in operator algebra. Contact: Felix Leditzky (leditzky@illinois.edu)