Gibbs Sampling of Periodic Potentials on a Quantum Computer

          @misc{ pirsa_22110094,
            doi = {10.48660/22110094},
            url = {https://pirsa.org/22110094},
            author = {Motamedi, Arsalan},
            keywords = {Condensed Matter},
            language = {en},
            title = {Gibbs Sampling of Periodic Potentials on a Quantum Computer},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {nov},
            note = {PIRSA:22110094 see, \url{https://pirsa.org}}
          }
          

Abstract

"Motivated by applications in machine learning, we present a quantum algorithm for Gibbs sampling from continuous real-valued functions defined on high dimensional tori. We show that these families of functions satisfy a Poincare inequality. We then use the techniques for solving linear systems and partial differential equations to design an algorithm that performs zeroeth order queries to a quantum oracle computing the energy function to return samples from its Gibbs distribution. We further analyze the query and gate complexity of our algorithm and prove that the algorithm has a polylogarithmic dependence on approximation error (in total variation distance) and a polynomial dependence on the number of variables, although it suffers from an exponentially poor dependence on temperature."