Date: 4/20/2021, 12pm
Speaker: Anurag Anshu, University of California, Berkeley
Topic: Sample-efficient learning of quantum many-body systems
QSEC’s quantum computing subgroup will organize and host a seminar series throughout the upcoming semester. These events are free and open to the public. For any questions, contact qsec@gmu.edu. Below is the abstract of Mr. Zhong’s talk and meeting information:
Abstract
We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs (thermal) state. The classical analog of this problem, known as learning graphical models or Boltzmann machines, is a well-studied question in machine learning and statistics. In this work, we give the first sample-efficient algorithm for the quantum Hamiltonian learning problem. In particular, we prove that polynomially many samples in the number of particles (qudits) are necessary and sufficient forlearning the parameters of a spatially local Hamiltonian in l_2-norm. Our main contribution is in establishing the strong convexity of the log-partition function of quantum many-body systems, which along with the maximum entropy estimation yields our sample-efficient algorithm. Classically, the strong convexity for partition functions follows from the Markov property of Gibbs distributions. This is, however, known to be violated in its exact form in the quantum case. We introduce several new ideas to obtain an unconditional result that avoids relying on the Markov property of quantum systems, at the cost of a slightly weaker bound. In particular, we prove a lower bound on the variance of quasi-local operators with respect to the Gibbs state, which might be of independent interest. Our work paves the way toward a more rigorous application of machine learning techniques to quantum many-body problems.
Speaker’s Bio:
Anurag Anshu is a postdoctoral researcher at the University of California, Berkeley. Prior to this, he was a joint postdoctoral researcher at the Institute for Quantum Computing and the Perimeter Institute for Theoretical Physics, Waterloo. He obtained his PhD from the Centre for Quantum Technologies, National University of Singapore, on August 31, 2018, in Computer Science. He is interested in quantum complexity theory, quantum many-body physics, quantum communication and quantum learning theory.
Meeting Information
Join Zoom Meeting ID:609 431 5466
https://gmu.zoom.us/j/6094315466