- Accueil »
- Sample-efficient learning of quantum many-body hamiltonians

Le contenu de cette page n’est pas disponible en français. Veuillez nous en excuser.

Playing this video requires the latest flash player from Adobe.

Download link (right click and 'save-as') for playing in VLC or other compatible player.

Speaker(s):

Scientific Areas:

Collection/Series:

PIRSA Number:

20090017

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 for learning 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.

Joint work with Srinivasan Arunachalam, Tomotaka Kuwahara, Mehdi Soleimanifar

Share This PageShare this on TwitterShare on FacebookPublish this post to LinkedInSubmit this post on reddit.com

©2012 Institut Périmètre de Physique Théorique