Guifre Vidal, Institute for Quantum Computing
Abstract:
Quantum many-body systems are hard to study because the associated Hilbert space, containing all possible many-body states, is huge: its dimension grows exponentially in the system size. In recent years, however, progress in our understanding of quantum entanglement has revealed that only a small region of this huge Hilbert space is actually relevant to the study of quantum many-body systems. Using tensor networks, we have then been able to efficiently describe some of the states in this small, physically relevant region of the many-body Hilbert space. In this Colloquium I will (i) review our current understanding of many-body entanglement, (ii) introduce tensor networks as an efficient description of many-body states, and (iii) give an overview of the main accomplishments of the tensor network program, as well as the challenges it currently faces.