Doorkeeper

AIP math-sci team's seminar

Thu, 16 May 2019 13:00 - 14:30

Keio Univ. Yagami-campus, Building 14, Room 631 A/B

3-14-1 Kouhoku-ku, Hiyoshi, Yokohama 223-8522, JAPAN

Register

Registration is closed

Get invited to future events

Free admission

Description

speaker: Tomotaka Kuwahara
title: Area-law conjecture for entanglement entropy
formula
abstract: In quantum computation, one of the primary problems is to solve the local Hamiltonian problem, namely finding the ground state (i.e., the lowest energy state) for a given many-body Hamiltonian. The problem is known to be the QMA complete problem in general [1]. On the other hand, from many numerical studies, the most important class, where the ground state has a spectral gap, is expected to be efficiently solved. This class corresponds to non-critical ground states and determines quantum phases of matter. In the analysis of this class, the entanglement entropy (or Von-Neumann entropy in subsystem) plays a central role. The area-law conjecture states that it is proportional to the surface region of subsystem if the ground state is gapped. This conjecture is a backbone of most of the classical algorithms such as the density-matrix-renormalization group [2] as well as classification of the quantum phases. Despite much effort on this conjecture, the area law is mathematically proved in highly limited cases [3,4,5]. In the present talk, I will give an overview of the conjecture, and show our recent achievement if the time allows.

[1] J. Kempe, A. Kitaev, O. Regev, SIAM Journal on Computing, 35(5), 1070-1097 (2006).
[2] S. R. White, Phys. Rev. Lett. 69, 2863 (1992).
[3] M. B. Hastings, J. Stat. Mech., P08024 (2007).
[4] Z. Landau, U. Vazirani and T.Vidick, Nature Physics, 11, 566–569 (2015)
[5] F. G. S. L. Brandao and M. Horodecki, Nature Physics, 9, 721–726 (2013)

time: 13:00 - 14:00 + 30 min
place: Keio Univ. Yagami-campus Bldg.14th, 6F

room: 631 A/B

If you are interested in, please feel free to join.

Best regards,

Tomotaka Kuwahara

About this community

RIKEN AIP Public

RIKEN AIP Public

Public events of RIKEN Center for Advanced Intelligence Project (AIP)

Join community