2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009;
Pittsburgh, Pennsylvania
Session A8: Quantum Information meets Many-Particle Physics
8:00 AM–11:00 AM,
Monday, March 16, 2009
Room: 414/415
Sponsoring
Unit:
GQI
Chair: David DiVincenzo, IBM Watson
Abstract ID: BAPS.2009.MAR.A8.4
Abstract: A8.00004 : Can multi-particle systems be too entangled to be useful for quantum computation?
9:48 AM–10:24 AM
Preview Abstract
Abstract
Author:
Jens Eisert
(Blackett Laboratory, Imperial College London)
In the context of ``quantum information meets many-particle
physics'', we pose the question of the role of entanglement in
the quantum computational power of many-particle quantum systems
(1). It is often argued that entanglement is at the root of the
speedup for quantum compared to classical computation, and that
one needs sufficient entanglement for this speedup to be
manifest. In measurement-based quantum computing, the need for a
highly entangled initial state is particularly obvious. In this
work we show that, remarkably, quantum states can be too
entangled - in the sense of having a too large geometric
entanglement - to be useful for the purpose of computation. What
is more, we can prove that this phenomenon occurs for the
dramatic majority of all states: the fraction of pure states on n
qubits not subject to the problem is smaller than e$^{-n{^2}}$.
Our results show that computational universality is actually a
rare property in quantum states. For the proof we make use of a
link between the ``quantum probabilistic method'' and ideas on
quantum many-body systems. This work stresses a new aspect of the
question concerning the role entanglement plays for quantum
computational speed-ups. We will also investigate a new
classification of primitives from projected entangled pair states
(PEPS) that can be used in order to systematically construct new
models for measurement-based computation (2,3). In an outlook, I
will - if time allows - mention other recent group activities
related to quantum information and many-particle physics,
including dynamical area laws and relaxation statements (4,5).
\\[4pt]
(1) ``Most quantum states are too entangled to be useful as
computational resources'', Phys. Rev. Lett., in press (2009)\\[0pt]
(2) ``Quantum computational webs'', arXiv:0810.2542\\[0pt]
(3) ``Novel schemes for measurement-based quantum computation'',
Phys. Rev. Lett. 98, 220503 (2007)\\[0pt]
(4) ``Exact relaxation in a class of nonequilibrium quantum
lattice systems'', Phys. Rev. Lett. 100, 030602 (2008)\\0[pt]
(5) ``Area laws for the entanglement entropy'', Rev. Mod. Phys.,
in press (2009).
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2009.MAR.A8.4