ELFT HÍRADÓ

[Janos Asboth <asboth.janos AT wigner.mta.hu>]

WIGNER SZFI SZEMINÁRIUMGILYÉN ANDRÁS

(CWI Amsterdam, vendéglátó: Kiss Tamás)
"On preparing ground states of gapped Hamiltonians:
 An efficient Quantum Lovász Local Lemma"

Időpont: 2016. november 10. (csütörtök) 14:00 (1 óra)
Hely: MTA Wigner FK SZFI, I. épület 1. emeleti Tanácsterem
Összefoglaló:

A frustration-free local Hamiltonian has the property that its ground state
minimises the energy of all local terms simultaneously. In general, even
deciding whether a Hamiltonian is frustration-free is a hard task, as it is
closely related to the QMA1-complete quantum satisfiability problem (QSAT)
-- the quantum analogue of SAT, which is the archetypal NP-complete problem
in classical computer science. This connection shows that the
frustration-free property is not only relevant to physics but also to
computer science.

The Quantum Lovász Local Lemma (QLLL) provides a sufficient condition for
frustration-freeness. A natural question is whether there is an efficient
way to prepare a frustration-free state under the conditions of the QLLL.
Previous results showed that the answer is positive if all local terms
commute.

In this work we improve on the previous constructive results by designing
an algorithm that works efficiently for non-commuting terms as well,
assuming that the system is ``recursively" gapped, by which we mean that
the system and all its subsystems have an inverse polynomial energy gap.
Also, our analysis works under the most general condition for the QLLL,
known as Shearer´s bound. Similarly to the previous results, our algorithm
has the charming feature that it uses only local measurement operations
corresponding to the local Hamiltonian terms.

*Részletes információ:* http://www.szfki.hu/seminar
Minden érdeklődőt szívesen látunk!

Asbóth János