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CATEGORIES:CQIF Seminar
SUMMARY:Preparing topological states on a quantum computer
- Toby Cubitt (Universidad Complutense de Madrid)
DTSTART;TZID=Europe/London:20120710T141500
DTEND;TZID=Europe/London:20120710T151500
UID:TALK38829AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/38829
DESCRIPTION:Projected Entangled Pair States (PEPS) are often p
resented as the natural class of states for modell
ing ground states of non-critical many-body quantu
m systems. On the other hand\, we know that an ora
cle which can generate an arbitrary PEPS\, given i
ts classical description\, is an unreasonably powe
rful computational resource (PP-complete).\n\nSo w
hich PEPS are "physical"? In other words\, which o
f them can be prepared efficiently on a quantum co
mputer?\n\nThis question was raised by Verstraete\
, Wolf\, Perez-Garcia\, and Cirac in 2006. Schwarz
\, Temme and Verstraete recently gave a solution f
or the sub-class known as "injective" PEPS (which
are always unique ground states of local Hamiltoni
ans)\, in the form of a new quantum algorithm for
constructing these states using a quantum computer
. The algorithm is efficient as long as the inject
ive PEPS is well-conditioned. This class of states
includes many physically interesting ones\, such
as the ground state of the 2D AKLT model.\n\nHowev
er\, the "injectivity" property rules out all topo
logical quantum states (which by definition cannot
be unique ground states of local Hamiltonians). T
he more general class of G-injective PEPS are defi
ned over a discrete symmetry group G. This more ge
neral class of PEPS includes many important topolo
gical quantum states: familiar examples such as Ki
taev's toric code\, and more exotic examples such
as resonating valence bond states. By generalising
the PEPS preparation algorithm to the larger clas
s of G-injective PEPS\, we show how to prepare the
se more exotic topological quantum states using a
quantum computer. The algorithm is again efficient
as long as the G-injective PEPS is well-condition
ed.\n\n(joint work with Martin Schwarz\, Kristan T
emme\, Frank Verstraete\, and David Perez-Garcia)
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:Ashley Montanaro
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