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SUMMARY:Preparing topological states on a quantum computer - Toby Cubitt (
 Universidad Complutense de Madrid)
DTSTART:20120710T131500Z
DTEND:20120710T141500Z
UID:TALK38829@talks.cam.ac.uk
CONTACT:Ashley Montanaro
DESCRIPTION:Projected Entangled Pair States (PEPS) are often presented as 
 the natural class of states for modelling ground states of non-critical ma
 ny-body quantum systems. On the other hand\, we know that an oracle which 
 can generate an arbitrary PEPS\, given its classical description\, is an u
 nreasonably powerful computational resource (PP-complete).\n\nSo which PEP
 S are "physical"? In other words\, which of them can be prepared efficient
 ly on a quantum computer?\n\nThis question was raised by Verstraete\, Wolf
 \, Perez-Garcia\, and Cirac in 2006. Schwarz\, Temme and Verstraete recent
 ly gave a solution for the sub-class known as "injective" PEPS (which are 
 always unique ground states of local Hamiltonians)\, in the form of a new 
 quantum algorithm for constructing these states using a quantum computer. 
 The algorithm is efficient as long as the injective PEPS is well-condition
 ed. This class of states includes many physically interesting ones\, such 
 as the ground state of the 2D AKLT model.\n\nHowever\, the "injectivity" p
 roperty rules out all topological quantum states (which by definition cann
 ot be unique ground states of local Hamiltonians). The more general class 
 of G-injective PEPS are defined over a discrete symmetry group G. This mor
 e general class of PEPS includes many important topological quantum states
 : familiar examples such as Kitaev's toric code\, and more exotic examples
  such as resonating valence bond states. By generalising the PEPS preparat
 ion algorithm to the larger class of G-injective PEPS\, we show how to pre
 pare these more exotic topological quantum states using a quantum computer
 . The algorithm is again efficient as long as the G-injective PEPS is well
 -conditioned.\n\n(joint work with Martin Schwarz\, Kristan Temme\, Frank V
 erstraete\, and David Perez-Garcia)
LOCATION:MR14\, Centre for Mathematical Sciences
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