What are the computational phases of quantum matter?
Abstract: The physical world around us, despite being built of only a small number of different constituents, is bewilderingly complex. Yet, it is not impervious to classification, as the periodic table of elements, Carl Linnaeus’ classification of plants, and the recent classification of topological insulators (among many other examples) illustrate.
Can matter, in particular quantum matter, also be classified according to the computational power it enables? In this talk, I will argue the answer is `Yes’, and discuss a particular approach, based on measurement-based quantum computation . In this computational scheme, the process of quantum computation is driven by *local* measurements on a highly entangled initial quantum state. Information is written onto that state, processed and read out by the measurements alone. The initial state thus becomes a resource on which the power of the computational scheme depends.
For the strongest resource states, measurement-based quantum computation is known to be universal, i.e., everything that can possibly be computed by a quantum computer can be computed in this fashion. We can thus be sure that a phase diagram (to be established) of computational matter has interesting regions. However, today we are very far away from mapping out this phase diagram.
The purpose of this talk is to give an overview of the phenomenology we have so far uncovered—some intuitive, some counter-intuitive. I will discuss the role of entanglement for computational power , and the recent finding that the ground state of an AKLT Hamiltonian in two dimensions is a computationally universal resource [3,4,5].
 R. Raussendorf and H.J. Briegel, PRL 86 (2001),
 D. Gross D, S. Flammia and J. Eisert, PRL 102 190501 (2009),
 TC. Wei, I. Affleck and R. Raussendorf, PRL 106 070501 (2011),
 A. Miyake, Ann. Phys. 326 1656 (2011),
 A. Darmawan, G. Brennen and S. Bartlett, New Journal of Physics 14, 013023 (2012)
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