Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal qudit Hamiltonians   A family of quantum Hamiltonians is said to be universal if any other
finite-dimensional Hamiltonian can be approximately encoded within the
low-energy space of a Hamiltonian from that family. If the encoding is
efficient, universal families of Hamiltonians can be used as universal analogue
quantum simulators and universal quantum computers, and the problem of
approximately determining the ground-state energy of a Hamiltonian from a
universal family is QMA-complete. One natural way to categorise Hamiltonians
into families is in terms of the interactions they are built from. Here we
prove universality of some important classes of interactions on qudits
($d$-level systems): (1) We completely characterise the $k$-qudit interactions
which are universal, if augmented with arbitrary 1-local terms. We find that,
for all $k \geqslant 2$ and all local dimensions $d \geqslant 2$, almost all
such interactions are universal aside from a simple stoquastic class. (2) We
prove universality of generalisations of the Heisenberg model that are
ubiquitous in condensed-matter physics, even if free 1-local terms are not
provided. We show that the $SU(d)$ and $SU(2)$ Heisenberg interactions are
universal for all local dimensions $d \geqslant 2$ (spin $\geqslant 1/2$),
implying that a quantum variant of the Max-$d$-Cut problem is QMA-complete. We
also show that for $d=3$ all bilinear-biquadratic Heisenberg interactions are
universal. One example is the general AKLT model. (3) We prove universality of
any interaction proportional to the projector onto a pure entangled state.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph