Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Verifying the output of quantum optimizers with ground-state energy
  lower bounds   Solving optimisation problems encoded in the ground state of classical-spin
systems is a focus area for quantum computing devices, providing upper bounds
to the unknown solution. To certify these bounds, they are compared to those
obtained by classical methods. However, even if the quantum bound beats them,
this says little about how close it is to the unknown solution. We consider the
use of relaxations to the ground-state problem as a benchmark for the output of
quantum optimisers. These relaxations are radically more informative because
they provide lower bounds to the ground-state energy. The chordal branch and
bound algorithm we present provides a series of systematically improving
confidence regions where the ground-state energy provably lies. Interestingly,
each step in the process requires only an effort polynomial in the system size.
Additionally, the algorithm exploits the locality and sparsity of relevant
Ising spin models in a systematic way. This yields certified solutions for many
of the problems that are currently addressed by heuristic optimisation
algorithms more efficiently and for larger system sizes. We apply the method to
verify the output of a D-Wave 2000Q device and identify instances where the
annealer does not reach the ground-state energy and, more importantly,
instances where it does, something impossible to do by means of standard
variational approaches. Our work provides a flexible and scalable method for
the verification of the outputs produced by quantum optimization devices.

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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: stat