Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ground State Spin Logic   Designing and optimizing cost functions and energy landscapes is a problem
encountered in many fields of science and engineering. These landscapes and
cost functions can be embedded and annealed in experimentally controllable spin
Hamiltonians. Using an approach based on group theory and symmetries, we
examine the embedding of Boolean logic gates into the ground state subspace of
such spin systems. We describe parameterized families of diagonal Hamiltonians
and symmetry operations which preserve the ground state subspace encoding the
truth tables of Boolean formulas. The ground state embeddings of adder circuits
are used to illustrate how gates are combined and simplified using symmetry.
Our work is relevant for experimental demonstrations of ground state embeddings
found in both classical optimization as well as adiabatic quantum optimization.

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The categories of this paper are: cs
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-th
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th