Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical mechanics of classical and quantum computational complexity   The quest for quantum computers is motivated by their potential for solving
problems that defy existing, classical, computers. The theory of computational
complexity, one of the crown jewels of computer science, provides a rigorous
framework for classifying the hardness of problems according to the
computational resources, most notably time, needed to solve them. Its extension
to quantum computers allows the relative power of quantum computers to be
analyzed. This framework identifies families of problems which are likely hard
for classical computers (``NP-complete'') and those which are likely hard for
quantum computers (``QMA-complete'') by indirect methods. That is, they
identify problems of comparable worst-case difficulty without directly
determining the individual hardness of any given instance. Statistical
mechanical methods can be used to complement this classification by directly
extracting information about particular families of instances---typically those
that involve optimization---by studying random ensembles of them. These pose
unusual and interesting (quantum) statistical mechanical questions and the
results shed light on the difficulty of problems for large classes of
algorithms as well as providing a window on the contrast between typical and
worst case complexity. In these lecture notes we present an introduction to
this set of ideas with older work on classical satisfiability and recent work
on quantum satisfiability as primary examples. We also touch on the connection
of computational hardness with the physical notion of glassiness.

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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: hep-ph