Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Difficult instances of the counting problem for 2-quantum-SAT are very
  atypical   The problem 2-quantum-satisfiability (2-QSAT) is the generalisation of the
2-CNF-SAT problem to quantum bits, and is equivalent to determining whether or
not a spin-1/2 Hamiltonian with two-body terms is frustration-free. Similarly
to the classical problem 2-SAT, the counting problem #2-QSAT of determining the
size (i.e. the dimension) of the set of satisfying states is #P-complete.
However, if we consider random instances of #2-QSAT in which constraints are
sampled from the Haar measure, intractible instances have measure zero. An
apparent reason for this is that almost all two-qubit constraints are
entangled, which more readily give rise to long-range constraints.
  We investigate under which conditions product constraints also give rise to
efficiently solvable families of #2-QSAT instances. We consider #2-QSAT
involving only discrete distributions over tensor product operators, which
interpolates between classical #2-SAT and #2-QSAT involving arbitrary product
constraints. We find that such instances of #2-QSAT, defined on Erdos--Renyi
graphs or bond-percolated lattices, are asymptotically almost surely
efficiently solvable except to the extent that they are biased to resemble
monotone instances of #2-SAT.

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The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph