Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How the High-energy Part of the Spectrum Affects the Adiabatic
  Computation Gap   Towards better understanding of how to design efficient adiabatic quantum
algorithms, we study how the adiabatic gap depends on the spectra of the
initial and final Hamiltonians in a natural family of test-bed examples. We
show that perhaps counter-intuitively, changing the energy in the initial and
final Hamiltonians of only highly excited states (we do this by assigning all
eigenstates above a certain cutoff the same value), can turn the adiabatic
algorithm from being successful to failing. Interestingly, our system exhibits
a phase transition; when the cutoff in the spectrum becomes smaller than
roughly $n/2$, $n$ being the number of qubits, the behavior transitions from a
successful adiabatic process to a failed one. To analyze this behavior, and
provide an upper bound on both the minimal gap as well as the success of the
adiabatic algorithm, we introduce the notion of "escape rate", which quantifies
the rate by which the system escapes the initial ground state (a related notion
was also used by Ilin and Lychkovskiy in arXiv:1805.04083). Our results
indicate a phenomenon that is interesting on its own right: an adiabatic
evolution may be robust to bounded-rank perturbations, even when the latter
closes the gap or makes it exponentially small.

36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom