Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complexity Theory and its Applications in Linear Quantum Optics   This thesis is intended in part to summarize and also to contribute to the
newest developments in passive linear optics that have resulted, directly or
indirectly, from the somewhat shocking discovery in 2010 that the BosonSampling
problem is likely hard for a classical computer to simulate. In doing so, I
hope to provide a historic context for the original result, as well as an
outlook on the future of technology derived from these newer developments. An
emphasis is made in each section to provide a broader conceptual framework for
understanding the consequences of each result in light of the others. This
framework is intended to be comprehensible even without a deep understanding of
the topics themselves.
  The first three chapters focus more closely on the BosonSampling result
itself, seeking to understand the computational complexity aspects of passive
linear optical networks, and what consequences this may have. Some effort is
spent discussing a number of issues inherent in the BosonSampling problem that
limit the scope of its applicability, and that are still active topics of
research. Finally, we describe two other linear optical settings that inherit
the same complexity as BosonSampling. The final chapters focus on how an
intuitive understanding of BosonSampling has led to developments in optical
metrology and other closely related fields. These developments suggest the
exciting possibility that quantum sensors may be viable in the next few years
with only marginal improvements in technology. Lastly, some open problems are
presented which are intended to lay out a course for future research that would
allow for a more complete picture of the scalability of the architecture
developed in these chapters.

36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th