Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theory of quantum system certification: a tutorial   The precise control of complex quantum systems promises numerous
technological applications including digital quantum computing. The complexity
of such devices renders the certification of their correct functioning a
challenge. To address this challenge, numerous methods were developed in the
last decade.
  In this tutorial, we explain prominent protocols for certifying the physical
layer of quantum devices described by quantum states and processes. Such
protocols are particularly important in the development of near-term devices.
Specifically, we discuss methods of direct quantum state certification, direct
fidelity estimation, shadow fidelity estimation, direct quantum process
certification, randomized benchmarking and cross-entropy benchmarking.
Moreover, we provide an introduction to powerful mathematical methods, which
are widely used in quantum information theory, in order to derive theoretical
guarantees for the protocols.

22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph