Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Theoretical Analyses of Quantum Counting against Decoherence Errors   In this paper, we analyze the quantum counting under the decoherence, which
can find the number of solutions satisfying a given oracle. We investigate
probability distributions related to the first order term of the error rate on
the quantum counting with the depolarizing channel. We also implement two
circuits for the quantum counting -- the ascending-order circuit and the
descending-order circuit -- by reversing ordering of application of
controlled-Grover operations. By theoretical and numerical calculations for
probability distributions, we reveal the difference of probability
distributions on two circuits in the presence of decoherence and show that the
ascending-order circuit is more robust against the decoherence than the
descending-order circuit. This property of the robustness is applicable to the
phase estimation such as the factoring.

33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an