Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantifying the magic of quantum channels   To achieve universal quantum computation via general fault-tolerant schemes,
stabilizer operations must be supplemented with other non-stabilizer quantum
resources. Motivated by this necessity, we develop a resource theory for magic
quantum channels to characterize and quantify the quantum "magic" or
non-stabilizerness of noisy quantum circuits. For qudit quantum computing with
odd dimension $d$, it is known that quantum states with non-negative Wigner
function can be efficiently simulated classically. First, inspired by this
observation, we introduce a resource theory based on completely
positive-Wigner-preserving quantum operations as free operations, and we show
that they can be efficiently simulated via a classical algorithm. Second, we
introduce two efficiently computable magic measures for quantum channels,
called the mana and thauma of a quantum channel. As applications, we show that
these measures not only provide fundamental limits on the distillable magic of
quantum channels, but they also lead to lower bounds for the task of
synthesizing non-Clifford gates. Third, we propose a classical algorithm for
simulating noisy quantum circuits, whose sample complexity can be quantified by
the mana of a quantum channel. We further show that this algorithm can
outperform another approach for simulating noisy quantum circuits, based on
channel robustness. Finally, we explore the threshold of non-stabilizerness for
basic quantum circuits under depolarizing noise.

29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc