Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sampling of globally depolarized random quantum circuit   The recent paper [F. Arute et al. Nature {\bf 574}, 505 (2019)] considered
exact classical sampling of the output probability distribution of the globally
depolarized random quantum circuit. In this paper, we show three results.
First, we consider the case when the fidelity $F$ is constant. We show that if
the distribution is classically sampled in polynomial time within a constant
multiplicative error, then ${\rm BQP}\subseteq{\rm SBP}$, which means that BQP
is in the second level of the polynomial-time hierarchy. We next show that for
any $F\le1/2$, the distribution is classically trivially sampled by the uniform
distribution within the multiplicative error $F2^{n+2}$, where $n$ is the
number of qubits. We finally show that for any $F$, the distribution is
classically trivially sampled by the uniform distribution within the additive
error $2F$. These last two results show that if we consider realistic cases,
both $F\sim2^{-m}$ and $m\gg n$, or at least $F\sim2^{-m}$, where $m$ is the
number of gates, quantum supremacy does not exist for approximate sampling even
with the exponentially-small errors. We also argue that if $F\sim2^{-m}$ and
$m\gg n$, the standard approach will not work to show quantum supremacy even
for exact sampling.

20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs