Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fine-grained quantum computational supremacy   Output probability distributions of several sub-universal quantum computing
models cannot be classically efficiently sampled unless some unlikely
consequences occur in classical complexity theory, such as the collapse of the
polynomial-time hierarchy. These results, so called quantum supremacy, however,
do not rule out possibilities of super-polynomial-time classical simulations.
In this paper, we study "fine-grained" version of quantum supremacy that
excludes some exponential-time classical simulations. First, we focus on two
sub-universal models, namely, the one-clean-qubit model (or the DQC1 model) and
the HC1Q model. Assuming certain conjectures in fine-grained complexity theory,
we show that for any $a>0$ output probability distributions of these models
cannot be classically sampled within a constant multiplicative error and in
$2^{(1-a)N+o(N)}$ time, where $N$ is the number of qubits. Next, we consider
universal quantum computing. For example, we consider quantum computing over
Clifford and $T$ gates, and show that under another fine-grained complexity
conjecture, output probability distributions of Clifford-$T$ quantum computing
cannot be classically sampled in $2^{o(t)}$ time within a constant
multiplicative error, where $t$ is the number of $T$ gates.

18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics