Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hardness of classically sampling one clean qubit model with constant
  total variation distance error   The one clean qubit model (or the DQC1 model) is a restricted model of
quantum computing where only a single input qubit is pure and all other input
qubits are maximally mixed. In spite of the severe restriction, the model can
solve several problems (such as calculating Jones polynomials) whose classical
efficient solutions are not known. Furthermore, it was shown that if the output
probability distribution of the one clean qubit model can be classically
efficiently sampled with a constant multiplicative error, then the polynomial
hierarchy collapses to the second level. Is it possible to improve the
multiplicative error hardness result to a constant total variation distance
error one like other sub-universal quantum computing models such as the IQP
model, the Boson Sampling model, and the Fourier Sampling model? In this paper,
we show that it is indeed possible if we accept a modified version of the
average case hardness conjecture. Interestingly, the anti-concentration lemma
can be easily shown by using the special property of the one clean qubit model
that each output probability is so small that no concentration occurs.

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn