Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noisy Simon Period Finding   Let $f: \mathbb{F}_2^n \rightarrow \mathbb{F}_2^n$ be a Boolean function with
period $\vec s$. It is well-known that Simon's algorithm finds $\vec s$ in time
polynomial in $n$ on quantum devices that are capable of performing
error-correction. However, today's quantum devices are inherently noisy, too
limited for error correction, and Simon's algorithm is not error-tolerant.
  We show that even noisy quantum period finding computations may lead to
speedups in comparison to purely classical computations. To this end, we
implemented Simon's quantum period finding circuit on the $15$-qubit quantum
device IBM Q 16 Melbourne. Our experiments show that with a certain probability
$\tau(n)$ we measure erroneous vectors that are not orthogonal to $\vec s$. We
propose new, simple, but very effective smoothing techniques to classically
mitigate physical noise effects such as e.g. IBM Q's bias towards the
$0$-qubit.
  After smoothing, our noisy quantum device provides us a statistical
distribution that we can easily transform into an LPN instance with parameters
$n$ and $\tau(n)$. Hence, in the noisy case we may not hope to find periods in
time polynomial in $n$. However, we may still obtain a quantum advantage if the
error $\tau(n)$ does not grow too large. This demonstrates that quantum devices
may be useful for period finding, even before achieving the level of full error
correction capability.

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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin