Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Average-Case Verification of the Quantum Fourier Transform Enables
  Worst-Case Phase Estimation   The quantum Fourier transform (QFT) is a key primitive for quantum computing
that is typically used as a subroutine within a larger computation, for
instance for phase estimation. As such, we may have little control over the
state that is input to the QFT. Thus, in implementing a good QFT, we may
imagine that it needs to perform well on arbitrary input states. Verifying this
worst-case correct behaviour of a QFT-implementation would be exponentially
hard (in the number of qubits) in general, raising the concern that this
verification would be impossible in practice on any useful-sized system. In
this paper we show that, in fact, we only need to have good average-case
performance of the QFT to achieve good worst-case performance for key tasks --
phase estimation, period finding and amplitude estimation. Further we give a
very efficient procedure to verify this required average-case behaviour of the
QFT.

28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ