Reduction from non-injective hidden shift problem to injective hidden shift problem
(pp0221-0230)
Mirmojtaba Gharibi
doi:
https://doi.org/10.26421/QIC13.3-4-4
Abstracts:
We introduce a simple tool that can be used to reduce non-injective
instances of the hidden shift problem over arbitrary group to injective
instances over the same group. In particular, we show that the
average-case non-injective hidden shift problem admit this reduction. We
show similar results for (non-injective) hidden shift problem for bent
functions. We generalize the notion of influence and show how it relates
to applicability of this tool for doing reductions. In particular, these
results can be used to simplify the main results by Gavinsky, Roetteler,
and Roland about the hidden shift problem for the Boolean-valued
functions and bent functions, and also to generalize their results to
non-Boolean domains (thereby answering an open question that they pose).
Key words:
quantum computing, efficient algorithm, hidden shift
problem, Boolean hidden shift problem, bent functions |