Paper 2022/1647
Quantum Algorithm for Oracle Subset Product
Abstract
In 1993 Bernstein and Vazirani proposed a quantum algorithm for the BernsteinVazirani problem, which is given oracle access to the function $f(a_1,\dots,a_n) = a_1x_1+\cdots + a_nx_n \pmod 2$ with respect to a secret string $x = x_1\dots x_n \in \{0,1\}^n$, where $a_1,\dots,a_n \in \{0,1\}$, find $x$. We give a quantum algorithm for a new problem called the oracle subset product problem, which is given oracle access to the function $f(a_1,\dots,a_n) = a_1^{x_1}\cdots a_n^{x_n}$ with respect to a secret string $x = x_1\dots x_n\in\{0,1\}^n$, where $a_1,\dots,a_n\in \mathbb Z$, find $x$. Similar to the BernsteinVazirani algorithm, it is a quantum algorithm for a problem that is originally polynomial time solvable by classical algorithms; and that the advantage of the algorithm over classical algorithms is that it only makes one call to the function instead of $n$ calls.
Metadata
 Available format(s)
 Category
 Foundations
 Publication info
 Preprint.
 Keywords
 Quantum Algorithm Oracle Subset Product
 Contact author(s)
 treyquantum @ gmail com
 History
 20221128: approved
 20221128: received
 See all versions
 Short URL
 https://ia.cr/2022/1647
 License

CC BY
BibTeX
@misc{cryptoeprint:2022/1647, author = {Trey Li}, title = {Quantum Algorithm for Oracle Subset Product}, howpublished = {Cryptology ePrint Archive, Paper 2022/1647}, year = {2022}, note = {\url{https://eprint.iacr.org/2022/1647}}, url = {https://eprint.iacr.org/2022/1647} }