A new quantum algorithm for the hidden shift problem in $\mathbb{Z}_{2^t}^n$
Abstract
In this paper we make a step towards a time and space efficient algorithm for the hidden shift problem for groups of the form $\mathbb{Z}_k^n$. We give a solution to the case when $k$ is a power of 2, which has polynomial running time in $n$, and only uses quadratic classical, and linear quantum space in $n\log (k)$. It can be a useful tool in the general case of the hidden shift and hidden subgroup problems too, since one of the main algorithms made to solve them can use this algorithm as a subroutine in its recursive steps, making it more efficient in some instances.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2021
- DOI:
- 10.48550/arXiv.2102.04171
- arXiv:
- arXiv:2102.04171
- Bibcode:
- 2021arXiv210204171C
- Keywords:
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- Quantum Physics
- E-Print:
- 13 pages