The arguments given in this paper suggest that Grover’s and Shor’s algorithms are more closely related than one might at first expect. Specifically, we show that Grover’s algorithm can be viewed as a quantum algorithm which solves a non-abelian hidden subgroup problem (HSP). But we then go on to show that the standard non-abelian quantum hidden subgroup (QHS) algorithm can not find a solution to this particular HSP. This leaves open the question as to whether or not there is some modification of the standard non-abelian QHS algorithm which is equivalent to Grover’s algorithm.
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Lomonaco, S.J., Kauffman, L.H. Is Grover’s Algorithm a Quantum Hidden Subgroup Algorithm?. Quantum Inf Process 6, 461–476 (2007). https://doi.org/10.1007/s11128-007-0066-1
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DOI: https://doi.org/10.1007/s11128-007-0066-1
Keywords
- Grover’s algorithm
- Shor’s algorithm
- quantum algorithms
- hidden subgroup algorithms
- hidden subgroup problems