Abstract. A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and hidden ...
Quantum algorithms for factoring and finding discrete logarithms have previously been generalized to finding hidden subgroups of finite Abelian groups. This paper explores the ...
We present the first explicit connection between quantum computation and lattice problems. Namely, our main result is a solution to the Unique Shortest Vector Problem (SVP) under ...
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodi...
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central prob...
Andrew M. Childs, Leonard J. Schulman, Umesh V. Va...