Questions tagged [hidden-subgroup-problem]

The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. The framework captures problems like factoring, discrete logarithm, graph isomorphism, and the shortest vector problem. (Wikipedia)

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Burnside Decomposition in Kuperberg's Hidden Shift

In "Another subexponential-time quantum algorithm for the dihedral hidden subgroup problem", Kuperberg writes that $\mathbb{C}[G]$ has a "Burnside decomposition" of $$\mathbb{C}[G]\cong \bigoplus_{V}...
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What is the hidden subgroup in Simon's problem?

Given access to an oracle for a function $f:\{0,1\}^n\to\{0,1\}^n$ such that $f(x)=f(y)$ iff $x\oplus y\in\{0,s\}$, Simon's algorithm allows to recover $s$ in $\mathcal O(n)$ queries to the oracle. ...
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Why does Fourier sampling allow to efficiently recover hidden subgroups?

The hidden subgroup problem is often cited as a generalisation of many problems for which efficient quantum algorithms are known, such as factoring/period finding, the discrete logarithm problem, and ...