Bad Qubits — Learn Quantum by Doing

Multiple choice

The Hidden Subgroup Problem gives a black-box function

f : G \to S

. What property must

f

have, relative to the hidden subgroup

H \leq G

, for the problem to be well-posed?

$f$ takes a distinct value on every single element of $G$ except inside $H$
$f$ is constant on the whole group $G$ regardless of $H$
$f$ is constant on every left coset of $H$ and distinct on different cosets ( $f(g) = f(g')$ iff $g'$ is in $gH$ )
$f$ is a one-to-one function on all of $G$ with no two inputs sharing an output