Timeline for Forming states of the form $\sqrt{p}\vert 0\rangle+\sqrt{1-p}\vert 1\rangle$

7 events

when toggle format	what		by	license	comment
Apr 13, 2021 at 8:43	history	edited	Léo Colisson	CC BY-SA 4.0	added 24 characters in body
Apr 12, 2021 at 16:34	comment	added	Sam Jaques		This is nice and I can imagine very useful in certain contexts, though there are other contexts (like the diffusion operator in Grover's algorithm or quantum walks) where we need to apply the adjoint. With the measurement, I don't see how this can be done.
Apr 4, 2021 at 9:25	history	edited	Léo Colisson	CC BY-SA 4.0	added 20 characters in body
Apr 4, 2021 at 9:05	comment	added	Léo Colisson		Yes exactly. Note that you can test if a state is smaller than $N$ by doing a few AND/OR on the most significant bits: If I denote by $x_i$ the $i$-th bit of $x$, it gives something like $x_0 = 0$ or $(x_0 = 1 $ and $x_1 = 0$) or $(x_0 = 1$ and $x_1 = 1$ and $x_1 = 0$)... Then, you need to implement the Unitary that corresponds to that circuit.
Apr 4, 2021 at 8:56	history	edited	Léo Colisson	CC BY-SA 4.0	added 24 characters in body
Apr 3, 2021 at 22:24	comment	added	Mark Spinelli		In other words, if $N=2^n+d$ then you can do a Hadamard transform on $n+1$ qubits; you can evaluate in an ancilla register whether your state so constructed is $\gt 2^n+d$ and post-select to throw away when this happens?
Apr 3, 2021 at 17:29	history	answered	Léo Colisson	CC BY-SA 4.0