# Mathematical Field Notes

## Lines through four lines

(Reposting this from an earlier blog which I gave up on, but liked the post so I added some pictures – all images produced using the amazing free alternative to Maple/Mathematica, Sage).

I was reading Fulton-Pandharipande (“Notes on stable maps and quantum cohomology”) the other day and came across the classical result that there are exactly two lines passing through a generic quadruple of lines in $\mathbb{CP}^3$. I encourage people to whom this fact is unfamiliar to convince themselves of it. It was unfamiliar to me and I found it hard to visualise, so I sat down and drew some pictures until I understood it.

Written by Jonny Evans

August 14, 2012 at 12:36 pm

## Quantum computers: Grover’s algorithm

TLDR: Classically you have to look through all N elements of a database until you find the right one (so runtime increases linearly in N); Grover’s algorithm has a surprising runtime of order $\sqrt{N}$ to do the same thing, using clever ideas from quantum mechanics.