# Deutch's Algorithm (or Two Birds One Quantum Gate)

Why is this important? Let’s say we have to find a binary function $f$, but we are only given the gate $U_f$ and our goal is to guess what $f$ could be based on the output of a circuit. (Don’t worry about the specifics of the gate, it can be a black box for now.) Classically, it should take two evaluations of the function just to determine the following result: $f(0) \oplus f(1)$.

# Transfer Orbit

Transfer orbits are inherently cool The idea of using gravity as a slingshot to give a boost to a rocket is (probably) enough to get anyone excited, even if you hate physics. However, as is often the case with undergraduate-level courses, there is hardly enough time to skim the contents of orbital mechanics, let alone delve into the details of how something specific with an application in the real world actually works.

# Electron Orbitals with Python

After learning about orbital angular momentum in my most recent quantum lecture, I decided to have a go at modelling the solutions and resulting 3D probability density functions using Python. After a fair bit of trial and error, it turned out a lot better than I though it would. Surprisingly, I had not encountered higher-order derivatives in numerical analysis before (probably because I am quite new to any kind of non-trivial modelling in physics) and had to write a recursive function to implement this, which I thought was neat.

# Phase Space

Note A lot of what I'm about to summarize comes from Classical Mechanics: The Theoretical Minimum by Leonard Susskind and George Hrabovsky. It's an amazing book with the perfect amount of rigour to make for an enjoyable read while remaining challenging if you're a beginning physics student - I highly recommend reading it. Also, just a disclaimer: Lagrangian and Hamiltonian mechanics are both quite new to me, and writing this will probably allow me understand what I've been reading more than teach the reader something - however, continue on if you want to see a fresh take on this subject or you're in a similar place, because this is all pretty fresh at the moment.

# Classical Probability Distribution

Probability distributions show up everywhere in science A good example of them can be found in classical physics, in the case of a ball being dropped off a cliff. The problem is set up such that there is a camera placed to the side of the cliff which is programmed to take pictures at a random time during the ball’s descent. Where is the ball most likely to be in the photo?