u/sensensenor

Grover's algorithm is one of the most famous quantum protocols ever developed, providing a quadratic speedup over classical approaches for the search problem. Unlike most quantum algorithms, Grover's algorithm is unique in that its applications are quite ubiquitous, as any classical algorithm that uses some kind of unstructured search can always be sped up using this procedure, even if the advantage gleaned is not as significant as it is for something like Shor's algorithm (assuming factoring is classically hard ofc). In this video, I derive the algorithm from geometric intuition and then demonstrate its optimality in terms of query complexity.

The Solovay-Kitaev Theorem is one of the foundational theorems of quantum computation, demonstrating how to efficiently approximate any single-qubit unitary to arbitrary accuracy using a sequence of gates finite gate-set (i.e. Clifford + T). The goal of this video was to explain both the intuition behind this theorem, and how it can be used to decompose single-qubit unitaries in practice. Enjoy!

The correlation produced by quantum entanglement has a different nature from that between classical random variables. I explore the differences between classical and quantum correlation in this video through a discussion of the EPR paradox and a comparison between the Bell and Tsirelson inequalities, ultimately ending with a demonstration of how such differences can be used to achieve "quantum advantage" when designing strategies for certain games.