Vienna Waits For You
The Hadamard Sandwich is a neat quantum circuit trick that shows up in several quantum algorithms! In this post, we will cover what the Hadamard Sandwich is, and its application in (1) the swap test, (2) the fixed point quantum search algorithm, and (3) the eigenvalue threshold algorithm.
On May 6th, 2021, Chuang et al. posted the paper A Grand Unification of Quantum Algorithms which claims that arguably the three most important algorithms in quantum computing: search, factoring and simulation, all have a common underlying structure: the quantum singular value transform. In this pedagogical paper, based heavily on work by Gilyen et al., they explain this structure, starting out with a primitive called quantum signal processing, which leads to the quantum eigenvalue transformation, and finally, the coveted quantum singular value transformation.
At this point, there are way too many backprop posts on the net, including another article titled Yet Another Introduction to Backpropagation. I add another one to the pile as proof to myself that I have understood this reasonably well, and perhaps something in here may help out someone who was stuck with backprop, and wandered onto this blog for help. (So, yes, just the former reason.)
In quantum information, there are two common notations to represent vectors and linear transformations between them: the bra-ket notation, and the matrix notation.
The following is a nice way to think about logarithms: \(\log_b a \equiv\) The number of times \(a\) is divided into \(b\) parts such that each part becomes \(1\).
Density matrices describe ensembles of quantum systems and are useful in two ways. Firstly, if you’re preparing a state probabilistically, and secondly if you want to describe a subsystem of a quantum state.
Lately, I have been listening to a lot of folk music, and by that I mean for hours on end, doing nothing else, aided both by having not much else that I want to do, and Youtube’s wonderful recommendation system that seemed to know where exactly to get me. I was listening to the likes of Simon and Garfunkel and Bob Dylan when I stumbled across the song — Five Hundred Miles, that I kept listening to, more because it sounded familiar (which is a huge factor that decides whether I enjoy a song) than anything else.