March 5, 2020

eigenvalue decomposition of Pauli matrices

At the heart of linear algebra is a task called eigenvalue decomposition. This task, in the simplest words possible, allows you to analyze a given matrix to determine how it’s constructed from a combination of basis vectors, called eigenvectors, and scalars, called eigenvalues. Many statistical models, machine learning algorithms, and scientific theories use eigenvector decomposition to go from a muddle of data to a understandable theory. Here, I’ll talk about using eigenvalue decomposition to inspect the fundamental logic gates used in quantum computing. Read more

December 25, 2019

mathematical tools

When performing some job, I may need to use certain tools: a scrub for cleaning the bathroom; a knife for cutting vegetables; a hand drill for securing a shelf; etc. Let’s suppose the job concerns problem-solving. I may reach for a high level mental model appropriate for the problem. When we arrive at a specialty problem, like in a field of mathematics, the tools become more specialized too. I’m currently participating in Machine Learning Tokyo’s もくもく reading group, discussing the textbook Mathematics for Machine Learning; the mathematical field of interest is linear algebra. Here are the tools I see that one needs to learn in order to complete exercises at the end of each chapter of the book: Read more

November 20, 2019

qsim - a quantum computing simulator

I’d like to introduce my latest project – qsim – a Go package for simulating quantum computations. This is a very rudimentary project that I’d like to expand considerably, but I think the core design has reached a good enough stage to share and garner feedback. Here is the code: What is qsim, and what does it mean to simulate quantum computations? In brief, we write a software program to run on a classical von Neuman computer that approximates the behavior of algorithms that could run on a quantum computer. Let’s dive in… Read more

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