06 Aug 2019This Summer and the Site
After a long absence I decided to recap what happened during the last few months and start updating this blog again.
23 May 2019Introduction to Topological Quantum Computation: Crash Course on Knots Theory
This is a series of posts on topological quantum computations. To address the reason why we introduce such “strange-looking” equations to calculate Jones polynomials, we have to know the history of knot theory, and understand how the pioneers came up with their ideas. This post provide a somewhat natural way to define Alexander Polynomials and skein relations from the coloring of knots, and ended on the note that the author is currently incapable of giving an equivalently convincing reason behind the definition of the Jones or the Kauffman polynomial.
14 May 2019Introduction to Topological Quantum Computation: Ising Anyons Case Study
This is a series of posts on topological quantum computations. In this post, the most promising candidate for TQC, Ising anyons, are discussed. A theoretical topological quantum computer is realized via Ising anyons’ initialization, braiding, and fusion. F and R matrices are calculated from the consistency requirement, i.e. Hexagon and Pentagon equations. Braiding matrices are introduced heuristically. A set of Clifford gates is implemented as the result of braiding. This post features lots of diagrams.
07 May 2019Computation and Currency
This is my wild thoughts on computation and currency. The story begins when a spaceship appeared near a lake one day…
01 May 2019Introduction to Topological Quantum Computation: Side Notes on Simulations
This is a series of posts on topological quantum computations. The aim of this series is to work my way to understanding the diagrams of “strands” widely used in the field. This post started as introducing a pitfall of using Stern-Gerlach experiment as quantum computers, and end with a discussion on simulations of QC and TQC using classical computers.
18 Apr 2019The Fortran Gram-Schmidt Process Pitfall
I tried using Gram-Schmidt Process the other day and just couldn’t get the correct result. It took me a few days trying to figure out why. Turns out that it’s just a simple precision error problem.
13 Apr 2019Introduction to Topological Quantum Computation: Anyons Model
This is a series of posts on topological quantum computations. The aim of this series is to work my way to understanding the diagrams of “strands” widely used in the field. This post discusses anyon model in general. Fusion diagram and hexagon and pentagon identities are introduced.
11 Apr 2019Introduction to Topological Quantum Computation: Basics of Quantum Computation
This is a series of posts on topological quantum computations. The aim of this series is to work my way to understanding the diagrams of “strands” widely used in the field. This post establishes the barebone basics of quantum computations.
20 Mar 2019Lie Algebra as Generator
In this post generator of Lie groups as well as its subgroup are considered. This short post is preparation for the application of Mathematical theory into QM and CM. This post is the third of a series of posts that start from Lie group and Lie algebra.
11 Mar 2019Lie Group as Differential Manifold
In this post Lie groups are regarded as a differential manifold, and one-parameter subgroups are introduced. This post is the second of a series of posts that start from Lie group and Lie algebra.
16 Jan 2019Fiber Bundles
Fiber bundle is introduced with intuitive examples of pasta and pancakes, Berry phase and Calabi-Yau space. Structure group is introduced as a natural consequence of transition functions.
12 Jan 2019Lie Groups and "Actions"
In this post Lie groups and it’s actions are introduced. This is the first of a series posts start from Lie group and Lie algebra, where I try to understand “infinitesimal operators” and “generators” used by physicists from a mathematical standpoint. Hopefully, this series ends with a good explanation of what “generators” are in Classical Mechanics as well as Quantum Mechanics.
09 Dec 2018Shadowsocks + Digital Ocean = VPN of 1TB/month
Code for using digital ocean service for VPN. It is cheap for .edu-e-mail owners (free 50$ on GitHub Student Pack).
01 Dec 2018Build Your Blog with GitHub Pages
Build Your Blog with GitHub Pages. This is a sketch of how to use my theme
PointingToTheMoon to write your blog. This theme is great for academic use, for it features simple post page with mathjax support and a side bar with toc. The main page on the other hand is somewhat fancy.
23 Nov 2018Thank You Word Cloud with Mathematica
Code for generating thank-you word cloud with Mathematica. It’s perfect for thank-you page of your slide-shows.
23 Nov 2018Introduction to de Rham Cohomology
Cohomology is viewed as a natural dual space of homology in this post. The bilinear map (i.e., the inner product) between these two spaces is just integration. At the end of this post, the cohomology group as an indicator of “holes” in space is discussed.
01 Nov 2018Introduction to Homology
Euler characteristics is a topological invariant, and can be interpreted as a “hole”-indicator. Homology is just a natural way of defining Euler characteristics in topological spaces. With triangulation of a manifold, we can define cycles and boundaries and combine them to homology groups. We see that the group is trivial for trivial spaces, and can distinguish manifolds in terms “holes” in them.
08 Oct 2018中英文邮件祝辞
之前写邮件看见同学最后致意里面写了顺祝工作商祺, 后来我就在邮件里面一直用”顺祝工作商祺”, 或者是”顺祝夏安”. 最近我导师提醒我说”工作商祺”不适合用在同学或者老师的信件中, 我才查了一下, 总结在下面.
06 Oct 2018You Should Try Fortran
I found Fortran incredibly fast compared to pure Python. Fortran’s reputation for hard to maintain is true only if you read the code without an understanding of the Physics. It’s still an active language. You should give it a try.
01 Sep 2018Fortran with VS2017
Instructions on using Fortran with VS2017
21 Aug 2018N-Forms and Tensors on Manifold
We are going to generalize the concept of vectors and one-forms to tensors and differential forms. In the meantime, the wedge product and exterior derivative were introduced. Exterior derivative lies the foundation for cohomology.
20 Aug 2018Vectors and One-Forms on Manifold
Since in general there is no way to define a “straight arrow” connecting two points, Vectors can only be “tangent vectors” on manifolds. In this post, tangent vectors are introduced heuristically, with emphasis on how and why should we define vectors as operators. Co-vectors, also called one-forms, are introduced as the dual. The reason for defining one-forms as differentials are introduced heuristically. This post also addresses the problem of inconsistency when the basis of vector act on that of one form.
08 Jun 2018第一性原理热统
Class project. My attempt at building Statistical Mechanics from First Principles. I think Statistical Mechanics can be applied to distinguishable particles such as millions of footballs. This post tries to develop such Statistical Mechanics, especially on the entropy. This post is not finished.
07 Jun 2018量子场论
My Study notes on QFT lesson for the final. Each step of deduction is present in this post. This post covers K-G equations and Dirac equations.
06 Jun 2018李群和李群的李代数
My understanding of Lie-group and its Lie-algebra. The statement “Lie-algebra is approximation of Lie-group” is inaccurate since they essentially live in different spaces. This post is not finished. Check posts under
Lie Group and/or
Lie Algebra where I rewrote and added more aspects of Lie group and Lie algebra.