## Quantum Information and error correction by Daniel Gottesman and Artur Ekert

During January to April in 2023, while studying quantum error correction in the textbook reading session of our research group, I discovered several wonderful resources other than Preskill’s notes. I list them below:

*Artur Ekert’s Introduction to Quantum Information on YouTube*. I have watched the last part about quantum error correction and I think Ekert’s explanation is the most intuitive one. It is crystal clear. He can use a simple diagram and baby example to make a complicated idea transparent.*Daniel Gottesman’s and Ben Yoshida’s Quantum Error Correction videos in Perimeter Institute*. I think I just finished watching half of them. Gottesman’s exposition of this topic has a different style than Ekert. It is more mathematical, with theorems followed by proofs. I feel these two are good to be watched together. In last lecture by Ben Yoshida, he even explains a fair advanced topic of treating black hole information paradox using the quantum error correction as a tool.*Daniel Gottesman’s Quantum Information videos in Perimeter Institute.*I only watched the last video about quantum channel capacity as a complement to Preskill’s notes. I think Gottesman’s proof is more complete and detailed than Preskill’s notes. I benefited a lot from Gottesman.

## Polyakov's great show in modern classical dynamics

Apart from black hole physics, the other experience that makes my 2023’s physics journey unforgettable is Polyakov’s Modern Classical Physics course, along with various topics inspired by this course. Polyakov uses classical physics to thread several beautiful modern topics together. Here are several examples:

- Optics and mechanics can be neatly united using variation principle (
*one ring to rule them all!*) - Understand of why the orbit of Kepler problem is closed by looking at the motion in momentum space in a very geometric way.
- How to go from a discrete particle picture to a continuous description of hydrodynamics.
- By analyzing the stability of the uniform density solution of the hydrodynamical system, how one can understand the formation of galaxy.
- How one can extract the equation of motion for our universe,
*Friedmann equations*, just by adding Newtonian gravity into the hydrodynamics equation and imposing certain symmetry of the solution we want to study. Notice that we don’t need Einstein’s general relativity here. - Shock wave solution and the effect of viscosity.
- 2D vortices in inviscid flow and the lifting force of an airfoil.
- Turbulent flow and Kolmogorov’s picture

It is amazing how wide the application of classical physics is! Before studying this course, I thought there is nothing very interesting in classical dynamics, since it looks like a pretty old subject. I was totally wrong! Below is a quote from Gerard ‘t Hooft,

I have a post about the first part of this course. You can find more information about this course and my lecture notes there.* I started this course in April and finished watching all the lecture videos in middle August*, right before my summer holiday. After the holiday, *I finished revising the lecture note in October*.

## Introductory courses: cosmology and superfluidity

Physics is a broad subject. I don’t want to dig into a single small topic without knowing a variety of broad applications to Nature. Polyakov’s course reminds me that it is the time to learn more subjects that interest me, first in an introductory level. *From April to October, I studied the following two introductory courses*.

My general relativity study last year raised my interests in cosmology. I have known about Hubble’s law and expanding universe since high school. More mathematical derivation is given in the Schutz’s general relativity textbook, but I felt like I needed more physical intuition. I’ve always known Susskind’s lectures are always full of physical intuitions. Naturally, ** I went and watched Susskind’s lecture series about cosmology**. I was amazed starting from his very first lecture. Susskind showed, using a very basic argument, the expanding universe solution is inevitable in Newton’s gravity. It was my first time seeing such an argument. Later, I saw it in Polyakov’s Modern Classical Dynamics class, formulated in hydrodynamics, which is more mathematically sophisticated. The two explanations complement each other. As a next step, I plan to read Ryden’s

*Introduction to Cosmology*textbook.

The other introductory level subject I learned is topics related to Bose-Einstein condensation. I found a textbook called ** Superconductivity, Superfluids and Condensates by James F. Annett**. As its name suggests, the book weaves three interrelated topics together, and I feel the author has done it nicely. The book starts with experimental facts and explains the basic physics clearly. I think it helps clarify many confusions I had when learning standard quantum many-body textbooks.

## Quantum many-body physics: second quantization, spin-wave theory of anti-ferromagnets and Hartree-Fock approximation

*From April to July*, my Professor, Naoki Kawashima, ** gave a lecture series about quantum many-body physics**. It is his first onsite lecture since I was enrolled in the University of Tokyo in 2019, so I didn’t want to miss it! Compared to Sachdev’s Quantum Theory of Solid course, there are two many differences:

- Theoretical tool for dealing with interaction. Sachdev’s course focuses on a perturbative approach using Feynman diagrams but Naoki’s course focuses on variational principle. You will see Hartree-Fock approximation is presented in two very different ways.
- Physical systems under consideration. In Sachdev’s course, screening and plasmons in interacting elctron gas is discussed. In Naoki’s lecture, anti-ferromagnet and its spin-wave theory is discussed. I would say Sachdev’s course covers more material, but it is good to see similar results derived in a variational approach.

## Thermodynamics and Statistical physics—my second pass

As a new semester started in October, I segued into another topic I have been felt uncomfortable with—*thermodynamics and statistical physics*. There are so many topics that were mysterious and confusing when I first learned this subject, including

- kinetic theory of gas: how to start with Newton’s $F=ma$ and derive statistical behavior of a large collection of particles?
- thermodynamic definition of temperature and entropy,
- physical meaning of statistical ensembles,

and so on. Many important concepts are unclear and messed up together, which cannot withstand a slight consideration. In summary, I think my understanding of this important and deep subject is very superficial now. I have to change this situation. * I want to build a more intuitive physical picture of this topic in my mind*.

The main learning source I choose this time is Kardar’s course 8.333 in MIT’s opencourseware website. I use it to provide the backbone of this semester’s study. For each topic, other textbooks will be used. I have finished about half of the lecture videos until the end of this year. I have found the following textbooks very helpful,

- For thermodynamics, Fermi’s textbook is excellent! Kardar is very brief on this and I feel Fermi’s textbook is a great supplement. The explanation is clear. There are few logical jumps so the book is a joy to read.
- For kinetic theory, Feynman’s Lectures on Physics, Volume I, Chapter 39 to 45, are excellent! Now, you can even listen to the original lecture recording while having the lecture notes in hand. I feel Susskind and Feynman have a very similar lecture style, which is full of clear-cut physical picture and devastatingly intuitive.