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References

1. Introduction to random unitary circuits and the measurement-induced entanglement phase transition
2. Quantum Entanglement Growth under Random Unitary Dynamics
3. Measurement-driven entanglement transition in hybrid quantum circuits
4. Measurement-induced quantum phases realized in a trapped-ion quantum computer
5. Entanglement Transitions in Unitary Circuit Games
6. Entanglement Transition in the Projective Transverse Field Ising Model
7. Topological order and entanglement dynamics in the measurement-only XZZX quantum code
8. Majorana Loop Models for Measurement-Only Quantum Circuits

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Probability Theory

1. "Introduction to Probability, Statistics, and Random Processes" by Pishro-Nik

Solid State Theory

Mathematics for Quantum Information Theory

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UPDATES!

We will start with chapter 1 of Jochen Rau on Jan 2022.

Winter Reading Mebbe

1. "Notes on Statistical Mechanics" by Leonard Susskind
2. "A Crash Course in Statistical Mechanics" by Noah Miller

Books, Notes and Lectures

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Linear Algebra Review

1. Linear Algebra Review, "Group Theory in a Nutshell for Physics" by A. Zee
2. Appendix A, "Mathematics for Physics" by Michael Stone & Paul M. Goldbart

Topology Review

1. "Chapter 1, The WE-Heraeus International Winter School on Gravity and Light" by Fredric Schuller
2. "Topology Tutorial, The WE-Heraeus International Winter School on Gravity and Light"
3. "Chapters 1-5, The Geometrical Anatomy of Theoretical Physics" by Fredric Schuller

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Questions from Week 1

1. What is the necessity for fields?
2. How do we go about constructing conservation laws for discrete transformations?
3. Are transformations of the field itself physically meaningful?
4. Apart from lie groups, are there any set of other groups that prove more useful in QFT?
5. Why do only think of one parameter Lie groups in the context of Noether's theorem?

Questions from Week 2

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Analytical Mechanics

Chapters 1, 5, 6 and 7 ##More Resources for Analytical Mechanics

1. Perimeter Institute's summer course on Noether's Theorem
2. Chapter 1, "Mathematics for Physics" by Michael Stone & Paul M. Goldbart
3. "Emmy Noether's Wonderful Theorem" by Dwight Neueunschwander
4. "Classical Mechanics" by Herebrt Goldstein, Charles P. Poole Jr.& John L. Safko
5. "Visualizing inverse Noether's Theorem and Symplectic Geometry" by Noah Miller
6. "Notes on Classical Mechanics" by David Tong

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• Observables are Hermitian elements of the observable algebra $\mathcal{A}$
• A $\mathcal{C}$-algebra is a set that is closed under addition, multiplication and multiplication by scalars $k \in \mathbb{C}$
• Each element $A \in \mathcal{A}$ has an adjoint $A^{\dagger}$
• An element $E \in \mathcal{A}$ is positive if $\exists \ A \in \mathcal{A}$ such that $E = A^{\dagger} A$
• For us $\mathcal{A}$ will always be the set of all bounded operators on a Hilbert space $\mathcal{B}(\mathcal{H})$
• Measurements themselves are described by assigning to each outcome of the device an effect $E \in \mathcal{A}$, which satisfies $0 \leq E \leq \mathbb{I}$
• A state $\omega$ on $\mathcal{A}$ is a positive normalized linear functional on $\mathcal{A}$, that follows the rules:
  • $\omega : \mathcal{A} \rightarrow \mathbb{C}$, is a linear map
  • $\omega(X^{\dagger}X) \geq 0$
• $\omega(\mathbb{I}) = 1$