This is an assortment of topics in Quantum Information Science. Whether you need *deep* knowledge in some of them depends on the subfield you are heading for. However, over the first year as a graduate student you would need to build at least a *superficial* understanding of most of these topics.

Be careful when searching online for some of the suggested textbooks. You probably would stumble upon repositories like Library Genesis that have the entire PDF files, but using them would be an illegal act of piracy.

These are common suggestions for an overview:

- Quantum Computation and Quantum Information by Nielsen and Chuang
- Preskill's lecture notes
- Aaronson's lecture notes and their second part

These are the differential equations describing a piece of quantum hardware.

`QuTiP`

's documentation covers a lot of techniques`QuantumOptics.jl`

is a similarly good resource- Quantum Measurement Theory and its Application is great for in-depth study of measurement modeling
- Quantum Optics - there are a few standard books on the topic (and good alternative suggestions online)
- Modern Quantum Mechanics by Sakurai and Napolitano is a great textbook on Quantum Mechanics from a physics perspective

A few models that you will probably encounter:

- Jaynes–Cummings coupling of an atom to a cavity
- Dispersive coupling of a transmon to a cavity
- Acousto-optic parametric coupling between mechanical displacement and optical wavelength
- The 3-level model of a color center (with selective optical transition)
- The collective motion of trapped ions

Common noise models:

- $T_1$ decay and $T_2$ dephasing times for two-level systems
- Amplitude damping and dephasing for oscillators
- Depolarization
- Pauli noise

Common techniques for modeling the noise:

And you will need to know how to go in the "interaction picture" and perform "rotating wave approximations". The Baker–Campbell–Hausdorff formula and Trotter product formula would be your friends.

Clifford circuits are a restricted class of circuits that do not provide a quantum computational advantage, but they are important for error correction and easy to simulate on a classical computer. The `QuantumClifford.jl`

documentation has a good list of reading materials.

Make sure you have at least a vague understanding of the Knill-Laflamme condition.

Much of the Clifford circuits reading list is applicable to the topic of qubit error correcting codes, but be sure that you first learn about classical binary linear codes and what the check matrix and generator matrix are.

For resilient encoding of information in quantum harmonic oscillators we use "bosonic" error correcting codes. Most important would be the GKP, cat, and binomial codes.

Similarly to Clifford circuits, Gaussian quantum optics does not provide computational advantage and is easy to simulate on a classical computer, but it is an important building block of quantum hardware. Gaussian Quantum Information in Rev. Mod. Phys. is a good overview.

Scott Aaronson's blog, essays, and books are a good introduction to the topic. His Quantum Computing Since Democritus is a good self-contained book.