Code examples and organization of introduction tutorial

[benmcdonough20]

I wrote a draft of the introduction tutorial. I would love feedback about

• What parts are clear / confusing
• What information is important / superfluous

To get this tutorial to a finished product, it would be great if someone could

1. Decide if the organization of the topics makes sense and reorganize if necessary
2. Add a few code examples of representing QHOs and intializing them into Fock states

Let me know your thoughts!

[jebc314]

Here’s my feedback about your draft of the introduction tutorial.

The introduction explains QHO clearly and gives a good conceptual understanding of it. The figure is quite helpful in visually showing the difference between a qubit and QHO.

The Dirac Notation section is clear as well and explains why Dirac notation is preferred over matrix notation for QHO well.

For the Superposition subsection, I’m just wondering does “with coefficients that are complex numbers” refers to the “state space” being a vector space over the field of complex numbers? I feel like the wording makes it unclear what the coefficients correspond to specifically. Other than that, this section is clear as well.

The Borne Rule subsection covers this important concept clearly, and the same for the following subsection on Normalization.

For the Generalizing to Bosonic Modes subsection, I think you imply the definition of the Kronecker delta when stating “These last two properties can be summarized as…”, but I think adding an explicit definition might make it clearer. Something like “Where the symbol \delta_{mn} is known as a Kronecker delta, in which it equals 1 when m and n are equal and 0 otherwise.”

Also, I don’t think you explained what bosonic modes are before using that term for the title Generalizing to Bosonic Modes, so this could confuse readers. Some fixes could be that this term gets explained in the introduction, or this section could be renamed to Generalizing to Quantum Harmonic Oscillators. (Similar point applies to "Quantum computing with bosonic modes" in The tensor product section).

The tensor product section explains the information clearly, and the same for the Product states and entanglement Section.

Overall, I think all the information presented is important. The introduction tutorial does a great job of presenting all the information, while staying engaging and cohesive with the organization.