Ciro Santilli @cirosantilli 40

Follow car terminology and be done with it. Also follows marking of all bike shifters.

Bibliography review:

Course outline given:

Non-relativistic QFT is a limit of relativistic QFT, and can be used to describe for example condensed matter physics systems at very low temperature. But it is still very hard to make accurate measurements even in those experiments.

Defines "relativistic" as: "the Lagrangian is symmetric under the Poincaré group".

Mentions that "QFT is hard" because (a finite list follows???):But I guess that if you fully understand what that means precisely, QTF won't be too hard for you!

Notably, this is stark contrast with rotation symmetry groups (SO(3)) which appears in space rotations present in non-relativistic quantum mechanics.

www.youtube.com/watch?v=T58H6ofIOpE&t=5097 describes the relativistic particle in a box thought experiment with shrinking walls

Companies have been really slow to support SVG features in their browsers, and that is very saddening: medium.com/@michaelmangial1/introduction-to-scalable-vector-graphics-6450c03e8d2e

You can't drop SVG support for canvas until there's a way to run untrusted JavaScript on the browser!

SVG does have some compatibility annoyances, notably SVG fonts. But we should as a society work to standardize and implement a fix those, the benefits of SVG are just too great!

Examples:

A member of the underlying field of a vector space. E.g. in ${\mathbb{R}}^3$, the underlying field is $\mathbb{R}$, and a scalar is a member of $\mathbb{R}$, i.e. a real number.

This is a bit "formal hocus pocus first, action later". But withing that category, it is just barely basic enough that 2021 Ciro can understand something.

By: Tobias J. Osborne.

Lecture notes transcribed by a student: github.com/avstjohn/qft

18 1h30 lectures.

Followup course: Advanced quantum field theory lecture by Tobias Osborne (2017).

One direct practical reason is that we need to map the matrix to real quantum hardware somehow, and all quantum hardware designs so far and likely in the future are gate-based: you manipulate a small number of qubits at a time (2) and add more and more of such operations.

While there are "quantum compilers" to increase the portability of quantum programs, it is to be expected that programs manually crafted for a specific hardware will be more efficient just like in classic computers.

TODO: is there any clear reason why computers can't beat humans in approximating any unitary matrix with a gate set?

This is analogous to what classic circuit programmers will do, by using smaller logic gates to create complex circuits, rather than directly creating one huge truth table.

The most commonly considered quantum gates take 1, 2, or 3 qubits as input.

The gates themselves are just unitary matrices that operate on the input qubits and produce the same number of output qubits.

For example, the matrix for the CNOT gate, which takes 2 qubits as input is:

The final question is then: if I have a 2 qubit gate but an input with more qubits, say 3 qubits, then what does the 2 qubit gate (4x4 matrix) do for the final big 3 qubit matrix (8x8)? In order words, how do we scale quantum gates up to match the total number of qubits?

The intuitive answer is simple: we "just" extend the small matrix with a larger identity matrix so that the sum of the probabilities third bit is unaffected.

More precisely, we likely have to extend the matrix in a way such that the partial measurement of the original small gate qubits leaves all other qubits unaffected.

For example, if the circuit were made up of a CNOT gate operating on the first and second qubits as in:

then we would just extend the 2x2 CNOT gate to:

TODO lazy to properly learn right now. Apparently you have to use the Kronecker product by the identity matrix. Also, zX-calculus appears to provide a powerful alternative method in some/all cases.

Bibliography: