Ciro Santilli @cirosantilli 37

Ciro Santilli 37 Updated 2025-07-16

We don't need to understand a super generalized version of tensor products to know what they mean in basic quantum computing!

Intuitively, taking a tensor product of two qubits simply means putting them together on the same quantum system/computer.

When we write the bra-ket notation:

∣ 00 ⟩

that is the same as

∣ 0 ⟩ \otimes ∣ 0 ⟩

The tensor product is called a "product" because it distributes over addition.

E.g. consider:

(\frac{∣ 0 ⟩ + ∣ 1 ⟩}{2}) \otimes ∣ 0 ⟩ = \frac{∣ 0 ⟩ \otimes ∣ 0 ⟩ + ∣ 1 ⟩ \otimes ∣ 0 ⟩}{2} = \frac{∣ 00 ⟩ + ∣ 10 ⟩}{2}

(1)

Intuitively, in this operation we just put a Hadamard gate qubit together with a second pure

∣ 0 ⟩

qubit.

And the outcome still has the second qubit as always 0, because we haven't made them interact.

The quantum state

\frac{∣ 00 ⟩ + ∣ 10 ⟩}{2}

is called a separable state, because it can be written as a single product of two different qubits. We have simply brought two qubits together, without making them interact.

If we then add a CNOT gate to make a Bell state:

\frac{∣ 00 ⟩ + ∣ 11 ⟩}{2} = \frac{∣ 0 ⟩ \otimes ∣ 0 ⟩ + ∣ 1 ⟩ \otimes ∣ 1 ⟩}{2}

(2)

we can now see that the Bell state is non-separable: we've made the two qubits interact, and there is no way to write this state with a single tensor product. The qubits are fundamentally entangled.

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Quantum Processes and Computation course of the University of Oxford by

Ciro Santilli 37 Updated 2025-07-16

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2022 page: www.cs.ox.ac.uk/teaching/courses/2022-2023/quantum/ (archive). Assignments are available:

2022 lecturer: Aleks Kissinger

The course would be better named ZX-calculus as it appears to be the only subject covered.

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Quantum Software course of the University of Oxford by

Ciro Santilli 37 Updated 2025-07-16

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2022 page: www.cs.ox.ac.uk/teaching/courses/qsoft/ Half of the problems are Jupyter Notebooks, not bad.

Like Quantum Processes and Computation course of the University of Oxford, also ZX-calculus-heavy.

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B2 Oxford physics course by

Ciro Santilli 37 Updated 2025-07-16

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www-thphys.physics.ox.ac.uk/people/AndreiStarinets/sr_mt_2022.html (archive) contains 2022 problem sets and notes, well done Mr Andrei Starinets!

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B4 Oxford physics course by

Ciro Santilli 37 Updated 2025-07-16

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www-pnp.physics.ox.ac.uk/~barra/teaching.shtml As of 2023, contains some good 2015 materials: web.archive.org/web/20220525094139/http://www-pnp.physics.ox.ac.uk/~barra/teaching.shtml It was called "Subatomic physics" back then.

2015 professor: Alan J. Barr.

Possible 2022 professor: Guy Wilkinson (unconfirmed): www.chch.ox.ac.uk/staff/professor-guy-wilkinson

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Bilibili by

Ciro Santilli 37 Updated 2025-07-16

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Champaign-Urbana metropolitan area by

Ciro Santilli 37 Updated 2025-07-16

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It is quite comical that two separate towns were founded one next to the other right in the middle of nowhere. And that both have so slightly weird names.

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Handscroll by

Ciro Santilli 37 Updated 2025-07-16

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Ciro Santilli's favorite. A mixture of painting and book.

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History of condensed matter physics by

Ciro Santilli 37 Updated 2025-07-16

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Bibliography:

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How to teach / Projects must aim for novelty by

Ciro Santilli 37 Updated 2025-07-16

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The projects you do must always aim to achieving some novel result.

You don't have to necessarily reach it. But you must aim for it.

Novel result can be taken broadly.

E.g., a new tutorial that explains something in a way never done before is novel.

But there must be something to your project that has never been done before.

You can start by reproducing other's work.

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Philip W. Anderson by

Ciro Santilli 37 Updated 2025-07-16

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History of the Josephson effect by

Ciro Santilli 37 Updated 2025-07-16

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In 1962 Brian Josephson published his inaugural paper predicting the effect as Section "Possible new effects in superconductive tunnelling".

In 1963 Philip W. Anderson and John M. Rowell published their paper that first observed the effect as Section "Possible new effects in superconductive tunnelling".

Some golden notes can be found at True Genius: The Life and Science of John Bardeen page 224 and around. Philip W. Anderson commented:

We were all - Josephson, Pippard and myself, as well as various other people who also habitually sat at the Mond tea and participated in the discussions of the next few weeks - very much puzzled by the meaning of the fact that the current depends on the phase

As part of the course Anderson had introduced the concept of broken symmetry in superconductors. Josephson "was fascinated by the idea of broken symmetry, and wondered whether there could be any way of observing it experimentally."

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University of Cambridge laboratory by

Ciro Santilli 37 Updated 2025-07-16

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Mond Laboratory by

Ciro Santilli 37 Updated 2025-07-16

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cudl.lib.cam.ac.uk/view/PH-CAVENDISH-P-00822/1

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Austria by

Ciro Santilli 37 Updated 2025-07-16

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Fugging, Upper Austria by

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Physics journal by

Ciro Santilli 37 Updated 2025-07-16

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The strongest are:

early 20th century: Annalen der Physik: God OG physics journal of the early 20th century, before the Nazis fucked German science back to the Middle Ages
20s/30s: Nature started picking up strong
40s/50s: American journals started to come in strong after all the genius Jews escaped from Germany, notably Physical Review Letters

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Paper by Brian Josephson by

Ciro Santilli 37 Updated 2025-07-16

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Physics Letters by

Ciro Santilli 37 Updated 2025-07-16

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