Quantum in Pictures

A: They are equivalent. When simplifying diagrams, draw the doubled spiders as pairs of single spiders and quantum noise as cup. After the diagram is simplified, you can either draw it with doubling or not.

Q: Is discarding in itself equal to a dashed box?

A: No. When discarding is applied to a single state, that is equal to a dashed box, which then disappears. In short, discarding gets rid of a state!

Q: What is a cup state? What do cups have to do with entanglement?

A: Cups represent the most entangled state between two particles. Since they look like a wire, you can see that as soon as you do something to one, particle, something happens to the other one!

Q: Why does the colour change box disappear when it is pushed through a state?

A: When we push a colour change box into a spider, it changes the colour of the spider, then pops out all the other wires. But for a state, there are no other wires, so it pops out all 0 other wires, i.e. it disappears!

Q: How do we know which outcome happens with a maybe box?

A: Doing a maybe box corresponds to doing some experiment in the lab. For example, we could use some sort of machine that flashes red when the first outcome happens and it flashes blue when the second one happens. Only by doing the experiment do we know which outcome we got.

Quantum Teleportation

Q: Why isn’t teleportation instantaneous?

A: A correction needs to be applied to Blaise’s qubit. The communication of which correction to apply happens over a classical channel, which cannot be done instantaneously.

Q: If you deterministically measure the cup state, you would get instantaneous teleportation?

A: Yes!

Q: If A knows when a cap-test goes wrong, why can't they just perform a correction locally?

A: The diagram shows you that A has no wires to correct anymore. The only kind of box that reaches backwards is the cap-test that we know is not a sure-box, and so we can't use another cap-test to fix it!

Q: Can we automate correction?

A: Sure! Blaise doesn't need to be a person. "He" could as well be a computer program that is waiting for a signal from Andrea and performs the right correction. This is how quantum teleportation is done in practice, because it is happening too fast for humans to keep up!

Spiders 🕷️ 🕸️

Q: Can phases of spiders change over time?

A: Phases of spiders do not change on their own, they only change by interacting with other spiders. But if we view wires as going forward in time, then spiders can change phase with time.

Q: Why do you need two different colours for the spiders?

A: The two colours correspond to two different ways to look at the particles. You need more than one way to look at the world!

Q: What is the meaning of spider phases?

A: You could think of the spider phase as the angle by which all the particles are being "rotated" together.

Q: What do you do with spiders with no legs?

A: You just ignore them! They don't matter.

Q: When we draw doubled spiders as pairs of single spiders, can we connect the horizontally flipped and unflipped copies of different doubled spiders?

A: No. The unflipped spiders need to be connected with unflipped spiders and viceversa.

Quantum circuits

Q: Why do we use complicated circuits or diagrams when we can implement the same functionality with simple ones?

A: First of all, when one is designing circuits, one is not always sure about the simplest way to implement the desidered protocol. Secondly, the simplest diagram may not always correspond to a quantum circuit. Thirdly, going from a complex diagram to a simpler one is essentially doing a mathematical calculation or a proof.

Q: How do you recognise doubly-flip-undoable in a circuit?

A: You can recognise it by checking whether there are two connected quantum gates which are the flipped version of each other.

Q: What is the CNOT gate used for?

A: It can be used for building quantum circuits and preparing connected states.

Q: How does the CNOT gate work?

A: You use the left bit of the CNOT gate to control whether the right bit is left untouched or a NOT gate is applied to it.

Q: Are there any other state that can be copied other than the zero states?

A: Yes! The 180° states can be copied as well.

Q: What are quantum circuits used for?

A: In general, you need quantum circuits to implement quantum algorithms on a quantum computer. In particular, you could use quantum circuits to prepare new quantum states as you want.

Q: Does the order of applying the rules matter?

A: In general it matters, just like it matters for whether putting on your shoes or socks first. In some special cases, the order of applying some rules doesn’t matter, just like it doesn’t matter whether you eat rice or vegetables first!

Q: How do you make a cup state for two qubits?

A: There are many ways to make a cup state. For instance, we could start with separate green and a red spider states and do a CNOT gate to them (try it yourself!). However, once we have a cup state, it doesn't matter any more how we made it, it matters what we do with it.

Q: Why can’t we use a cap test on a real quantum circuit?

A: A cap test is a maybe box. We can *try* to do it, in which case we might get a cap test, but we might also get something else. Have a look at the video about quantum teleportation to see what "something else" means.

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