I would instead give the example of the Hamming code. As you probably know, you can construct a quantum code, the Steane code, which is just analogous to Hamming code.

The Steane code is the simplest triangular color code. i.e. you can arrange all the qubits on a 2D triangular lattice, and only do nearest neighbor interactions [1]. The surface code is a similar quantum code, in which the qubits can also be placed on a 2D lattice, except that lattice is made up of squares.

Why do we care about 2D surfaces and nearest neighbor interactions. Because it makes building quantum hardware easier.

EDIT:

[1] The Steane code's picture is shown here. https://errorcorrectionzoo.org/c/steane Seven data qubits are on the vertices of the triangles. 2 syndrome qubits on each of the faces.

Eh. It was always sort of muddy. We never actually had an implementation of doc2vec as described in the paper.

I feel like this is basically how humanity operates as a whole, and that seems to produce usable results, so why the heck not?

No problem, said von Neumann. https://www.scottaaronson.com/qclec/27.pdf

I've never seen so much money spent on a fundamentally flawed tech, since maybe Theranos. I'm really starting to doubt the viability of the current crop of quantum computing attempts. I think there probably is some way to harness quantum effects, but I'm not sure computing with inherently high margin of error is the right way to do it.

The full error correction system involves qubits. This paper is mainly about the decoder, which is responsible for taking the symptom data produced by the quantum circuit and determining the most likely errors that caused those symptoms. In the blog post it's not stated what code is being run, but in the illustration it's clear it's a surface code [1] and this is confirmed in the paper's abstract [2].

Disclaimer: am one of the authors, but not a main contributor. I wrote the simulator they used and made some useful suggestions on how to use it to extract information they wanted for training the models more efficiently, but know nothing of transformers.

[1]: https://errorcorrectionzoo.org/list/quantum_surface

[2]: https://www.nature.com/articles/s41586-024-08148-8.pdf

The world of quantum has all these interesting gotchas.

In a quantum computer, your logical quantum state is encoded in lots of physical qubits (called data qubits) in some special way. The errors that occur on these qubits are indeed arbitrary, and for enough physical qubits are indeed not practically classically simulatable.

To tackle these errors, we do "syndrome measurement" i.e. interact the data qubits with another set of physical qubits (called syndrome qubits), in a special way, and then measure the syndrome qubits. The quantum magic that happens is that the arbitrary errors get projected down to a countable and finite set of classical errors on the data and syndrome qubits!!! Without this magic result we would have no hope for quantum computers.

Anyway, this is where a decoder - a classical algorithm running on a classical computer - comes in. OP is a decoder. It takes the syndrome qubit measurements and tries to figure out what classical errors occurred and what sort of correction, if any, is needed on the data qubits.

Quantum computing is not intractable and can be still simulated with a sufficient amount of time. This work used quantum simulator to generate data points then use it to train a transformer, which doesn't seem that different from other neural network use cases to optimize computation heavy problems.

The question would be whether this approach still works when it is scaled to thousands or even millions of qubits. The team is optimistic that that is the case, but we will see.

The model could choose which measurement operations to make on the qubits, and which operations to take to repair the qubits?

In some quantum error correcting codes, there is a large set of operators that, when there are currently no errors, measuring these will not change the state (well, assuming the measurement is made without error), but would result in some information about the kind of error if there is an error, and this info can be used to choose what operations to take to correct the error.

For a number of such schemes, there’s a choice of a strategy of what schedule to check which of the measurements with, and how to correct the errors.

It's not a perfect detector. If you give up perfection and settle for X% accuracy, then you can use a classical system (FWIU).

The error correction itself requires qbits, but reading out the final answer apparently becomes more probabilistic and complex, to the point where a neural net is a reasonable solution for interpretation and denoising.

QUANTUM AI BLOCKCHAIN!

Short NVDA is what those guys are.

The tide goes out.

The whole "tries all possible combinations" thing is a very misleading oversimplification in the first place.

Instead, think of it more like a completely different set of operations than classical computers that, if you were to try and replicate/simulate them using a classical computer, you would have no choice but to try all possible combinations in order to do so. Even that is oversimplifying, but I find it at least doesn't hint at "like computers, but faster", and is as close as making the parallelism pov "correct" as you're going to get.

What these operations do is pretty exotic and doesn't really map onto any straightforward classical computing primitives, which puts a pretty harsh limit of what you can ask them to do. If you are clever enough, you can mix and match them in order to do some useful stuff really quickly, much faster than you ever could with classical computers. But that only goes for the stuff you can make them do in the first place.

That's pretty much the extent I believe someone can "understand" quantum computing without delving into the actual math of it.

Every quantum algorithm is a unitary operation in a Hilbert space. If you want to understand the theory then you will have to do the actual work of learning about Hilbert spaces and unitary operators.

>It’s always something-something tries all possible combinations

"If you take nothing else from this blog: quantum computers won't solve hard problems instantly by just trying all solutions in parallel." - Scott Aaronson

This short comic he helped author actually summarizes the core idea fairly well https://www.smbc-comics.com/comic/the-talk-3

https://www.youtube.com/watch?v=F_Riqjdh2oM

This video is the simplest explanation that I have found for Quantum Computing which doesn't do the whole pop-sciency "is both zero and one at the same time" nonsense.

>viola

A large violin provides little answers.