Using a 28-qubit trapped-ion #quantum processor, researchers report the first experimental demonstration of high-fidelity logical magic states prepared by code switching, with a logical error rate below the dominant physical operation infidelity. 🔗 https://t.co/VXyhLPwdTh

This is where the magic happens ✨ In a landmark scientific breakthrough, we're the 1st company to demonstrate a fully fault-tolerant universal gate set with repeatable error correction - the final piece to unlocking industrial-scale quantum computing.

If I've gotten a similar help from a human, I would have definitely included that person as a coauthor. So I feel a bit uneasy just putting O3 in the acknowledgement section of the paper. What do you think I should have done?

For this reason, I view the AI tools (especially O3) to be already useful for my research. I would say 60~80% of what it says is useless. But once in a while it produces some gems like this. As far as I can sift it through, that's good enough for me.

Would I have been able to figure out the relevance of LFSR to my problem on my own, without O3? Honestly, I don't see it happening. So in many ways, I view O3's insight to be an extremely important part of this paper.

But it was okay, because the particular XORs being used in this scheme could be easily parallelized using fanout, which was free in my problem anyway. So I could fix O3's mistake easily!

That could very well be true, but I couldn't find the proof of this statement anywhere. So I asked O3 if this is a known fact. It admitted that this is not known, and this part of the argument was rushed.

The point is, for all intents and purposes (n<=660), it seems that the number of XORs needed is small (at most 4). Extrapolating this, O3 concluded that the number of XORs should be O(1) and therefore the whole thing must be O(1) depth.

One small mistake though was the reason behind why LFSR is an O(1)-depth circuit. O3 correctly identifed that there is a cyclic shift and some XORs. That cyclic shift can be done in O(1)-depth is easy to see, so that part was fine. But the XOR part was trickier.

It became very quickly clear that indeed LFSR givess rise to a reversible linear map over bitstrings with period of 2^n-1. So that was promising.

O3 provided several reasons on why this should do the job. Honestly, this was a hodgepodge of correct and incorrect statements. But at least I could check these statements myself.

So I asked O3 if there is any constant-depth classical circuit with exponentially large period, and it told me about the linear-feedback shift register ( https://t.co/WGbk8quQq5), which I wasn't aware of.

One simple strategy is to have n qubits and have a cyclic shift. This can be done in O(1) depth with some ancillas, and we can make the period large by considering shifts over a larger set of qubits. But the period scales only linearly with the number of qubits. Not so useful...

I knew for some time that, to achieve constant T-depth, it would suffice to have a constant-depth Clifford with a large period. But it wasn't so obvious how to get such a Clifford.

One of the key contributors to this project was actually ChatGPT (model O3). I asked it to become a coauthor but it refused (very politely actually), so I just ended up acknowledging its help.

To be clear, I think the method in my paper will be useful only in a limited setting, like when the rotation angle is fixed and known (e.g., qDRIFT). But who knows? Maybe with future improvements this constant T-depth idea might become more broadly useful.

The moral of the story is that there's something we didn't understand very well about constant T-depth quantum circuits. They seem to be surprisingly powerful, capable of computations that I for one thought was impossible.

And that's not the only example. You can say the same thing about many subroutines, e.g., addition, multiplication, quantum Fourier transform... With a catalyst state, they can be all done in constant T-depth (or equivalently Toffoli depth) and a log-depth Clifford. Very strange!

This is a strange form of "superactivation." Constant-depth Toffoli doesn't give us n-qubit Toffoli. Clifford doesn't give us n-qubit Toffoli. But combining the two (plus a catalyst), we do get n-qubit Toffoli. Weird!

So naively, constant-depth Toffoli plus arbitrary Clifford shouldn't let us get n-qubit Toffoli. But with a catalyst state, apparently we can!