Checking our forecast for quantum computing in 2024

Scott Aaronson has a nice post discussing recent experimental progress in quantum computing from Google, Microsoft, and Quantinuum. In particular, he says

Let me end by sticking my neck out. If hardware progress continues at the rate we’ve seen for the past year or two, then I find it hard to understand why we won’t have useful fault-tolerant QCs within the next decade. (And now to retreat my neck a bit: the “if” clause in that sentence is important and non-removable!)

If you’ll permit me to indulge, I’d like to compare the reported progress to the predictions from the 2020 forecasting paper by Jaime Sevilla and me.

I understand the Google results to be that they have ~10^-3 physical two-qubit error rates and they they would have ~10^-6 logical error rates if they had ~1500 physical qubits, but they actually have 101 in the present device.

For forecasting purposes, Jaime and I defined a figure of merit, the “generalized logical qubit” (GLQ) count. See Eq. (1) and Fig. 1. It essentially equals the surface-code logical qubit count in the limit of low errors and many qubits (assuming we demand 10^-18 logical error rate), but is smoothly defined with fractional values when error rates are larger and/or physical qubit counts are smaller. Our naive (log linear regression) forecast from data at the time was that 1 GLQ would be achieved 2026-2033 and 4,100 GLQs (the rough number necessary to be cryptographically dangerous) would be achieved in 2029-2060 (both 90% confidence intervals — not Bayesian credences!). Our forecasts for 2024 were 0.02-0.3 GLQs.

I’m pleased to see that the above Google numbers correspond to a GLQ count of about 0.03, which is consistent with our model (though this is perhaps not impressive since it’s only been 4 years and our confidence intervals were wide). At this rate, we predict only about 3 GLQ in a decade’s time (2034), where, as mentioned, this would mean logical qubits with a 10^-18 error rate.

If you relax the logical error rate you demand to 10^-10 (the number discussed in Google’s paper and corresponding to smaller computations), I think you’re still only looking at like a dozen or two logical qubits by 2034, which is still classically simulable. So I think one decade seems too soon to have something useful…if our forecast continues to hold up.

Our model is just linear extrapolation of error rates and physical qubit counts on log plots. There are plenty of events that could undermine it, causing a breakdown between the model and reality. Possibilities include some brilliant scientific insight, or an unforeseen experimental barrier, but I think the most likely issue would be a jump (positive or negative) in the interest of outside funders. In particular, now that the fault tolerance error-rate threshold has been crossed, funders may decide that it’s worth turning on the spigots because it’s now plausible that things can be brute-forced if necessary: even if two-qubit-gate error rates don’t progress much, it’s in principle possible (assuming assumptions) to throw tons of physical qubits at the problem and just pay an extremely high overhead for each logical qubit. There are still major hurdles with this sort of scaling, but the path forward seems more clear and predictable.

EDIT: Note well that in our paper we equatedFor what it’s worth, Google has decided to equate “fault-tolerance” with a logical error rate below 1e-6. It’s all a bit arbitrary.^a “fault-tolerance” with “a logical qubit with logical error rate below 1e-18”, but I think there’s a very reasonable alternative thing people can mean by “fault-tolerance”: it means you have a machine where each layer of error correction reduces (rather than increases) logical error rate. The recent results from Google and Quantinuum have more-or-less reached this mark, assuming assumptions. The issue is that, with current physical error rates, they would have to incur a truly enormous overhead to reach our threshold 1e-18 logical error rate even for a single logical qubit.

If you allow 1e-6 logical error rate, then our results say that getting 100 logical qubits is possible by 2030. I’m very skeptical that these could actually be used for anything actually interesting (rather than the sort of proof-of-concept demonstrations a la quantum supremacy). But Aaronson and some other smart people disagree.