Staggering toward quantum fault-tolerance

Happy Hanukkah! I’m returning to Austin from a Bay Area trip that included the annual Q2B (Quantum 2 Business) conference. This year, for the first time, I opened the conference, with a talk on “The Future of Quantum Supremacy Experiments,” rather than closing it with my usual ask-me-anything session.

The biggest talk at Q2B this year was yesterday’s announcement, by a Harvard/MIT/QuEra team led by Misha Lukin and Vlad Vuletic, to have demonstrated “useful” quantum error-correction, for some definition of “useful,” in neutral atoms (see here for the Nature paper). To drill down a bit into what they did:

• They ran experiments with up to 280 physical qubits, which simulated up to 48 logical qubits.
• They demonstrated surface codes of varying sizes as well as color codes.
• They performed over 200 two-qubit transversal gates on their encoded logical qubits.
• They did a couple demonstrations, including the creation and verification of an encoded GHZ state and (more impressively) an encoded IQP circuit, whose outputs were validated using the Linear Cross-Entropy Benchmark (LXEB).
• Crucially, they showed that in their system, the use of logically encoded qubits produced a modest “net gain” in success probability compared to not using encoding, consistent with theoretical expectations (though see below for the caveats). With a 48-qubit encoded IQP circuit with a few hundred gates, for example, they achieved an LXEB score of 1.1, compared to a record of ~1.01 for unencoded physical qubits.
• At least with their GHZ demonstration and with a particular decoding strategy (about which more later), they showed that their success probability improves with increasing code size.

Here are what I currently understand to be the limitations of the work:

• They didn’t directly demonstrate applying a universal set of 2- or 3-qubit gates to their logical qubits. This is because they were limited to transversal gates, and the Eastin-Knill Theorem shows that transversal gates can’t be universal. On the other hand, they were able to simulate up to 48 CCZ gates, which do yield universality, by using magic initial states.
• They didn’t demonstrate the “full error-correction cycle” on encoded qubits, where you’d first correct errors and then proceed to apply more logical gates to the corrected qubits. For now it’s basically just: prepare encoded qubits, then apply transversal gates, then measure, and use the encoding to deal with any errors.
• With their GHZ demonstration, they needed to use what they call “correlated decoding,” where the code blocks are decoded in conjunction with each other rather than separately, in order to get good results.
• With their IQP demonstration, they needed to postselect on the event that no errors occurred (!!), which happened about 0.1% of the time with their largest circuits. This just further underscores that they haven’t yet demonstrated a full error-correction cycle.
• They don’t claim to have demonstrated quantum supremacy with their logical qubits—i.e., nothing that’s too hard to simulate using a classical computer. (On the other hand, if they can really do 48-qubit encoded IQP circuits with hundreds of gates, then a convincing demonstration of encoded quantum supremacy seems like it should follow in short order.)

As always, experts are strongly urged to correct anything I got wrong.

I should mention that this isn’t the first experiment to claim a net gain from the use of a quantum error-correcting code: that honor (unless I’m mistaken) goes to Google from February of this year. But the Google experiment just encoded the qubits and measured them, rather than applying hundreds of logical gates to the encoded qubits.

Assuming the result stands, I think it’s plausibly the top experimental quantum computing advance of 2023 (coming in just under the deadline!). We clearly still have a long way to go until “actually useful” fault-tolerant QC, which might require thousands of logical qubits and millions of logical gates. But this is already beyond what I expected to be done this year, and (to use the AI doomers’ lingo) it “moves my timelines forward” for quantum fault-tolerance. It should now be possible, among other milestones, to perform the first demonstrations of Shor’s factoring algorithm with logically encoded qubits (though still to factor tiny numbers, of course). I’m slightly curious to see how Gil Kalai and the other quantum computing skeptics wiggle their way out now, though I’m absolutely certain they’ll find a way! Anyway, huge congratulations to the Harvard/MIT/QuEra team for their achievement.

In other QC news, IBM got a lot of press for announcing a 1000-qubit superconducting chip a few days ago, although I don’t yet know what two-qubit gate fidelities they’re able to achieve. Anyone with more details is encouraged to chime in.

Yes, I’m well-aware that 60 Minutes recently ran a segment on quantum computing, featuring the often-in-error-but-never-in-doubt Michio Kaku. I wasn’t planning to watch it unless events force me to.

Do any of you have strong opinions on whether, once my current contract with OpenAI is over, I should focus my research efforts more on quantum computing or on AI safety?

On the one hand: I’m now completely convinced that AI will transform civilization and daily life in a much deeper way and on a shorter timescale than QC will — and that’s assuming full fault-tolerant QCs eventually get built, which I’m actually somewhat optimistic about (a bit more than I was last week!). I’d like to contribute if I can to helping the transition to an AI-centric world go well for humanity.

On the other hand: in quantum computing, I feel like I’ve somehow been able to correct the factual misconceptions of 99.99999% of people, and this is a central source of self-confidence about the value I can contribute to the world. In AI, by contrast, I feel like at least a thousand times more people understand everything I do, and this causes serious self-doubt about the value and uniqueness of whatever I can contribute.