Quantum developments!

Perhaps like the poor current President of the United States, I can feel myself fading, my memory and verbal facility and attention to detail failing me, even while there’s so much left to do to battle the nonsense in the world. I started my career on an accelerated schedule—going to college at 15, finishing my PhD at 22, etc. etc.—and the decline is (alas) also hitting me early, at the ripe age of 43.

Nevertheless, I do seem to remember that this was once primarily a quantum computing blog, and that I was known to the world as a quantum computing theorist. And exciting things continue to happen in quantum computing…


First, a company in the UK called Oxford Ionics has announced that it now has a system of trapped-ion qubits in which it’s prepared two-qubit maximally entangled states with 99.97% fidelity. If true, this seems extremely good. Indeed, it seems better than the numbers from bigger trapped-ion efforts, and quite close to the ~99.99% that you’d want for quantum fault-tolerance. But maybe there’s a catch? Will they not be able to maintain this kind of fidelity when doing a long sequence of programmable two-qubit gates on dozens of qubits? Can the other trapped-ion efforts actually achieve similar fidelities in head-to-head comparisons? Anyway, I was surprised to see how little attention the paper got on SciRate. I look forward to hearing from experts in the comment section.


Second, I almost forgot … but last week Quantinuum announced that it’s done a better quantum supremacy experiment based on Random Circuit Sampling with 56 qubits—similar to what Google and USTC did in 2019-2020, but this time using 2-qubit gates with 99.84% fidelities (rather than merely ~99.5%). This should set a new standard for those looking to simulate these things using tensor network methods.


Third, a new paper by Schuster, Haferkamp, and Huang gives a major advance on k-designs and pseudorandom unitaries. Roughly speaking, the paper shows that even in one dimension, a random n-qubit quantum circuit, with alternating brickwork layers of 2-qubit gates, forms a “k-design” after only O(k polylog k log n) layers of gates. Well, modulo one caveat: the “random circuit” isn’t from the most natural ensemble, but has to have some of its 2-qubit gates set to the identity, namely those that straddle certain contiguous blocks of log n qubits. This seems like a purely technical issue—how could randomizing those straddling gates make the mixing behavior worse?—but future work will be needed to address it. Notably, the new upper bound is off from the best-possible k layers by only logarithmic factors. (For those tuning in from home: a k-design informally means a collection of n-qubit unitaries such that, from the perspective of degree-k polynomials, choosing a unitary randomly from the collection looks the same as choosing randomly among all n-qubit unitary transformations—i.e., from the Haar measure.)

Anyway, even in my current decrepit state, I can see that such a result would have implications for … well, all sorts of things that quantum computing and information theorists care about. Again I welcome any comments from experts!


Incidentally, congratulations to Peter Shor for winning the Shannon Award!

36 Responses to “Quantum developments!”

  1. Physpostdoc Says:

    Also Peter Shor won the 2025 Shannon Award!
    https://www.itsoc.org/news/shannon-award-2025

  2. Scott Says:

    Physpostdoc #1: Congrats to Peter! I didn’t know whether this “Shor code” was a big deal or not, but now… 😀

  3. gentzen Says:

    Perhaps like the poor current President of the United States, I can feel myself fading, my memory and verbal facility and attention to detail failing me, even while there’s so much left to do to battle the nonsense in the world.

    The press conference convinced me that there is no need for Biden to directly step down as president. But it also convinced me that there is no chance for him to win the election, or do a good job the next four years, should he win despite all.

    However, due to the election in France, I did read a bit of international press (in addition to US and German press). Suggesting that Christiano Ronaldo was responsible for Portugal not doing better in its last two EM games is among the less damaging things they wrote. And during the press conference, journalists brought up those topics themselves, like skipping a meeting with German chancellor Scholz. OK, the Obama administration spying the smartphone of Angela Merkel was perhaps more embarrassing (“you don’t do that to a friend”), but why do you have to embarras your close allies at all? I guess that is precisely the reason why American journalist brought up those topics, to drive home the message to Biden that he really should step aside.

    I wrote on here on May 23rd, 2021

    Your courage to face the dark times, to accept the comments of the other side, to engage with them, to warn about what would happen next, to ensure that common knowledge really became common knowledge, all that was extremely helpful for me. It enabled me to reply to those (close to me) that were sympathetic to what happened that they just don’t know enough about the US, just like I don’t know enough about Russia. They told me that Biden is too old and has dementia. I replied that he is the same age as my mother and that she would definitively not be too old. She was delighted.

    I would not vote for Biden, or defend him this time. Not even if there was a slim chance that it could prevent Trump. I would vote for Robert F. Kennedy Jr., so that at least my opposition gets documented, opposition both to Trump, and to an old man who is unable to accept that it is time to give the younger generation their chance.

  4. Scott Says:

    gentzen #3: Thanks for the kind words! But while I fervently hope Biden drops out, if he stays in, I will vote for him in November if he’s a mummified corpse in embalming fluid. Such a corpse would still have more coherent cognition than the conspiracy-addled RFK Jr., to say nothing of the … other candidate in the race.

  5. Raoul Ohio Says:

    gentzen #3

    So we have a way too old guy trying to keep the world limping along, a way too old nazi poser, and an insane antivaxer buffoon.

    Not sure how old RFK is.

  6. fred Says:

    Of course there’s always the question of what’s the actual role of POTUS in practice, given he’s just the tip of a massive administration, and the various lobbies are the ones pulling the strings in the end.
    Another proof of this is that lack of mental acuity hasn’t prevented W.Bush, Reagan, and Trump to successfully “role play” as POTUS, and too much intellectual ability seems kind of a waste (young and intelligent POTUS like JFK, Clinton, and Obama are just as shackled as all the others).
    There’s also personality and ability to inspire, and Biden is losing all this (unless you happen to be impressed by his willingness to never give up), but, practically, the only thing that really matters is experience dealing with all the various corrupted clowns in congress and senate, and Biden is right that he has plenty of that, even in his current state.

    Finally, popes are typically expected to stick to the job till the very end, so I guess I’m adopting that model for Biden. 😀
    It’s not like there’s no contingency for POTUS dying while in office (i.e. the VP takes over).

  7. fred Says:

    Ideally, I was hoping for Biden to do really poorly at yesterday’s press conf, so that dems would move along to replace him, but he did just well enough to reset the conversation about replacing him… I guess it’s really good news for the GOP.

  8. fred Says:

    Raoul Ohio #5

    “Not sure how old RFK is.”

    Next time I pass by the NYC Public Library on 5th Ave, I’ll go in to try and find out.
    A shame there isn’t an easier way to discover facts.

  9. fred Says:

    I noticed after Biden’s press conference that young commentators on the left and ultra-left are not only getting more and more cruel in the way they talk about him, but they also are unleashing their ageism with comments like:

    “I’ve never seen an old person, or even just older person, ever feel embarrassed”

    The thing about age (unlike sex and skin color) is that they too will be old one day, assuming they make it that far.
    I guess wokeism still has to ways to go 😛

  10. Craig Gidney Says:

    The Oxford result looks pretty cool to me. If I had to speculate at why it didn’t grab a lot of attention, my guesses would be:

    – Overkill. The surface code’s threshold is around 99% gate fidelity. So 99.9% is more than sufficient for fault tolerance. Going to 99.99% is great, it reduces overheads, it increases options, but there’s a sense in which it’s beating a dead horse. The actual limiting factors will be elsewhere in the system.

    – Hero Worship. There’s a huge gulf between the difficulty of demonstrating a “hero gate” with a certain fidelity, and the difficulty of making it so that most of your gates have that fidelity in a large system. Fault tolerance requires the latter, not the former. Ion trap groups have a bit of a history of benchmarking at small scale, and then incorrectly extrapolating this to large scales. For example, planning to put 50 qubits in the trap, then benchmarking with 2 qubits in the trap, despite fidelity going down with qubits-in-trap. I don’t think that specific problem is happening here; skimming the paper the Oxford design looks more like the Quantinuum design or the Sussex design where ions are kept sparse and moved from place to place to do operations. In that case I think the challenge is consistency: you need to make most of the operating areas good, not just one operating area good, and that needs to be stable over time. A major indicator that a group is thinking in systems instead of heroes, that’s easy to check for, is whether they provide histograms of gate fidelities instead of a single-number best-of fidelity.

    – Geometry. This system is still on a linear track. You can emulate a 2D connectivity on a 1D track in order to run a surface code or other 2D code, but each qubit will experience $O(\sqrt{n})$ position-exchange operations. Those operations are not perfect, they incur error, so this eventually blows the threshold. Ion trap groups have plans to make 2D tracks. If you’re looking for the next “big news” in ion traps, that’s what I’d be watching for.

  11. Craig Gidney Says:

    I probably didn’t make this clear enough in my comment: this paper does actually provide histograms of fidelity over time, so they are thinking systemically. And I forgot to mention what are probably the more important reasons. The meta reasons:

    – Reaction Time. The preprint came out two days ago. Give it a month before deciding if it made a splash or not.

    – Virality. The fidelity is the easiest thing to communicate about the paper, but it isn’t really the interesting part of the paper. The interesting part of the paper is how the fidelity was achieved.

  12. Victory Omole Says:

    Craig Gidney #10

    > – Overkill. The surface code’s threshold is around 99% gate fidelity. So 99.9% is more than sufficient for fault tolerance. Going to 99.99% is great, it reduces overheads, it increases options, but there’s a sense in which it’s beating a dead horse. The actual limiting factors will be elsewhere in the system.

    The slow gate times on Ions compared to Superconducting means that they will have to make up for it elsewhere by reducing overheads and increasing options. The surface code is too expensive for a modality that’s not constrained to nearest neighbor connectivity and has relatively slow gates.

  13. William Gasarch Says:

    “… but this time using 2-quibit gates with a 99.84% fidelites (rather than merely 99.5).”

    Is this really an important improvement (theoretially or practically) or are you being
    sarcastic?

  14. The Urian Says:

    Dear Scott,

    you should read “A Mathematicians Apology” from Hardy:
    https://en.wikipedia.org/wiki/A_Mathematician%27s_Apology

  15. Scott Says:

    William Gasarch #13: It’s significant. The circuit fidelity goes roughly like pm, where p is the gate fidelity and m is the number of gates. Thus, how close p is to 1 directly controls how many gates you can apply.

  16. seth Says:

    It’s a little funny to have both those papers in the same post. From Oxford ionics’ website

    “Better beats bigger
    Is a quantum computer with 1,000,000 qubits better than one with 100 qubits? It depends on how good the qubits are and how they’re wired up: the error rate and connectivity.”

    From the Schuster paper it looks like as you increase the number of qubits you probably only need log(n) layers to show advatage, so like 1/n log(n) error rates. Maybe better isn’t as much better than bigger as they thought.

  17. Scott Says:

    The Urian #14:

      Dear Scott,
      you should read “A Mathematicians Apology” from Hardy

    Did you think it possible that I didn’t read it as a teenager? 🙂

    Maybe what’s left for me is to write “A Quantum Complexity Theorist’s Apology” (although what else have I been doing on this blog all these years?)

  18. Victory Omole Says:

    > I was surprised to see how little attention the paper got on SciRate

    Scirate users tend to lean on the theory side than experiment. You’ll find more of them at
    QIP and less of them at SQuInT.

    The experiments that stand out have something to do with what theoretical folks care about. For example, the Quantinuum experiment you mentioned has to do with random circuit sampling. 2-qubit fidelities alone are too low-level for Sciraters. Of course, there are exceptions. If a team did 99.9% CZ fidelities across 500 qubits tomorrow, that will grab Scirate’s attention.

    Let’s look at the first page of the list of all-time Scirate papers. If we don’t count classical simulation of quantum circuits as experiments, the experimental papers that wowed Sciraters are Harvard/MIT/UMD/NIST/QuEra’s logical quantum processor and Google’s machine learning from quantum data, both which are “full-stack” experiments than component level.

  19. JimV Says:

    Another off-topic comment I should have successfully resisted: I had gained some respect for Biden for saving us from Trump and for a successful term in office but lost it after his debate performance. I feel that, with some preparation (looking up facts on Roe vs. Wade, and the USA economy under Trump and Biden, and whether illegal immigrants add to or reduce crime statistics–pretty sure they reduce crime statistics as a percent of the population and add to the economy) I could have done a much better job at a very important task. Also, although his NATO press conference performance was probably good enough to have won the debate had he done as well then, I didn’t like a couple of his answers. Nobody is asking to let Ukraine bomb Moscow; and he would take cognitive tests if told he needs to–well I’m telling him he needs to!

    However, the time to withdraw was about a year ago. We need to take the focus off Biden and put it on Trump for the rather short remaining time before the election.

    In conclusion, I raise my glass in toast to all those contributing to Quantum Computation, and to this blog for which it stands.

  20. Prasanna Says:

    Scott#4
    How did the most powerful nation on earth, and also torchbearer of liberal democracy with highest levels of scientific and economic achievement,get to this place ? How did this system prevent even 1 out of 300+ million people from raising to the occasion?Does this not say something about human frailty?

  21. Scott Says:

    Prasanna #20: I mean, substantially worse has happened. Germany, the scientific and cultural superpower of its time, got taken over by you-know-who. Russia got taken over by the Bolsheviks and more recently by Putin, both of whom not only weren’t the best you could find in that vast country but were nearly the worst. Biden isn’t even a bad guy at all; he’s merely old and frail, a situation with countless precedents in the history of nations and empires. And our system survived Trump once, as I wasn’t sure it would; maybe it can survive him a second time (though I wouldn’t bet on it). As for why we have to look for such slender reeds of optimism — I mean, would you prefer a concrete answer in terms of the choices that brought us to this point, or a more abstract answer in terms of game theory and equilibria and coalitions and Arrow’s Theorem? Either way, you could probably articulate it as well as I could.

  22. AP Says:

    I missed the comments section of the last post, so I’ll just share this little gem here in case it amuses anyone. While playing cards over lunch at a famous big tech company, the question once arose “how do I know if this deck is in a randomly shuffled order?” The questioner didn’t want to know whether the shuffling *process* was random, but whether the deck in its present form was. I tried to convince him that this is much like asking whether a specific chosen integer is “random,” but I’m not sure the light bulb clicked.

  23. Fulmenius Says:

    AP #22, I think, your colleague’s question is sound, at least in a certain sense. Given a specific shuffling process and a specific initial state of the deck, it is reasonable to ask how much information the knowledge of the initial state of the deck gives you about the state of the deck after shuffling. Suppose, for instance, that shuffling consists of randomly dividing a deck into two contiguous subdecks, then shuffle-permutating them. Although the new configuration is somewhat random, the relative order inside each of the two parts of the deck is conserved. This could plausibly give the player who knows the initial order an advantage in a game where cards are drawn from the deck in order.

  24. gentzen Says:

    AP #22: There are 52! different possible orderings for the deck. And 52! is a number with 68 digits, in decimal notation. Some 68-digit numbers certainly contain less informations than others, for example 1234567890123456789012345678901234567890123456789012345678901234567 contains very little information, and therefore is not “random”. But note that it doesn’t need to be that obvious. Already if the actual number would only contain 60 digits instead of the 68 possible digits, if would fail to be “random”.
    For a deck of cards, the type of regularity you would look after are the distribution of the four suits, whether ranks are (significantly) more clustered than they should be, and maybe slightly too much ordered by rank for identical suit than expected for a well shuffled deck.
    I would basically look for regularities that could be relevant for the game at hand, and could be expected in a “running” game (i.e. not the first round), if somebody didn’t shuffle well.

    Is this somewhat related to that what you wanted to convey to the questioner? Or is this more related to the position of the questioner that you want to debunk?

  25. gentzen Says:

    Scott #4: Now that I replied to AP, I fear I also have to reply to you and the others

    Such a corpse would still have more coherent cognition than the conspiracy-addled RFK Jr.

    One way to deal with conspiracy theories is to look at their funny side (sorry, those videos are all German, but they are really funny, even today)
    https://www.youtube.com/watch?v=6MQilDqX52M (WDR-Kinderchor feat. Jan Böhmermann – “Meine Oma 2.0” | ZDF Magazin Royale )
    https://www.youtube.com/watch?v=D2A9UB90Bz4 (Der Impfausweis-Kontrolleur | Deville)
    https://www.facebook.com/KroymannARD/videos/die-matheleugnerin/1567345356947599/ (Die Matheleugnerin | Maren Kroymann)

    Raoul Ohio #5: Of course, Kennedy himself is not the point here, he won’t win the election anyway. The point is rather:

    Kennedy could be benefiting from a well-documented lack of enthusiasm for a rematch between Biden and Trump that could also have pushed some voters to look elsewhere, experts say. And while a small number of third-party or independent candidates have joined the race, Kennedy is the most prominent of them.

    Typically, third-party candidates pull most of their votes from one candidate over the other. But Kennedy has fluctuated between pulling from Biden and pulling from both candidates equally. His environmental background and legacy last name likely appeal to Democrats, but the noted vaccine skeptic who has publicly advanced a number of conspiracy theories also likely appeals to members of the same anti-establishment faction that have thus far cast their lot with Trump.

    Jennifer Lawless, professor of politics at the University of Virginia, says Kennedy comes with a lot of uncertainty; he could be a spoiler for Trump in one state and for Biden in another.

    “What the [Kennedy] campaign has highlighted is that there really are a lot of people on both sides of the aisle who are looking for some alternative,” she says.

    Fred #6, 9: This debate is not about ageism, but about real measurable consequences related to age that everybody who watched was forced to see now.

    Of course there’s always the question of what’s the actual role of POTUS in practice, given he’s just the tip of a massive administration, and the various lobbies are the ones pulling the strings in the end.

    That sounds even more fatalistic to me than my own reaction (i.e. to effectively not vote at all, by voting for Kennedy). It also feels close to conspiracy theories to me: Of course POTUS is important and has power.

    JimV #19: I didn’t talk about what “we” or the dems should to. I talked about my own judgement, and what I would do personally. I am frustrated, and what I would do is to act in a way that this frustration gets documented.

    However, the time to withdraw was about a year ago. We need to take the focus off Biden and put it on Trump for the rather short remaining time before the election.

    Why? A year ago, Biden seemed to do fine. Is this the sort of ageism that fred talked about? If we don’t want to fall for this, we have to be willing to take action, if and when the risks associated with old age actually manifest themselves.

    Maybe Biden’s performance at the press conference felt good enough to some. But it was not a good performance, not at all. This sort of performance was the reason why Biden had been shielded from public appearences since the beginning of 2024. Your expectations after the catastrophic debate debacle have simply been extremely low.

  26. fred Says:

    Gentzen
    “Fred #6, 9: This debate is not about ageism,”

    I never said the debate was about ageism, I said that young woke observers are now feeling totally free to let their ageism run loose, by spewing general stereotypes about the previous generations, just based on the “sin” that they’re older than them.

  27. Mark Spinelli Says:

    Scott,

    Regarding Schuster, Haferkamp, and Huang’s result, can you please explain further what the significance of “k-designs” are to random circuits?

    Am I correct in analogizing this as saying that a random circuit of depth k, when applied to the all-0’s ket, looks only somewhat similar to a Haar-random state, much as a deck of cards that’s been shuffled with only three or four dove-tail shuffles, when applied initially to the ordered deck, will likely have *any particular card* be in a random order?

    But Bayer and Diaconis showed that it takes seven shuffles to assure ourselves that the entire distribution is close in total variation distance to being uniform over the 52! possible deck orderings. Analogously it takes a really deep circuit to be assured that an n-qubit state will be close in TVD to being Haar-random over all n-qubit states…?

  28. AG Says:

    Sam Bankman-Fried is hardly less exalted/appalling than Donald Trump Jr. This blessed Republic will survive them all (and you and me too).

  29. AP Says:

    Genzen #25: Help me understand this perspective. Suppose I tell you I’m choosing a number from 1 to 100 and get 64. Can’t you just say “well in binary, that’s 1000000, which has an unlikely number of zeros?” Why doesn’t this depend on your encoding? More generally, why should the concept of randomness (which is a property of patterns) make sense for individual numbers?

    Fulmenius #23: But you are still talking about the process, right? The whole point is that he wanted to know whether the *deck itself* in its given configuration was random, independent of the process.

    I’m far from an expert in this subject, and am happy to hear from anyone who is.

  30. AG Says:

    A deck of cards arranged in Clubs, Diamonds, Hearts, Spades; in increasing order, does not strike me as “random”.

  31. Random Circuit Sampling: Fourier Expansion and Statistics | Combinatorics and more Says:

    […] Quantinuum announced an impressive 56-qubit Random Circuit Sampling experiment based on their ion-trapped computers. For the paper click here. For a blog post on Shtetl Optimized (referring also to two other notable new advances) see here. […]

  32. gentzen Says:

    AP #29: The nasty thing about probability for us humans is that it is a question of orders of magnitude, but the relevant magnitudes are already beyond the range where we have a good intuitive grasp.

    Regarding your example with 64, if you repeatedly throw a dice, and the first six throws all show “head”, you would at least get suspicious. Sadly, this is still not a very unlikely event. So after experiencing that we all too often see a pattern where there is none, we get suspicious of the relevance of any patterns we see. And then we fail to get the relevance, even when patterns occur which are really unlikely and highly suspicious.

    So what are reasonable orders of magnitude? I once proposed that it starts to get suspicious at 1/42, and it won’t get any more suspicious than 1/3500000, i.e. 1/9876543 or 1/987654321 are just as suspicious as 1/3500000.

    When challenged, this is how I tried to justify those bounds:

    The 1/42 bound and the 2.3% are related by 97.7 / 2.3 = 42.478 and come from my faulty memory of something Christian Kredler mentioned in his course on stochastics, namely the question on the minimal sample size allowing reasonable statistics. He said something like that “we would probably still have 3-4 categories, so 20 would be too small. Something between 30 and 40 could make sense, perhaps a bit more. Don’t dismiss this, you might believe now that you will always work with large sample sizes, say >200, but when you have to do the interviews, it will consume time and money. The temptation to do only very few will be high.”

    The 1 : 3.5 million are the odds corresponding to five-sigma according to many independent sources, for example here: “In short, five-sigma corresponds to a p-value, or probability, of 3×10-7, or about 1 in 3.5 million.”
    … So the 1 : 3.5 million odds turned out to be the most extreme measure used in practice.
    The “past experience” refers to “war stories” particle physicists told in connection to the five-sigma bound, like the following: “A similar thing happened in 2011, when the CDF collaboration at Fermilab saw an excess of events at about 4 sigma. These were not fluctuations, but they required better understanding of the background.”

    Your question “Why doesn’t this depend on your encoding?” is much trickier and harder to address. My first step to addressing it is just to highlight that this is the really challenging part, independent of our human limitations:

    We can compare our probabilistic model to the real system by a great variety of different observations, however only very few of them are “intended”. (This is independent of the observations that are actually possible on the real system with reasonable effort.) At this point it really gets arbitrary or subjective in a way that cannot be fixed by appeals to existing practice and past experience.

    On the other hand, there is a good answer to your question “More generally, why should the concept of randomness (which is a property of patterns) make sense for individual numbers?” Just like the card deck example reduced to a single number, even a complete poker round with many games reduces to a single number. Same thing for the experiments at the large hadron collider. It is simply an extermely huge number. So there is no way around finding a way to make sense of randomness for single numbers (with a tiny bit of context, i.e. which other numbers could have occured at all).

  33. OhMyGoodness Says:

    Mystical frameworks provide fertile ground for interesting narratives, Lord of the Rings applied to contemporary politics. Yes…that is what they called me…Gandalf the Gray…but I am Gandalf the White. I hope this progresses on a wide scale, such interesting vistas beckon.

  34. Iso Says:

    There’s a catch in case of Quantinuum: They perform a 2Q gate in 80 ms with F_2q = 99.8%. A large scale SC system can do this in < 20 ns with a fidelity of 99.5%, which is a factor 10⁶. Consider what this means for qc-as-service and #customers you can serve per compute time.

  35. Shtetl-Optimized » Blog Archive » Quantum Computing: Between Hope and Hype Says:

    […] just the last few weeks, we saw the group at Google announce that they’d used the Kitaev surface code, with distance 7, to encode one logical qubit using […]

  36. Shtetl-Optimized » Weblog Archive » Quantum Computing: Between Hope and Hype – Aiquantumtools.com Says:

    […] simply the previous couple of weeks, we noticed the group at Google announce that they’d used the Kitaev floor code, with distance 7, to encode one logical qubit utilizing […]

Leave a Reply

You can use rich HTML in comments! You can also use basic TeX, by enclosing it within $$ $$ for displayed equations or \( \) for inline equations.

Comment Policies:

After two decades of mostly-open comments, in July 2024 Shtetl-Optimized transitioned to the following policy:

All comments are treated, by default, as personal missives to me, Scott Aaronson---with no expectation either that they'll appear on the blog or that I'll reply to them.

At my leisure and discretion, and in consultation with the Shtetl-Optimized Committee of Guardians, I'll put on the blog a curated selection of comments that I judge to be particularly interesting or to move the topic forward, and I'll do my best to answer those. But it will be more like Letters to the Editor. Anyone who feels unjustly censored is welcome to the rest of the Internet.

To the many who've asked me for this over the years, you're welcome!