### From quantum supremacy to classical fallacy

Wednesday, October 2nd, 2019**Retrospective Comment (Dec. 26, 2019):** While I basically stand by what I wrote in this post, I wanted to call attention to the fact that, in its aftermath, one of the authors of the p-bit paper—Kerem Camsari—displayed a striking degree of intellectual courage and honesty. He showed up in the comments section to defend the motivation for the p-bit model, but also to concede the points I’d raised about scaling. Notably, on some matters, he explicitly broke with his own coauthors. He treated having his paper harshly criticized on *Shtetl-Optimized* not as a personal attack, but as an opportunity to learn and grow. I’m not sure that I would’ve been able to do the same in his shoes, and I regard it as one of the happier outcomes in this blog’s history. –SA

Maybe I should hope that people *never* learn to distinguish for themselves which claimed breakthroughs in building new forms of computation are obviously serious, and which ones are obviously silly. For as long as they don’t, this blog will always serve at least one purpose. People will cite it, tweet it, invoke its “authority,” even while from my point of view, I’m offering nothing more intellectually special than my toddler does when he calls out “moo-moo cow! baa-baa sheep!” as we pass them on the road.

But that’s too pessimistic. Sure, most readers *must* more-or-less already know what I’ll say about each thing: that Google’s quantum supremacy claim is serious, that memcomputing to solve NP-complete problems is not, etc. Even so, I’ve heard from many readers that this blog was at least helpful for double-checking their initial impressions, and for making common knowledge what before had merely been known to many. I’m fine for it to continue serving those roles.

Last week, even as I dealt with fallout from Google’s quantum supremacy leak, I also got several people asking me to comment on a *Nature* paper entitled Integer factorization using stochastic magnetic tunnel junctions (warning: paywalled). See also here for a university press release.

The authors report building a new kind of computer based on asynchronously updated “p-bits” (probabilistic bits). A p-bit is “a robust, classical entity fluctuating in time between 0 and 1, which interacts with other p-bits … using principles inspired by neural networks.” They build a device with 8 p-bits, and use it to factor integers up to 945. They present this as another “unconventional computation scheme” alongside quantum computing, and as a “potentially scalable hardware approach to the difficult problems of optimization and sampling.”

A commentary accompanying the *Nature* paper goes much further still—claiming that the new factoring approach, “if improved, could threaten data encryption,” and that resources should now be diverted from quantum computing to this promising new idea, one with the advantages of requiring no refrigeration or maintenance of delicate entangled states. (It should’ve added: and how big a number has Shor’s algorithm factored anyway, 21? Compared to 945, that’s peanuts!)

Since I couldn’t figure out a gentler way to say this, here goes: it’s **astounding** that this paper and commentary made it into *Nature* in the form that they did. Juxtaposing Google’s sampling achievement with p-bits, as several of my Facebook friends did last week, is juxtaposing the Wright brothers with some guy bouncing around on a pogo stick.

If you were looking forward to watching me dismantle the p-bit claims, I’m afraid you might be disappointed: the task is over almost the moment it begins. **“p-bit” devices can’t scalably outperform classical computers, for the simple reason that they are classical computers.** A little unusual in their architecture, but still well-covered by the classical Extended Church-Turing Thesis. Just like with the quantum adiabatic algorithm, an energy penalty is applied to coax the p-bits into running a local optimization algorithm: that is, making random local moves that preferentially decrease the number of violated constraints. Except here, because the whole evolution is classical, there doesn’t seem to be even the *pretense* that anything is happening that a laptop with a random-number generator couldn’t straightforwardly simulate.

Even so, I wouldn’t be writing this post if you opened the paper and it immediately said, in effect, “look, *we know*. You’re thinking that this is just yet another stochastic local optimization method, which could clearly be simulated efficiently on a conventional computer, thereby putting it into a different conceptual universe from quantum computing. You’re thinking that factoring an n-bit integer will self-evidently take exp(n) time by this method, as compared to exp(n^{1/3}) for the Number Field Sieve, and that no crypto is in even remote danger from this. But here’s why you should still be interested in our p-bit model: because of other advantages X, Y, and Z.” Alas, in vain one searches the whole paper, *and* the lengthy supplementary material, *and* the commentary, for any acknowledgment of the pachyderm in the pagoda. Not an asymptotic runtime scaling in sight. Quantum computing is there, but stripped of the theoretical framework that gives it its purpose.

That silence, in the pages of *Nature*—*that’s* the part that convinced me that, while on the negative side this blog seems to have accomplished nothing for the world in 14 years of existence, on the positive side it will likely have a role for decades to come.

**Update:** See a response in the comments, which I appreciated, from Kerem Cansari (one of the authors of the paper), and my response to the response.

**(Partly) Unrelated Announcement #1:** My new postdoc, Andrea Rocchetto, had the neat idea of compiling a Quantum Computing Fact Sheet: a quick “Cliffs Notes” for journalists, policymakers, and others looking to get the basics right. The fact sheet might grow in the future, but in the meantime, check it out! Or at a more popular level, try the Quantum Atlas made by folks at the University of Maryland.

**Unrelated Announcement #2:** Daniel Wichs asked me to give a shout-out to a new Conference on Information-Theoretic Cryptography, to be held June 17-19 in Boston.

**Third Announcement:** Several friends asked me to share that Prof. Peter Wittek, quantum computing researcher at the University of Toronto, has gone missing in the Himalayas. Needless to say we hope for his safe return.