## Quantum supremacy via BosonSampling

December 3rd, 2020A group led by Jianwei Pan, based mainly in Hefei and Shanghai, announced today that it achieved BosonSampling with 40-70 detected photons—up to and beyond the limit where a classical supercomputer could feasibly verify the results. For more, see also Emily Conover’s piece in *Science News*, or Daniel Garisto’s in *Scientific American*, both of which I consulted on. (Full disclosure: I was one of the reviewers for the Pan group’s *Science* paper, and will be writing the Perspective article to accompany it.)

The new result follows the announcement of 14-photon BosonSampling by the same group a year ago. It represents the second time quantum supremacy has been reported, following Google’s celebrated announcement from last year, and the first time it’s been done using photonics rather than superconducting qubits.

As the co-inventor of BosonSampling (with Alex Arkhipov), obviously I’m gratified about this.

For anyone who regards it as boring or obvious, here and here is Gil Kalai, on this blog, telling me why BosonSampling would never scale beyond 8-10 photons. (He wrote that, if aliens forced us to try, then much like with the Ramsey number R(6,6), our only hope would be to attack the aliens.) Here’s Kalai making a similar prediction, on the impossibility of quantum supremacy by BosonSampling or any other means, in his plenary address to the International Congress of Mathematicians two years ago.

Even if we set aside the quantum computing skeptics, many colleagues told me they thought experimental BosonSampling was a dead end, because of photon losses and the staggering difficulty of synchronizing 50-100 single-photon sources. They said that a convincing demonstration of quantum supremacy would have to await the arrival of quantum fault-tolerance—or at any rate, some hardware platform more robust than photonics. I always agreed that they might be right. Furthermore, even if 50-photon BosonSampling *was* possible, after Google reached the supremacy milestone first with superconducting qubits, it wasn’t clear if anyone would still bother. Even when I learned a year ago about the Pan group’s intention to go for it, I was skeptical, figuring I’d believe it when I saw the paper.

Obviously the new result isn’t dispositive. Maybe Gil Kalai really WON, BY A LOT, before Hugo Chávez hacked the Pan group’s computers to make it seem otherwise? (Sorry, couldn’t resist.) Nevertheless, as someone whose intellectual origins are close to pure math, it’s strange and exciting to find myself in a field where, once in a while, the world itself gets to weigh in on a theoretical disagreement.

Since excitement is best when paired with accurate understanding, please help yourself to the following FAQ, which I might add more to over the next couple days.

**What is BosonSampling?** You must be new here! In increasing order of difficulty, here’s an *MIT News* article from back in 2011, here’s the Wikipedia page, here are my PowerPoint slides, here are my lecture notes from Rio de Janeiro, here’s my original paper with Arkhipov…

**What is quantum supremacy?** Roughly, the use of a programmable or configurable quantum computer to solve *some* well-defined computational problem much faster than we know how to solve it with any existing classical computer. “Quantum supremacy,” a term coined by John Preskill in 2012, does *not* mean useful QC, or universal QC, or scalable QC, or fault-tolerant QC, all of which remain outstanding challenges. For more, see my Supreme Quantum Supremacy FAQ, or (e.g.) my recent Lytle Lecture for the University of Washington.

**If Google already announced quantum supremacy a year ago, what’s the point of this new experiment?** To me, at least, quantum supremacy seems important enough to do at least twice! Also, as I said, this represents the first demonstration that quantum supremacy is possible *via photonics*. Finally, as the authors point out, the new experiment has one big technical advantage over Google’s: namely, many more possible output states (~10^{30} of them, rather than a mere ~9 quadrillion). This makes it infeasible to calculate the whole probability distribution over outputs and store it on a gigantic hard disk (after which one could easily generate as many samples as one wanted), which is what IBM proposed doing in its response to Google’s announcement.

**Is BosonSampling a form of universal quantum computing?** No, we don’t even think it can simulate universal *classical* computing! It’s designed for exactly one task: namely, demonstrating quantum supremacy and refuting Gil Kalai. It *might* have some other applications besides that, but if so, they’ll be icing on the cake. This is in contrast to Google’s Sycamore processor, which in principle *is* a universal quantum computer, just with a severe limit on the number of qubits (53) and how many layers of gates one can apply to them (about 20).

**Is BosonSampling at least a step toward universal quantum computing?** I think so! In 2000, Knill, Laflamme, and Milburn (KLM) famously showed that pure, non-interacting photons, passing through a network of beamsplitters, are capable of universal QC, provided we assume one extra thing: namely, the ability to measure the photons at intermediate times, and change which beamsplitters to apply to the remaining photons depending on the outcome. In other words, “BosonSampling plus adaptive measurements equals universality.” Basically, KLM is the holy grail that Pan’s and other experimental optics groups around the world have been working toward for 20 years, with BosonSampling just a more achievable pit stop along the way.

**Are there any applications of BosonSampling?** We don’t know yet. There are proposals in the literature to apply BosonSampling to quantum chemistry and other fields, but I’m not yet convinced that these proposals will yield real speedups over the best we can do with classical computers, for any task of practical interest that involves estimating specific numbers (as opposed to sampling tasks, where BosonSampling almost certainly *does* yield exponential speedups, but which are rarely the thing practitioners directly care about).

**How hard is it to simulate BosonSampling on a classical computer?** As far as we know today, the difficulty of simulating a “generic” BosonSampling experiment increases roughly like 2^{n}, where n is the number of detected photons. It *might* be easier than that, particularly when noise and imperfections are taken into account; and at any rate it might be easier to spoof the statistical tests that one applies to verify the outputs. I and others managed to give some theoretical evidence against those possibilities, but just like with Google’s experiment, it’s conceivable that some future breakthrough will change the outlook and remove the case for quantum supremacy.

**Do you have any amusing stories?** When I refereed the *Science* paper, I asked why the authors directly verified the results of their experiment only for up to 26-30 photons, relying on plausible extrapolations beyond that. While directly verifying the results of n-photon BosonSampling takes ~2^{n} time for any known classical algorithm, I said, surely it should be possible with existing computers to go up to n=40 or n=50? A couple weeks later, the authors responded, saying that they’d now verified their results up to n=40, but it burned $400,000 worth of supercomputer time so they decided to stop there. This was by far the most expensive referee report I ever wrote!

Also: when Covid first started, and facemasks were plentiful in China but almost impossible to get in the US, Chaoyang Lu, one of the authors of the new work and my sometime correspondent on the theory of BosonSampling, decided to mail me a box of 200 masks (I didn’t ask for it). I don’t think that influenced my later review, but was appreciated nonetheless.

Huge congratulations to the whole team for their accomplishment!