With double exponential growth, “it looks like nothing is happening, nothing is happening, and then whoops, suddenly you’re in a different world,” Neven said.<p>This is just a clever way to spin the fact that we are experiencing growth much slower than exponential growth now into a prediction of much faster future growth, without any evidence. Or perhaps an internal joke the physicists would make. Next time I have a really flat function, I'm going to fit it with a triple exponential like so:<p><pre><code> https://www.wolframalpha.com/input/?i=plot+exp(exp(exp(x))),+x%3D-20..-5,+y%3D0..5</code></pre>
Two interacting factors are claimed to be responsible for Neven’s Law. The first is the exponential advantage q-bits have over regular bits according to the article. (But isn’t this the case only for some algorithms? i.e. Shore’s)<p>The next exponential factor is stated to be the “rapid improvement of quantum processors”. Really? Is the number of q-bits in true quantum computers growing exponentially—-and not steadily, but say logarithmically? Moore’s Law was a law because it was so surprising that the semiconductor industry kept it going for so long. Is that really happening with quantum computers? I didn’t realize that breakthroughs in Q computing were happening like that.
I always thought that the "ultimate laptop" , in other words nature, has a fundamental limit of computation due to entropy as Seth Lloyd prescribed. So we know Moore's Law isn't dead yet, crowning terms like Nevin's will create a stream of self-ordained Laws , and this will not help at all. I think it is more important to be contrarian, and be against quantum computing like Gil Kalai than push a Moore's Law narrative on mesoscopic materials. I would go against any effort to create a theory of exponentiation . I think this is such a weak paradigm since we haven't yet even figured out what a classical quantum computer would do. In a sense, quantum computing needs an upper bound due to its computational complexity rather than anticipated supremacy. <a href="https://www.quantamagazine.org/gil-kalais-argument-against-quantum-computers-20180207/" rel="nofollow">https://www.quantamagazine.org/gil-kalais-argument-against-q...</a>
Quantum computing is rising? I was under the impression that is has been stagnating for like half a decade now. Can a QC finally factor 15? Like factor(15)=3*5?
“Neven says that Google’s best quantum chips have recently been improving at an exponential rate.”<p>That may be the real news here. Are there any other sources about this?
So how many Qbits are they up to? And how fast is that number increasing?<p>Comparing to classical like this is kind of dumb since quantum is known to be exponentially faster. Or doubly or whatever. Just stop comparing and tell us how many bits.
Double exponential growth is crazy fast, but some problem grow much faster and follow the <i>hyperoperation sequence</i> growth rate. Knuth wrote a fun paper in Science in 1976 [1]. (Easy & interesting but sadly my link is to a paywall.)<p>That was the first place I saw his arrow notation to describe some of these numbers.<p><pre><code> 5↑3 = 5*(5*5)
5↑↑3 = 5↑(5↑5)
5↑↑↑3 = 5↑↑(5↑↑5)
5↑↑↑↑3 = 5(↑^4)3
</code></pre>
These numbers get BIG, the up arrow notation can express the Ackermann function.<p>[1] <a href="https://science.sciencemag.org/content/194/4271/1235" rel="nofollow">https://science.sciencemag.org/content/194/4271/1235</a>
If the law is true, and quantum computing is the key enabler of AGI, then the law is either the best or worst news in human history. And we may be living in the final generations of our species. Not to be dramatic. I'm kinda hoping that Nevin is an inferior prophet to Moore.
This is the hill that DWave died on with "Rose's Law." Make 3 chips small chips, make sweeping predictions on a log plot, call it a law. Yawn.<p>My biggest disappointment is in Scott Aaronson. He should know the difference between making something useful and making something hard to simulate.