Neven’s Law is for Quantum Computers as Moore’s Law for Regular Computers

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Neven’s law says quantum computers are improving at a doubly exponential rate.

Dec 2018 – Google’s best quantum computer chip matched up to a laptop
Jan 2019 – Google’s best quantum computer chip matched up to a powerful desktop
Feb 2019 – Google’s best quantum computer chip was better than any single server and had to match up against Google’s server network. Google’s Hartmut Neven, the director of the Quantum Artificial Intelligence lab had to run jobs comprised of a million processors to match up to his quantum computer chip.

Moore’s law was exponential growth where power doubled every 2 years. You go from

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32

Quantum computers are gaining on classical ones is a result of two exponential factors combined with each other.

1. Quantum computers have an intrinsic exponential advantage over classical ones: If a quantum circuit has four quantum bits, for example, it takes a classical circuit with 16 ordinary bits to achieve equivalent computational power.

2. The best quantum chips have recently been improving at an exponential rate. This is being driven by a reduction in the error rate in the quantum circuits. Reducing the error rate has allowed the engineers to build larger quantum processors.

A double exponential function is a constant raised to the power of an exponential function. The general formula is f(x)=a^{b^{x}}=a^{(b^{x})}}

2^2^1 = 4
2^2^2 = 16
2^2^3 = 64
2^2^4 = 256
2^2^5 = 1028

38 thoughts on “Neven’s Law is for Quantum Computers as Moore’s Law for Regular Computers”

  1. The effect of tech on average peoples lives, transport, electricity, and medicine vs unlimitedly accessible information and contact to anyone in the world, it’s kind of apples and oranges. If it’s the tech itself, maybe, but as far as the effect of tech I wouldn’t compare the two.

  2. Depends on what you define as utility, visual rendering, neural networks, capabilities and adaptability within a closed system, syncing and connectivity, hierarchies and structures of operation, storage, entertainment and information access. All of these things have dramatically increased in the last 20 years, even the last 10 years of smartphones.
    You might think we’re at a point of diminishing returns but even now VR requires fairly modern hardware and people are working on improving GPUs in performance and power efficiency for cryptocurrencies.
    It’s hard to see anything coming up that doesn’t look like incremental change as far as classical computers go, but even those incremental changes are quite significant for the usage of modern software.
    Of course I hope I’m ignorant and that we find significant advancements in all fields

  3. You’ve got your table wrong. 2^2^3 = 2^8 = 256. 2^2^4 = 2^16 = 65536. 2^2^5 = 2 ^32 = 4294967296. Etc. This isn’t normal technological change. If it holds true, we will be in a whole new world very soon.

  5. OK, double exponential may or may not be the right term for quantum computing rate of progress, but double exponential takes the form

    F = a^(b^n) where a and b are typically constants and n varies.

    The above table was calculated as (a^b)^n, which is just exponential.
    A true double exponential would be:

    2^(2^1) = 2^(2) = 4
    2^(2^2) = 2^(4) = 16
    2^(2^3) = 2^(8) = 256
    2^(2^4) = 2^(16) = 65536
    2^(2^5) = 2^(32) = 4294967296

  7. If you really think so, this means that our minds work very
    differently (or that you have never played at GTA5).
    I’d rather see twiddlywinks as an example that analog
    computers can work better than early digital computers
    (you let the physical system do the computations).
    The simpler technologies reach maturity faster, and
    this gives the illusion of slowing progress ( a 1890 fork
    is the same as a 2019 fork, therefore no progress at all)
    but if , say, from 1995 to 1997 same computer cost increased
    from 1 gigaflop to 2 gigaflops, from 2010 to 2012 it increased
    from 1 teraflop to 2, therefore the rate of progress was 1000 times faster. Moreover, in the last 50 years there was an
    enormous accumulation of knowledge and understanding, particularly about biology, that still has to find visible applications. It is like the precision mechanics of 1700 waiting the advent of the steam engine. For me, a race that can
    do GTA5 can accomplish anything (the PS3 version is the best).

  10. You can waste just as much time and get just as much enjoyment out of watching Stone Age cave paintings and
    the Mona Lisa. Dont take offence, but you have no soul.

  11. How so is it better? You can waste just as much time and get just as much enjoyment out of playing pac man vs gta5. All those increases in graphics and processing speed lead to no or very little increase in utility.

  15. That’s because it’s a philosophical position. It isn’t part of science (even if science also is a radically optimistic endeavor in itself), rather, a way to look at things and where progress is going, both without hype or gloominess.

  17. A few technical and scientific areas undergo S-curve growth for a while in some measurable aspect of their function or processes.

    Most other areas of civilization grow at a much more leisurely pace, with linear progression at best.

    Futurism assuming perpetual exponential growth is delusional, assuming no growth is dimwitted.

    Rational optimism lies in seeing what is what, and where it can really take us.

  18. Since your on this site, I am more than sure your both smart enough and educated enough to find the study for yourself. Or better yet if you don’t believe the results, do the study and make a name for yourself by proving him wrong.

  19. Sorry that’s the wrong link. You haven’t linked to a study, just an illustration of what the study’s conclusion means.

  21. This study was done by Ray Kurzweil. If you don’t know who he is look him up on wikipedia. His peer group consisted of Stephen Hawkings, Elon Musk, and a whole lot more great scientists. He did a very hard science study of the acceleration of technology since the time of christ to present. (~ 2000 years) His results were so unbelievable a lot of other scientists, engineers, laymen, etc. wanted to prove the great man wrong. They all came up with same results.
    BTW The way to figure error rate for a future projection of this study. (Projection Years/2000) X 100 = % error rate (20 yrs/ 2000 yrs) X 100 =1%
    That’s not much for 20 years
    Here is the study. Check out forcast for 20 years.
    Remember you are lucky to have seen a ~16X(??) growth rate in your whole life.

    http://theemergingfuture.com/docs/Speed-Technological-Advancement.pdf

  22. I wrote a database program on the 8088, I sold to avon distributors using pascal and zackery. To change the background color after linkinging it it took 2 hrs. to compile. I would go a movie and come home about the time it was done. When the 80386 came around it would compile that background change in about 3 min. I can’t even imagine what it would take on my 16-core, 32-thread 3.4-GHz Threadripper 1950X with 128GB of DDR4 memory

  24. Looking at the effects of tech on the average people’s lives, I think that 1890 to 1955 was a lot more significant than the same time period of 1955 to 2019.

    1890 -1955 went from horse and cart with occasional trips on trains to motor cars and occasional trips on aircraft.
    1955 – 2019 went to… better cars and better aircraft

    1890 -1955 went from wood stoves and kerosine lamps to electric stoves and electric lights
    1955 – 2019 went to… better electric stoves (marginally) and better electric lamps

    1890 -1955 went from science fiction speculation about aircraft to actual space launches (only two years away from orbit) .
    1955 – 2019 went to… better space launches

    1890 -1955 went from leeches to antibiotics
    1955 – 2019 went to… better antibiotics and antivirals

    I’m not seeing an acceleration

  26. I wouldn’t go so far as that; I learned programming in the mid 70’s on a Honeywell mainframe, today I do CAD on a nearly plain vanilla workstation. (How the mighty are fallen, we engineers no longer get bleeding edge computers… I don’t even get to spec out my box, and IT hasn’t a clue.)

    I assure you that no amount of mad programming skilz would have enabled that 70’s mainframe to do what my CAD station does. It didn’t even have enough memory to hold the models this one copes with.

    OTOH, the software back then accomplished a lot more per machine cycle than today’s software, due to the effort put into optimizing it. And I’ve noticed the system actually slowing the last couple of years, because IT is ever less interested in configuring things right.

  27. That’s the thing with computers is a 2x increase in processing power doesn’t lead anywhere close to a 2x increase in utility. Not even a 1000x increase in processing power leads to a 2x increase in utility most of the time. Most of the useful things you can do with a computer today, you could do back in 1960.

  28. The more I follow technology, it’s highly doubtful we’re even on an exponential curve let alone a double exponential. If you look at the 1950’s, there were massive leaps in air travel, rocketry, computers, cars, nuclear energy, etc. You see nothing like that today in any of the other areas besides computers. If you ask me, for the last 30 years or so, progress has been remarkably slow in technologies that actually make everyday life better.

    I do think the 2020’s are setting up to be a decade of remarkable progress in technology like the 1950s were. There will be huge advancements in AI, energy, and travel that make everyday lives better in a tangible way. Still progress will be on a linear curve, not exponential.

  29. Accelerating? I mean the internet is a great library and having it on my phone is very convenient. Drones have remarkable control systems that came out of military applications; sure has improved photography, which has improved by bounds.. Other than that I’m not seeing this huge acceleration. I’m seeing slow adoption of electric cars, which were around in 1903, and the space race picking up where 1969 left off. It’s pretty cool that they cured hepatitis C and beat AIDS into submission with drugs (lord knows they put enough money into the latter). A hip replacement is pretty remarkable but I wouldn’t call it break-neck acceleration. All it means is that they can keep Dick Cheney alive for another 10 years and hit me with 300% more advertising on the phone than by all available sources in 1999.

  30. Mind, in my experience, 99.5% of increases in processing power get consumed by less efficient programs and higher overhead.

  32. Why not just say 2^(n+1) , it seems simpler

    Anyway, what are the modern equivalent of Chip Foundries, when it comes to Quantum Computing?

  33. Moore’s law is that the cost of a transistor decreases by half, about every 12 months.

  34. You cant really compare the ramp rate of Von Neumann and quantum cpus, qcpus are destined for their own cloud and not the mass market like cpus. The industry is looking to ramp quantum computer as fast as possible; that was never the goal for classic chips. Intel et al were designing and selling cpus with the intention of replacing them at regular intervals, with models containing just enough additional power to make them an attractive upgrade. Many of the ramp up way points could have been skipped over during the development lifetime of classic cpus.

  35. You hit the nail on the head, if things keep accelerating like this, the progress we will see in the next several decades, will completely overshadow what we saw in the past.
    I am not sure the exact way that Brian gets the formula but the astonishing math contained therein does capture the break neck acceleration.
    Technology is fueling more technology.

  36. This is the same rate as technology is advancing. Technological growth is astounding. Among the technologys, medical growth is the fastest.
    If you think you have seen a lot of changes in your lifetime you haven’t seen anything yet.

  37. Is this the big future of math?!
    Do the exponent at the top first. Otherwise, place the parenthesis if you want 1024. You can’t spell right. You have your facts wrong. You can’t do math right. Jeez. But I still like the blog.

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