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Moore's law has had a pretty impressive run. For more than 40 years, Gordon Moore's prediction that the density of components in integrated circuits would double roughly every two years has held true. The result is that the microchips that run our digital world are 2-to-the-20th power, or several million times more powerful than anything that was available back then.
(In the late '60s, I wrote programs for the CDC 6600, then the most powerful supercomputer in the world. It churned out 3 million operations per second. The processor in a current iPhone performs more than 3 billion operations per second, and today's fastest supercomputer 122 quadrillion.)
By way of putting this exponential growth of computing power into perspective, imagine if you were a million times richer or a million times smarter than you were a few decades ago, and could expect to keep doubling your wealth or your smarts every two years. Not too shabby.
But that's all so yesterday. Now, as the era of quantum computing surges into view, there's a new sheriff in town--Hartmut Neven--bringing us Neven's law.
Earlier this year, Neven, an economist, physicist and current head of Google's Quantum Artificial Intelligence lab, made the stunning observation that the power of quantum computers is growing not at an exponential rate, but at a doubly exponential rate. Rather than, for example, doubling ever two years, their power is doubling at a rate that itself doubles every two years.
That may not sound like a big difference. But to get a sense of what it means, check out the following table:
Step (n) Exponential Growth Doubly Exponential Growth
(2 to the n'th power) (2 to the 2 to the n'th power)
1 2 4
2 4 16
3 8 256
4 16 65,536
5 32 4,294,967,296
6 64 1.8 x 10^19 = 1,800,000,000,000,000,000
If Neven is right, the amount of progress that classical computing made over the last 40 years will be compressed into the next six years of quantum computing development. Or, as he describes it, "It looks like nothing is happening, nothing is happening, and then whoops, suddenly you're in a different world."
The tipping point that will notify us that we're in that different world will be quantum supremacy--the point at which a quantum computer can out-perform the most powerful classical computer. Since quantum computers are still in their infancy, you might think that will take a long time. Not so. Based on the explosive rate of progress in his lab and those of his competiors, Nevens thinks that will happen this year.**And, if progress in quantum computing does follow a doubly exponential curve as Nevens predicts, quantum computers will not just gradually outstrip classical computers; they will almost immediately leave them in the dust.
And it may not only be classical computers that are left wondering what just happened. As those of you who have been following developments in artificial intelligence (AI) know, some very smart people have been warning us about the risks of runaway AI--the emergence of a superhuman artificial intelligence (AGI) that could quickly build an even more intelligent system that could build a still more intelligent system etc. The result could be the emergence of an immensely powerful machine-or internet-based intelligence that might well not have our interests at heart.
Those dire warnings didn't take into account quantum AI which, as you recall, is the raisin d'etre of Neven's lab. If the exponential growth of AI based in classical computers presents us with a looming existential threat, what about the doubly exponential growth of quantum AI?
Remember that sequence: 4, 16, 256, 65536, 4294967296 . . .
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*To help keep track of the pace of progress in quantum computing, here's a milestone as of September, 2019, IBM's soon-to-be-available 53-qubit quantum computer:
https://techcrunch.com/2019/09/18/ibm-will-soon-launch-a-53-qubit-quantum-computer/
**And just to emphasize the rate of change Neven predicted, in mid-September, 2019, well before the end of the year, his lab has published a paper demonstrating quantum supremacy. A 54-qubit quantum computer in their lab took just 200 seconds to solve a problem that would take a supercomputer 10,000 years to do. You can read about it here.
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Robert Adler
(In the late '60s, I wrote programs for the CDC 6600, then the most powerful supercomputer in the world. It churned out 3 million operations per second. The processor in a current iPhone performs more than 3 billion operations per second, and today's fastest supercomputer 122 quadrillion.)
By way of putting this exponential growth of computing power into perspective, imagine if you were a million times richer or a million times smarter than you were a few decades ago, and could expect to keep doubling your wealth or your smarts every two years. Not too shabby.
IBM Q Quantum Computer*
Credit: Lars Plougmann
But that's all so yesterday. Now, as the era of quantum computing surges into view, there's a new sheriff in town--Hartmut Neven--bringing us Neven's law.
Earlier this year, Neven, an economist, physicist and current head of Google's Quantum Artificial Intelligence lab, made the stunning observation that the power of quantum computers is growing not at an exponential rate, but at a doubly exponential rate. Rather than, for example, doubling ever two years, their power is doubling at a rate that itself doubles every two years.
That may not sound like a big difference. But to get a sense of what it means, check out the following table:
Step (n) Exponential Growth Doubly Exponential Growth
(2 to the n'th power) (2 to the 2 to the n'th power)
1 2 4
2 4 16
3 8 256
4 16 65,536
5 32 4,294,967,296
6 64 1.8 x 10^19 = 1,800,000,000,000,000,000
If Neven is right, the amount of progress that classical computing made over the last 40 years will be compressed into the next six years of quantum computing development. Or, as he describes it, "It looks like nothing is happening, nothing is happening, and then whoops, suddenly you're in a different world."
The tipping point that will notify us that we're in that different world will be quantum supremacy--the point at which a quantum computer can out-perform the most powerful classical computer. Since quantum computers are still in their infancy, you might think that will take a long time. Not so. Based on the explosive rate of progress in his lab and those of his competiors, Nevens thinks that will happen this year.**And, if progress in quantum computing does follow a doubly exponential curve as Nevens predicts, quantum computers will not just gradually outstrip classical computers; they will almost immediately leave them in the dust.
And it may not only be classical computers that are left wondering what just happened. As those of you who have been following developments in artificial intelligence (AI) know, some very smart people have been warning us about the risks of runaway AI--the emergence of a superhuman artificial intelligence (AGI) that could quickly build an even more intelligent system that could build a still more intelligent system etc. The result could be the emergence of an immensely powerful machine-or internet-based intelligence that might well not have our interests at heart.
Those dire warnings didn't take into account quantum AI which, as you recall, is the raisin d'etre of Neven's lab. If the exponential growth of AI based in classical computers presents us with a looming existential threat, what about the doubly exponential growth of quantum AI?
Remember that sequence: 4, 16, 256, 65536, 4294967296 . . .
-----
*To help keep track of the pace of progress in quantum computing, here's a milestone as of September, 2019, IBM's soon-to-be-available 53-qubit quantum computer:
https://techcrunch.com/2019/09/18/ibm-will-soon-launch-a-53-qubit-quantum-computer/
**And just to emphasize the rate of change Neven predicted, in mid-September, 2019, well before the end of the year, his lab has published a paper demonstrating quantum supremacy. A 54-qubit quantum computer in their lab took just 200 seconds to solve a problem that would take a supercomputer 10,000 years to do. You can read about it here.
-----
Robert Adler
