Moore’s Law Is Replaced by Neven's Law for Quantum Computing

By Hubert Yoshida posted 06-25-2019 00:00



Moore’s Law

In 1965, Gordon Moore, the CEO of Intel, published a paper which described a doubling in every year in the number of components per integrated circuit and projected this rate of growth would continue for at least another decade. In 1975 Moore revised his prediction to predict that the number of transistors in a dense integrated circuit would double every two years over the next decade. While this remained true for many decades and created an amazing increase in compute power which fueled tremendous revolutions in technology, Moore’s law has been dead for several years since we have reached the limits of how small we can make integrated circuits which are now down to the size of atoms, where transistors begin to fail and leak their electrons into other component.

Kryder’s Law

In storage we had a similar law, known as Kryder’s law. Mark Kryder, from Seagate, assumed that disk drive density, also known as areal density, would double every thirteen months. Over a 41 year period, areal densities increased by 50 million times. However, by 2015 Kryder’s law was no longer valid.

Neven’s Law

However, the growth in the power of compute is about to explode beyond our (at least my) wildest dreams. Moore’s Law is being replaced by Neven’s Law. Neven’s law is named after Hartmut Neven, the director of Google's Quantum Artificial Intelligence Lab. Hartmut has stated that the growth in power with each new improvement to Google's best quantum processor is growing at not just an exponential rate, like in Moore's Law, but at a doubly-exponential rate. 

He basis this prediction on the fact that qubits that are used in quantum computing do the same work or hold the same amount of data as 2classical bits. 2 qubits equals 4 bits4 qubits equals 16 bits16 qubits equals 65, 536 bits, and so on. In addition, he is seeing an exponential rate of improvement in Googles best quantum processors.   

What Does Doubly Exponential Growth Actually Mean? 

According to an online article by, a doubling -exponential rate would mean replacing the in the doubling function with another doubling function, or 22n.

Since Moore's Law is a doubling function, we can represent Moore's Law like this, where n represents a two year interval:

   n     Classical computing power (2n) 
* 1      2

* 2     4
* 3     8
* 4     16
* 5     32 
* 6     64
* 7     128
* 8     256
* 9     512
* 10   1024

Neven's Law with double exponential growth would look something like this, where n equals each new improvement to Google's quantum processor:

        n      2n       2(2n)         Quantum Computing Power Relative to Classical Computing Power

     * 1       2         2           4
     * 2      4         24            16
     * 3      8         28            256
     * 4      16       216           65,536
     * 5      32       232          4,294,967,296
     * 6      64       264          18,446,744,073,709,551,616
     * 7      128      2128         3.4028236692093846346337460743177e+38
     * 8      256     2256         1.1579208923731619542357098500869e+77
     * 9      512      2512         1.3407807929942597099574024998206e+154
     * 10    1024    21024       1.797693134862315907729305190789e+308

After the list goes above 6, the numbers start becoming so large and abstracted you lose the sense of the gulf between where Google is and where it will be at the next step.”

What does all this power mean?

It means that we will be able to solve computational problems which were never before possible with conventional computers. While quantum computers will not be able to solve transactional problems as fast as conventional computers, it can solve compute intensive problems like encryption and optimization in seconds where a classical computer would take the entire life of the Universe just to attempt to solve it.

“For example modern computers may be able to use raw processing power to crack earlier 256-bit, 512-bit, and even higher bit-count encryption keys, but all one would need to do is multiply the bit-count used for your key by two and your new scheme is literally exponentially stronger than the one that just got cracked. A classical computer doesn't get exponentially better at solving these problems as the numbers involved increase. This limitation, known as time complexity, eventually put some things beyond a classical computers capacity to ever really solve. Lengthening RSA encryption-keys can very quickly begin to add millions, billions, and even trillions of years to the time needed to crack the encryption key using a classical computer.”

How long will it be to see Quantum Computers in Production?

While many experts in the quantum computing field believe that we wouldn't see a quantum computer until 2025 or even as late as 2030, Neven’s Law would lead us to believe that Google would establish quantum computing by the end of this year. I believe that in the next few years we will see solutions coming from quantum or quantum-like computers. What is lacking today are higher level languages to map problems to qubits. This is like the early days of classical computers where everything was done in machine language by developers and researchers.  

Powering Good

Quantum Computers will be especially helpful to solve social innovation problems which require computational optimization. Many social innovation challenges require a large host of inputs to recommend the optimum distribution route or medical treatment for example. There is also the dark side where encryption codes can be easily cracked, and researchers are working on ways to preserve the privacy of data in the age of quantum computing.  

I blogged about Hitachi’s progress with quantum computers in Social Innovation Drives Computing Innovations for Powering Good.


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