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

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