Superconducting quantum chips and ion trapped quantum computers are in the 16 qubit to 100 qubit range. Rigetti Computing is seeking an application that will give it a practical advantage over conventional computers. Other companies are pushing other metrics to gauge progress.
Google has said they are at 72 qubits but there are reports that that announcement in March 2018 was premature. There is only 20 qubit quantum computers that can be accessed via cloud computer interfaces.
Neven has said that Google’s quantum systems could become faster than any classical computers by the end of 2019. This suggests that quantum supremacy should occur with noisy superconducting qubits with 70-200 qubits.
Noisy qubits should not need error correction up to 500 to 10000 qubits. The higher qubit ranges can be reached with lower error rates going from one in a hundred to one in ten thousand.
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
Google’s Neven’s Law says there is a double exponential improvement in quantum systems. n equals each new improvement to Google’s quantum processor. Google is exponentially increasing the power of its processors on a monthly to semi-monthly basis. However, there has been no announcement or confirmation that the 72 qubit chip or follow on chip works since march 2018.
n 2n 2(2n) Quantum Computing Power Relative to Classical Computing Power * 1 2 22 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
5 steps of improvement is a billion times more powerful
6 steps is a billion times a billion times
Between steps 7 and 8 is a universe of atoms of classical computing.
IBM has talked about quantum volume which also considers how many steps of quantum computation a system can perform.
Making tweeks to the current quantum systems can make giant improvements to their utility.
Google does not have its full 72 qubit system working.
Any of the competing quantum systems that fully uses 100-200 qubits will have quantum supremacy for some applications.
Getting to a fully useful 200-400 qubits should have overall quantum supremacy.
Getting to fully useful 400-800 qubits should make quantum systems vastly better than current systems for any application where they can be used.