Ciro Santilli @cirosantilli 37

The term "IBM Q" has been used in some promotional material as of 2020, e.g.: www.ibm.com/mysupport/s/topic/0TO50000000227pGAA/ibm-q-quantum-computing?language=en_US though the fuller form "IBM Quantum Computing" is somewhat more widely used.

They also internally named an division as "IBM Q": sg.news.yahoo.com/ibm-thinks-ready-turn-quantum-050100574.html

Psalm 46:10 from the bible:

Their main innovation seems to be their 3D design which they call "Coaxmon".

Funding:

One key insight, is that the matrix of a non-trivial quantum circuit is going to be huge, and won't fit into any amount classical memory that can be present in this universe.

This is because the matrix is exponential in the number qubits, and $2^{100}$ is more than the number of atoms in the universe!

Therefore, off the bat we know that we cannot possibly describe those matrices in an explicit form, but rather must use some kind of shorthand.

But it gets worse.

Even if we had enough memory, the act of explicitly computing the matrix is not generally possible.

This is because knowing the matrix, basically means knowing the probability result for all possible $2^N$ outputs for each of the $2^N$ possible inputs.

But if we had those probabilities, our algorithmic problem would already be solved in the first place! We would "just" go over each of those output probabilities (OK, there are $2^N$ of those, which is also an insurmountable problem in itself), and the largest probability would be the answer.

So if we could calculate those probabilities on a classical machine, we would also be able to simulate the quantum computer on the classical machine, and quantum computing would not be able to give exponential speedups, which we know it does.

To see this, consider that for a given input, say 000 on a 3 qubit machine, the corresponding 8-sized quantum state looks like:and therefore when you multiply it by the unitary matrix of the quantum circuit, what you get is the first column of the unitary matrix of the quantum circuit. And 001, gives the second column and so on.

As a result, to prove that a quantum algorithm is correct, we need to be a bit smarter than "just calculate the full matrix".

Which is why you should now go and read: Section "Quantum algorithm".

This type of thinking links back to how physical experiments relate to quantum computing: a quantum computer realizes a physical experiment to which we cannot calculate the probabilities of outcomes without exponential time.

So for example in the case of a photonic quantum computer, you are not able to calculate from theory the probability that photons will show up on certain wires or not.

Start by looking at: Maxwell-Boltzmann vs Bose-Einstein vs Fermi-Dirac statistics.

In the context of quantum computing of the 2020's, a "classical computer" is a computer that is not "quantum", i.e., the then dominating CMOS computers.

After learning this term, Ciro Santilli finally understood that his actual major was MR, and not bullshit like applied mathematics or control theory.

Stopped 2019 apparently. Shame. We need something to be upstreamed!

It is hard to beat the list present at Quantum computing report: quantumcomputingreport.com/players/.

The much less-complete Wikipedia page is also of interest: en.wikipedia.org/wiki/List_of_companies_involved_in_quantum_computing_or_communication It has the merit of having a few extra columns compared to Quantum computing report.

Also of interest: quantumzeitgeist.com/interactive-map-of-quantum-computing-companies-from-around-the-globe/

They put a lot of expensive equipment together, much of it made by other companies, and they make the entire chip for companies ordering them.