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It would be nice if all these new quantum computer announcements came with a measure of power that many people are more interested in than raw qubit quantity:

How big a number can it factor reliably using Shor's algorithm?

According to [1], that record still stands at only 21. All larger numbers you've heard of being factored suffered from one or more of:

1) factoring numbers of a special form (n+i)*(n-i) for very small i

2) using an algorithm with prior knowledge of the predetermined factors

3) using adiabatic computing/quantum annealing rather than Shor's algorithm

Shor's algorithm (or its adaptation to elliptic curve discrete log) is the only one threatening widely used cryptographic primitives, once we have a few thousand logical qubits to work with, which due to the necessary quantum error correction translates to millions of raw qubits.

> An Eagle quantum computer can deal with system models in 2127 states simultaneously.

Obvious typo in there; they mean 2^{127} states.

[1] https://en.wikipedia.org/wiki/Integer_factorization_records#...

I guess you already know that if those announcements don't include an earth shattering factorization record it's because they probably didn't achieve anything worth noting.
I keep wondering when one of these machines will finally be able to do some tangible, practical work, like taking some input and producing correct output, and do it faster than a traditional computer by atleast one order of magnitude.

Right now it's just quantum-schmantum.

Everything I've read so far about Quantum Computers indicates that it's going to be a while before we see any real business applications for it. I wonder where they are going to slot into the business workflow, what their role will be and what they will replace.

My bet is they will likely replace existing mainframes and become the "Mainframe 2.0". The other thing I see these machines replacing is HPC clusters, maybe. Right now it's really hard to say, I've heard one of the biggest issues with QC's is the fact that they have to run a very specific workflow to be efficient. I wonder what business workflows in 20-30 years will benefit from QC workflows.

Since qubits are so dear, and quantum operations so fraught, we have to perform operations on their contents and write the results into other qubits, like an ALU operating on a register bank.

A tricky thing is that every operation has to preserve all the input information, and be at least in principle reversible, so there is no such thing as fan-in, and deliberate fan-out is ruinously expensive.

My question about quantum computers is: is anybody using Bose-Einstein condensates as qubits? It is my impression that they are more resistant to decoherence than your usual quantum state, which seems useful. Or, is it so hard to make one that making thousands is not practical?

Bosonic qubits are stable but that also means they don't interact very much with each other making it harder to create complex entangled states of them. Also, you can do irreversible operations by adding on some ancillary qubits that you entangled and measure and uncompute.
Quantinuum is generating truly random encryption keys using QC systems. The correlated noise in some QC systems is low-enough to guarantee truly random key generation... so a useful application to enhance high-value computer/information security.
I'm amazed they've been able to make a business out of this. At D-Wave, we have been able to generate truly random numbers for aeons; we use them for calibration, but they don't have any real business value presently. Truly random RNGs have been commercially available for ages, and if you need such a high level of randomness, you're probably sensitive enough that you don't want to accept them from some 3rd party over the internet.

If you want some quantum-generated random numbers, sign up for D-Wave Leap and you can trivially generate your own for free... or perhaps, run an optimization algorithm to do something a little more useful.

True and China is a forerunner:

https://www.scientificamerican.com/article/china-reaches-new...

Is this really that much of a problem? Like, even if you only get 1 random bit out of 100, you just sample and hash 100 times as many samples. What can you do with quantum noise that you can’t do with thermal noise?
Perhaps this one will be able to reliably factor 35!
That would be rather impressive!

35! is quite large!

Sold for parts 2 years later when it doesn’t work