I Will quantum computers be able to factor larger numbers in the future?

[Fooality]

Quantum computers are in use now.

 

[A. Neumaier]

quantum computers are in use now.

Please give a reference for quantum computers in actual use that tells what they can actually do.

 

[Fooality]

Wikipedia is all one needs for that:
https://en.wikipedia.org/wiki/D-Wave_Systems

On May 11, 2011, D-Wave Systems announced D-Wave One, described as "the world's first commercially available quantum computer", operating on a 128-qubit chipset[4] using quantum annealing (a general method for finding the global minimum of a function by a process using quantum fluctuations)[5][6][7][8] to solve optimization problems. In May 2013, a collaboration between NASA,Google and the Universities Space Research Association (USRA) launched a Quantum Artificial Intelligence Lab based on the D-Wave Two 512-qubit quantum computer that would be used for research into machine learning, among other fields of study.[9]

These things have been declassified, and commercially available, for 5 years. Looking at the history of declassification and secrecy, its reasonable to assume people have been playing with them behind the scenes for 25 years.

 

[Nugatory]

The "talk" pages of many wikipedia articles are more interesting than the article itself. Just sayin'...

 

[A. Neumaier]

D-Wave Systems

don't improve upon classical computing equipment:
http://https://arxiv.org/abs/1401.7087
They perform a quantum version of simulated annealing, with comparable results. Calling this quantum computing is misleading - the system is not programmable and therefore has much less power than a Turing machine, let alone a modern classical computer. It cannot even sort a list of 1000 entries.

 

[Demystifier]

Is 15 still the biggest number that has been factorized by a quantum computer?

 

[Demystifier]

commercially available quantum computer"

One should not be misled by the word "commercial". It means that you can buy it if you want, but it doesn't mean that it is used for practical purposes such as business, banking, security, intelligence or military. It's only use at the moment is for academic studies of quantum computers as such.

 

[Strilanc]

The first big milestone to watch for is so-called "quantum supremacy", where a quantum computer can do some well-defined computational task (no matter how esoteric) that would be too expensive to do on the world's fastest super computers.

Is 15 still the biggest number that has been factorized by a quantum computer?

Sort of? The amount of cheating by making optimizations based on knowing the answer already has decreased over time, so a "15" today means something different than a "15" ten years ago.

as far as I can tell, the new work is a genuine milestone in experimental QC, because it dispenses with most of the precompilation tricks that previous demonstrations of Shor’s algorithm used.

I've heard that factoring numbers is a difficult error-sensitive task for a quantum computer, compared to other problems they're expected to be good at. So I expect we'll be simulating chemistry, or whatever, way before we're factoring 10-digit numbers.