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Comment by elephantum | Hacker News Reader

Do I understand correctly, that largest quantum computer that exists today contains less than 100 qubits?

Also it does not seem that there's an exponential grow in this area: https://www.statista.com/statistics/993634/quantum-computers....

They hit the wall in 2017.

We should be safe for now :)

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Those quantum computers can't execute Shor's algorithm, which is required to attack RSA. AFAIK the best relevant factoring result is still 21=3*7 from 2012.

There are claims of bigger factored numbers, but they exploited special cases (e.g. factors differing by only two bits) and have no hope of being extended to attack cryptography.

https://crypto.stackexchange.com/questions/59795/largest-int...

A 2019 paper manged to factor 21 on a 16 qubit ibmqx5, but failed to go up to 35:

> the algorithm fails to factor N=35. This is due to the cumulative errors coming from the increasing number of two-qubits gates necessary to implement the more complex MEF needed for this case

https://arxiv.org/abs/1903.00768

Jennifer and Peter Shor wrote a limerick that seems relevant:

   If computers that you build are quantum,
   Then spies of all factions will want 'em.
   Our codes will all fail,
   And they'll read our email,
   Till we've crypto that's quantum, and daunt 'em.

And Volker Strassen responded at a conference:

   To read our E-mail, how mean
   of the spies and their quantum machine;
   Be comforted though,
   they do not yet know
   how to factorize twelve or fifteen.

Source: http://www-math.mit.edu/~shor/notapoet.html

> Till we've crypto that's quantum, and daunt 'em.

Luckily there are asymmetric algorithms which are are secure against quantum computers, so we don't have to resort to quantum-key-exchanges.

"Secure against quantum" doesn't really mean much because too little is known to make that claim confidently. AFAIK the term generally refers to algorithms that don't rely on factoring being hard, but instead make some different hardness assumptions that we currently don't have classical or quantum algorithms for.

For practically all computationally secure crypto we use "secure" for "no known attacks faster than we'd like". QCs just extend the set of efficient algorithms.

Indeed, but there is a much longer history of people trying and failing to break the schemes, and we have come to understand the hardness assumptions in classical crypto as probably quite reasonable.

>There are claims of bigger factored numbers, but they exploited special cases

Also, my understanding is that almost all of these factorizations utilize a "compiled" version of Shor's algorithm. Meaning that you need to know the factors in advance. So it's essentially "confirming" rather than "finding" the factors.

AFAIK factoring 21 is "compiled" Shor, so even that result simplifies the problem a bit.

According the first link in my post, the numbers bigger than 21 were chosen to have specific mathematical properties and attacked with algorithms even less realistic that compiled Shor.

IBM has 1000 qubits on their roadmap by 2023 [1]. I'm interested to see how that goes, and what we can learn from it about scaling up these systems into the thousands of qubits.

Edit: for anyone interested in learning more about quantum computation, I have a list of resources on my website [2].

[1] https://www.ibm.com/blogs/research/2020/09/ibm-quantum-roadm...

[2] https://cameronperot.com/resources/#quantum-physics

Since I didn't see it mentioned, I assume those are 1000 noisy qubits, so they'll require error correction. I wonder how many ideal qubits they are equivalent to.

>largest quantum computer that exists today contains less than 100 qubits

The numbers reported in the press are physical qubits not logical qubits. You need multiple physical qubits + error correction to create a single logical qubit. The main type of error correction used today is something called "surface codes". With this type of error correction it's estimated that MILLIONS of physical qubits will be required to create a SINGLE fully error corrected logical qubit.

https://www.ncbi.nlm.nih.gov/books/NBK538709/

We do not have actual quantum computers today and we don't seem to be much closer to having them than we were a decade ago. What we have are really interesting quantum science experiments that get misrepresented by the press (and a handful of companies with a commercial interest in doing so).

The largest production quantum computer that exists today - as in, the largest you personally can get access to - has 5,436 qubits: the D-Wave Advantage system.

Admittedly, it's not a gate-model machine that can run Shor's Algorithm, but it is a quantum computer, and at more than double the number of qubits plus far higher inter-qubit connectivity than our previous D-Wave 2000Q, it definitely demonstrates tremendous progress.

If you have a moment, you can sign up to use it for free at https://cloud.dwavesys.com - we have an online IDE, Jupyter notebook training material and tons of docs, a community forum, and of course some shiny demos that submit problems to the live QPU if you want to try them out.

And the error rate of 10^-3 seems problematic, as well.

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