101–110 of 127 posts
Earlier quoted context omitted.
And to extend off this comment, there are methods being worked on for building qubits that are intrinsically noise-free and don’t need the exponential number of error correcting operations. When those are available, you’ll see a step function increase in capabilities.
For a circuit of size C, the size of a fault tolerant circuit to compute the same thing is O(C polylog C) https://arxiv.org/abs/quant-ph/9906129
Earlier quoted context omitted.
Interesting - why is Shor's sensitive to noise? Is that the Rphase gates?
Yeah, for Shor's algorithm to factor an integer of order 2^k you need controlled phase gates with phases roughly order 2^{-k} (very roughly, with some caveats, but lets just say you need some small ones) these very small phase gates are susceptible to even very small errors. This is a gross oversimplification. For the true version see here https://arxiv.org/abs/2306.10072
Earlier quoted context omitted.
Interesting - why is Shor's sensitive to noise? Is that the Rphase gates?
Yeah, for Shor's algorithm to factor an integer of order 2^k you need controlled phase gates with phases roughly order 2^{-k} (very roughly, with some caveats, but lets just say you need some small ones) these very small phase gates are susceptible to even very small errors. This is a gross oversimplification. For the true version see here https://arxiv.org/abs/2306.10072
Earlier quoted context omitted.
The record for integer factoring on quantum computers was on the order of factoring fifteen into three times five the last time I checked. Can we do three digits now?
Significantly larger numbers than 15 have been factored [1] but not using Shor's algorithm. Shor's algorithm is particularly sensitive to noise/errors in your quantum computer and isn't going to be useful unless we get a properly error corrected machine working. The algorithms used in [1] are considerably less fancy (with worse asymptomatic performance) but are more resilient to noise. [1] https://arxiv.org/abs/2012.…
Earlier quoted context omitted.
biggest number factored by a quantum computer isn't the right question. the right question is biggest number factored using a polynomial time algorithm. the answer to that as far as I know of still 15 (although I would be interested in papers that show more progress)
Application of Shor's algorithm is currently limited by available error correction. Long-lived qubits would eliminate that need and drastically increase capabilities.
Earlier quoted context omitted.
Code based systems are still in, and classic McEliece could be extended to ~50 MiB for a keypair and still be way more practical than QKD. Just run the max current classic McEliece spec hybrid post quantum with X448.
NSA is that you?
OP recommended McElice, not DUAL_EC_DRDBG. Is there something I should know about the former?
Earlier quoted context omitted.
Significantly larger numbers than 15 have been factored [1] but not using Shor's algorithm. Shor's algorithm is particularly sensitive to noise/errors in your quantum computer and isn't going to be useful unless we get a properly error corrected machine working. The algorithms used in [1] are considerably less fancy (with worse asymptomatic performance) but are more resilient to noise. [1] https://arxiv.org/abs/2012.…
I couldn't quickly find any info, but does this algorithm show the kind of exponential quantum speed up needed to break RSA? Because if it's just slightly faster than the best known classical algorithms, then it's enitely irrelevant to the question of when we need to switch our encryption schemes (even though it may be a significant advancement in the area of quantum algorithms research).
These sort of variational algorithms are appealing (to some people) because they're potentially usable on the sort of noisy small quantum computers we have today and in the near term future, but they aren't very fancy. I think in general what you'd expect to get out of them is a sort of Grover's algorithm-like square root speedup.
Earlier quoted context omitted.
Interesting - why is Shor's sensitive to noise? Is that the Rphase gates?
Yeah, for Shor's algorithm to factor an integer of order 2^k you need controlled phase gates with phases roughly order 2^{-k} (very roughly, with some caveats, but lets just say you need some small ones) these very small phase gates are susceptible to even very small errors. This is a gross oversimplification. For the true version see here https://arxiv.org/abs/2306.10072
Earlier quoted context omitted.
biggest number factored by a quantum computer isn't the right question. the right question is biggest number factored using a polynomial time algorithm. the answer to that as far as I know of still 15 (although I would be interested in papers that show more progress)
Application of Shor's algorithm is currently limited by available error correction. Long-lived qubits would eliminate that need and drastically increase capabilities.
Earlier quoted context omitted.
Yeah, for Shor's algorithm to factor an integer of order 2^k you need controlled phase gates with phases roughly order 2^{-k} (very roughly, with some caveats, but lets just say you need some small ones) these very small phase gates are susceptible to even very small errors. This is a gross oversimplification. For the true version see here https://arxiv.org/abs/2306.10072
This is a minority point of view on quantum computing, as I understand.
Now, I got to the bottom of page 6 and my maths failed me: I can't follow the expansion, but I expect that the reviewers of Physica A or where ever the gentleman who wrote this sends it off to will be able to check. I do follow the principle of the proof though and it's pretty intuitive to me, for what that's worth.
Anyway, I can't say I give a hoot what the majority or minority think - and nor should anyone else. Read the paper for yourself and make up your mind.
* The author thanks Al Aho, Dan Boneh, P ́eter Ga ́cs, Zvi Galil, Fred Green, Steve Homer, Leonid Levin, Dick Lipton, Ashwin Maran, Albert Meyer, Ken Regan, Ron Rivest, Peter Shor, Mike Sipser, Les Valiant, and Ben Young for insightful comments. He also thanks Eric Bach for inspiring discus- sions on some of the number theoretic estimates, and we hope to report some further improvements soon [7]. A similar result can be proved for Shor’s algorithm computing Discrete Logarithm, and will be reported later.