Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer · HackerPapers discussions

Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer — mentioned by Strilanc

Tue, 03 Jan 2023 20:54:16 GMT

I want to contrast this paper with Shor's factoring paper [1]. One of the things that stands out to me about Shor's paper is how meticulous he is. He is considering the various ways the algorithm might fail, and proving it doesn't fail in that way. For example, the algorithm starts by picking a random seed and you can show that some choices of seed simply don't work. He proves a lower bound on how many have to work. Also, given a working seed, sometimes the quantum sampling process can correctly return a useless result. He bounds how often that can occur as well. He never says "I think this…

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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer — mentioned by kirrent

Thu, 08 Feb 2018 22:21:48 GMT

Shor's original paper discusses the fundamental need for several runs and gives the time complexity. https://arxiv.org/pdf/quant-ph/9508027.pdf The paper you linked to is just saying that the need for several runs and 2006 readout error rates together led to awful scaling (though still better than classical factorisation). That isn't surprising. Error rates in all parts of even modern quantum computers are still too high to scale well. Especially when repetition is called for. Ultimately, complexity is calculated using logical qbits. Kalai doesn't think that even with error correction codes…

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Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer — mentioned by Cieplak

Thu, 25 Aug 2016 04:49:04 GMT

@tptacek > I believe you to be wrong about the idea that tenably factoring 1024 or 2048 bit moduli implies a solution to the elliptic curve discrete modulus problem Probably. This mathy stuff is way over my head. I'm just repeating what I read in Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer [1] published by Peter W. Shor on behalf of AT&T Research in 1995. Supposedly his proof is valid, predicated on the existence of quantum computers. Quantum computers actually exist [insert epistemological joke here]. [1]…

Paper and discussion history. A mention is not an endorsement.