Shor's Algorithm Does Not Factor Large Integers in the Presence of Noise · HackerPapers discussions

Shor's Algorithm Does Not Factor Large Integers in the Presence of Noise — mentioned by gsf_emergency_2

Tue, 15 Jul 2025 10:37:26 GMT

Lemonnier only cites pp22 A first approach to programming with quantum effects is the quantum λ-calculus [SV09]. Nevertheless, that language does not handle quantum programming as an algebraic effect, since it requires measurement into classical data to control the flow of execution. pp23 1st para has more of the same In the quantum λ-calculus, a qubit has to be measured before influencing the control of a program. These models are not of interest to this thesis, because the use of measurement breaks superposition, therefore it does not preserve the aforementioned quantum effect. [SV09] Peter…

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Shor's Algorithm Does Not Factor Large Integers in the Presence of Noise — mentioned by sgt101

Wed, 11 Dec 2024 17:48:56 GMT

There's a specific view (as I understand it) that QFT's don't scale https://arxiv.org/abs/2306.10072 but some folks seem to dismiss this for reasons I just don't grok at all.

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Shor's Algorithm Does Not Factor Large Integers in the Presence of Noise — mentioned by JanisErdmanis

Tue, 28 May 2024 20:40:23 GMT

I have forgotten the source where I stumbled on the requirement for a qubit error rate to run the Shor algorithm. I would greatly value it if someone could put a key reference here. A recent result considers a generic error model and a subclass for particular kinds of prime numbers [1]. The important result is $epsilon > cn^{−1/3}$ where epsilon represents qubit error rate and n number of bits in the factorised number. As $n = 2^N$ where N is a number of qubits, the result: error_rate < const/2^{N/3} Therefore, the error rate must decrease exponentially with the number of logical qubits with…

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Shor's Algorithm Does Not Factor Large Integers in the Presence of Noise — mentioned by sgt101

Sun, 14 Apr 2024 11:17:08 GMT

I'm not sure that you are correct. I've tried to read https://arxiv.org/abs/2306.10072 in the last day and if my reading is right (I am very stretched by this stuff so I am very happy to be corrected) then no amount of error correction will rescue Shor's - only zero error phase gates. I suspect that a similar story is true for native QML, as quantum memory scales it's just going to get exponentially harder to maintain it.

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Shor's Algorithm Does Not Factor Large Integers in the Presence of Noise — mentioned by eigenket

Sat, 13 Apr 2024 16:17:46 GMT

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

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