Circuit for Shor's algorithm using 2n+3 qubits · HackerPapers discussions

Circuit for Shor's algorithm using 2n+3 qubits — mentioned by ryao

Tue, 22 Apr 2025 17:06:09 GMT

> Is there some minimum number of qubits at which some minimum viable quantum-supreme task can theoretically be achieved? That is a very broad range of possibilities, so allow me to narrow it to cryptography. I am by no means an expert on this, but I spent the weekend reading about quantum motivations to change the cryptographic algorithms society uses and as at as I can tell, nobody knows what the hard lower bound is for breaking hardness assumptions in classical cryptography. The best guess is that it is many orders of magnitude higher than what current machines can do. We are so far from…

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Circuit for Shor's algorithm using 2n+3 qubits — mentioned by smburdick

Mon, 11 Mar 2024 23:25:12 GMT

From [1]: > We implemented the algorithm on IBM quantum processors using only 5 qubits Last December, a team based out of Harvard demonstrated the ability to scale up to 48 logical qubits: https://arxiv.org/abs/2312.03982 It has been shown that, to factor an integer with n bits, Shor's algorithm requires ~2n logical qubits: https://arxiv.org/pdf/quant-ph/0205095.pdf

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Circuit for Shor's algorithm using 2n+3 qubits — mentioned by FartyMcFarter

Sun, 31 Jul 2022 13:57:36 GMT

> and how many are needed According to this paper, one can use 2n+3 qubits to factor an integer with n bits: https://arxiv.org/abs/quant-ph/0205095 Those would be perfect qubits, if you use noisy qubits you'd need many more (maybe a factor of 1000x more), since quantum error correction imposes a lot of overhead.

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Circuit for Shor's algorithm using 2n+3 qubits — mentioned by archgoon

Thu, 14 Dec 2017 08:29:37 GMT

According to this paper: https://arxiv.org/abs/quant-ph/0205095 You can implement Shor's algorithm to factor an N-bit number with just 2n+3 qubits. So the 20 qubit processor would be able to factor any 8 bit number (not necessarily faster than a classical computer could, or even a human could, mind you).

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