Shor's Algorithm Does Not Factor Large Integers in the Presence of Noise
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916244632895488 |
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| author | Cai, Jin-Yi |
| author_facet | Cai, Jin-Yi |
| contents | We consider Shor's quantum factoring algorithm in the setting of noisy quantum gates. Under a generic model of random noise for (controlled) rotation gates, we prove that the algorithm does not factor integers of the form $pq$ when the noise exceeds a vanishingly small level in terms of $n$ -- the number of bits of the integer to be factored, where $p$ and $q$ are from a well-defined set of primes of positive density. We further prove that with probability $1 - o(1)$ over random prime pairs $(p,q)$, Shor's factoring algorithm does not factor numbers of the form $pq$, with the same level of random noise present. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10072 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shor's Algorithm Does Not Factor Large Integers in the Presence of Noise Cai, Jin-Yi Quantum Physics Discrete Mathematics F.2.0; E.3 We consider Shor's quantum factoring algorithm in the setting of noisy quantum gates. Under a generic model of random noise for (controlled) rotation gates, we prove that the algorithm does not factor integers of the form $pq$ when the noise exceeds a vanishingly small level in terms of $n$ -- the number of bits of the integer to be factored, where $p$ and $q$ are from a well-defined set of primes of positive density. We further prove that with probability $1 - o(1)$ over random prime pairs $(p,q)$, Shor's factoring algorithm does not factor numbers of the form $pq$, with the same level of random noise present. |
| title | Shor's Algorithm Does Not Factor Large Integers in the Presence of Noise |
| topic | Quantum Physics Discrete Mathematics F.2.0; E.3 |
| url | https://arxiv.org/abs/2306.10072 |