dorsal/arxiv
View SchemaAn integral version of Shor's factoring algorithm
| Authors | Felix M Lev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109103 |
| URL | https://arxiv.org/abs/quant-ph/0109103 |
Abstract
We consider a version of Shor's quantum factoring algorithm such that the quantum Fourier transform is replaced by an extremely simple one where decomposition coefficients take only the values of $1,i,-1,-i$. In numerous calculations which have been carried out so far, our algorithm has been surprisingly stable and never failed. There are numerical indications that the probability of period finding given by the algorithm is a slowly decreasing function of the number to be factorized and is typically less than in Shor's algorithm. On the other hand, quantum computer (QC), capable of implementing our algorithm, will require a much less amount of resources and will be much less error-sensitive than standard QC. We also propose a modification of Coppersmith' Approximate Fast Fourier Transform. The numerical results show that the probability is signifacantly amplified even in the first post integral approximation. Our algorithm can be very useful at early stages of development of quantum computer.
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"abstract": "We consider a version of Shor\u0027s quantum factoring algorithm such that the\nquantum Fourier transform is replaced by an extremely simple one where\ndecomposition coefficients take only the values of $1,i,-1,-i$. In numerous\ncalculations which have been carried out so far, our algorithm has been\nsurprisingly stable and never failed. There are numerical indications that the\nprobability of period finding given by the algorithm is a slowly decreasing\nfunction of the number to be factorized and is typically less than in Shor\u0027s\nalgorithm. On the other hand, quantum computer (QC), capable of implementing\nour algorithm, will require a much less amount of resources and will be much\nless error-sensitive than standard QC. We also propose a modification of\nCoppersmith\u0027 Approximate Fast Fourier Transform. The numerical results show\nthat the probability is signifacantly amplified even in the first post integral\napproximation. Our algorithm can be very useful at early stages of development\nof quantum computer.",
"arxiv_id": "quant-ph/0109103",
"authors": [
"Felix M Lev"
],
"categories": [
"quant-ph"
],
"title": "An integral version of Shor\u0027s factoring algorithm",
"url": "https://arxiv.org/abs/quant-ph/0109103"
},
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"source": {
"execution_id": "b0774bf1-7ea9-479a-8fb3-88ce384d56f8",
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