dorsal/arxiv
View SchemaQuantum Algorithms for some Hidden Shift Problems
| Authors | Wim van Dam, Sean Hallgren, Lawrence Ip |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211140 |
| URL | https://arxiv.org/abs/quant-ph/0211140 |
| Journal | Proceedings of the ACM-SIAM Symposium on Discrete Algorithms, pages 489-498 (2003) |
Abstract
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to capture shift structure has received far less attention in the context of quantum computation. In this paper, we present three examples of ``unknown shift'' problems that can be solved efficiently on a quantum computer using the quantum Fourier transform. We also define the hidden coset problem, which generalizes the hidden shift problem and the hidden subgroup problem. This framework provides a unified way of viewing the ability of the Fourier transform to capture subgroup and shift structure.
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"abstract": "Almost all of the most successful quantum algorithms discovered to date\nexploit the ability of the Fourier transform to recover subgroup structure of\nfunctions, especially periodicity. The fact that Fourier transforms can also be\nused to capture shift structure has received far less attention in the context\nof quantum computation.\n In this paper, we present three examples of ``unknown shift\u0027\u0027 problems that\ncan be solved efficiently on a quantum computer using the quantum Fourier\ntransform. We also define the hidden coset problem, which generalizes the\nhidden shift problem and the hidden subgroup problem. This framework provides a\nunified way of viewing the ability of the Fourier transform to capture subgroup\nand shift structure.",
"arxiv_id": "quant-ph/0211140",
"authors": [
"Wim van Dam",
"Sean Hallgren",
"Lawrence Ip"
],
"categories": [
"quant-ph"
],
"journal_ref": "Proceedings of the ACM-SIAM Symposium on Discrete Algorithms,\n pages 489-498 (2003)",
"title": "Quantum Algorithms for some Hidden Shift Problems",
"url": "https://arxiv.org/abs/quant-ph/0211140"
},
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