dorsal/arxiv
View SchemaReply to Andrew Hodges
| Authors | Tien D. Kieu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602214 |
| URL | https://arxiv.org/abs/quant-ph/0602214 |
Abstract
We separate the criticisms of Hodges \cite{Hodges2005} and others into those against the algorithm itself and those against its physical implementation. We then point out that {\em all} those against the algorithm are either misleading or misunderstanding, and that the algorithm is self consistent. The only central argument against physical implementations of the algorithm, on the other hand, is based on an assumption that its Hamiltonians cannot be effectively constructed due to a lack of infinite precision. However, so far there is no known physical principle dictating why that cannot be done. To show that the criticism may not be a forgone conclusion, we point out the virtually unknown fact that, on the contrary, simple instances of Diophantine equations with apparently {\em infinitely precisely} integer coefficients have {\em already} been realised in experiments for certain quantum phase transitions. We also speculate on how central limit theorem of statistics might be of some help in the effective implementation of the required Hamiltonians.
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"abstract": "We separate the criticisms of Hodges \\cite{Hodges2005} and others into those\nagainst the algorithm itself and those against its physical implementation. We\nthen point out that {\\em all} those against the algorithm are either misleading\nor misunderstanding, and that the algorithm is self consistent. The only\ncentral argument against physical implementations of the algorithm, on the\nother hand, is based on an assumption that its Hamiltonians cannot be\neffectively constructed due to a lack of infinite precision. However, so far\nthere is no known physical principle dictating why that cannot be done. To show\nthat the criticism may not be a forgone conclusion, we point out the virtually\nunknown fact that, on the contrary, simple instances of Diophantine equations\nwith apparently {\\em infinitely precisely} integer coefficients have {\\em\nalready} been realised in experiments for certain quantum phase transitions. We\nalso speculate on how central limit theorem of statistics might be of some help\nin the effective implementation of the required Hamiltonians.",
"arxiv_id": "quant-ph/0602214",
"authors": [
"Tien D. Kieu"
],
"categories": [
"quant-ph"
],
"title": "Reply to Andrew Hodges",
"url": "https://arxiv.org/abs/quant-ph/0602214"
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