dorsal/arxiv
View SchemaExperimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
| Authors | Lieven M. K. Vandersypen, Matthias Steffen, Gregory Breyta, Costantino S. Yannoni, Mark H. Sherwood, Isaac L. Chuang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112176 |
| URL | https://arxiv.org/abs/quant-ph/0112176 |
| DOI | 10.1038/414883a |
| Journal | Nature 414, 883-887 (20/27 Dec 2001) |
Abstract
The number of steps any classical computer requires in order to find the prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at least using algorithms known at present. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes. Quantum computers, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm. Although important for the study of quantum computers, experimental demonstration of this algorithm has proved elusive. Here we report an implementation of the simplest instance of Shor's algorithm: factorization of ${N=15}$ (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a molecule as quantum bits, which can be manipulated with room temperature liquid state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to many quantum bit systems, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameter-free but predictive model of decoherence effects in our system.
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"abstract": "The number of steps any classical computer requires in order to find the\nprime factors of an $l$-digit integer $N$ increases exponentially with $l$, at\nleast using algorithms known at present. Factoring large integers is therefore\nconjectured to be intractable classically, an observation underlying the\nsecurity of widely used cryptographic codes. Quantum computers, however, could\nfactor integers in only polynomial time, using Shor\u0027s quantum factoring\nalgorithm. Although important for the study of quantum computers, experimental\ndemonstration of this algorithm has proved elusive. Here we report an\nimplementation of the simplest instance of Shor\u0027s algorithm: factorization of\n${N=15}$ (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a\nmolecule as quantum bits, which can be manipulated with room temperature liquid\nstate nuclear magnetic resonance techniques. This method of using nuclei to\nstore quantum information is in principle scalable to many quantum bit systems,\nbut such scalability is not implied by the present work. The significance of\nour work lies in the demonstration of experimental and theoretical techniques\nfor precise control and modelling of complex quantum computers. In particular,\nwe present a simple, parameter-free but predictive model of decoherence effects\nin our system.",
"arxiv_id": "quant-ph/0112176",
"authors": [
"Lieven M. K. Vandersypen",
"Matthias Steffen",
"Gregory Breyta",
"Costantino S. Yannoni",
"Mark H. Sherwood",
"Isaac L. Chuang"
],
"categories": [
"quant-ph"
],
"doi": "10.1038/414883a",
"journal_ref": "Nature 414, 883-887 (20/27 Dec 2001)",
"title": "Experimental realization of Shor\u0027s quantum factoring algorithm using nuclear magnetic resonance",
"url": "https://arxiv.org/abs/quant-ph/0112176"
},
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