dorsal/arxiv
View SchemaThe Learnability of Quantum States
| Authors | Scott Aaronson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608142 |
| URL | https://arxiv.org/abs/quant-ph/0608142 |
| DOI | 10.1098/rspa.2007.0113 |
Abstract
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a state using a number of measurements that grows only linearly with n. Besides possible implications for experimental physics, our learning theorem has two applications to quantum computing: first, a new simulation of quantum one-way communication protocols, and second, the use of trusted classical advice to verify untrusted quantum advice.
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"abstract": "Traditional quantum state tomography requires a number of measurements that\ngrows exponentially with the number of qubits n. But using ideas from\ncomputational learning theory, we show that \"for most practical purposes\" one\ncan learn a state using a number of measurements that grows only linearly with\nn. Besides possible implications for experimental physics, our learning theorem\nhas two applications to quantum computing: first, a new simulation of quantum\none-way communication protocols, and second, the use of trusted classical\nadvice to verify untrusted quantum advice.",
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"doi": "10.1098/rspa.2007.0113",
"title": "The Learnability of Quantum States",
"url": "https://arxiv.org/abs/quant-ph/0608142"
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