dorsal/arxiv
View SchemaOn Quantum Versions of the Yao Principle
| Authors | Mart de Graaf, Ronald de Wolf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109070 |
| URL | https://arxiv.org/abs/quant-ph/0109070 |
Abstract
The classical Yao principle states that the complexity R_epsilon(f) of an optimal randomized algorithm for a function f with success probability 1-epsilon equals the complexity max_mu D_epsilon^mu(f) of an optimal deterministic algorithm for f that is correct on a fraction 1-epsilon of the inputs, weighed according to the hardest distribution mu over the inputs. In this paper we investigate to what extent such a principle holds for quantum algorithms. We propose two natural candidate quantum Yao principles, a ``weak'' and a ``strong'' one. For both principles, we prove that the quantum bounded-error complexity is a lower bound on the quantum analogues of max mu D_epsilon^mu(f). We then prove that equality cannot be obtained for the ``strong'' version, by exhibiting an exponential gap. On the other hand, as a positive result we prove that the ``weak'' version holds up to a constant factor for the query complexity of all symmetric Boolean functions
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"abstract": "The classical Yao principle states that the complexity R_epsilon(f) of an\noptimal randomized algorithm for a function f with success probability\n1-epsilon equals the complexity max_mu D_epsilon^mu(f) of an optimal\ndeterministic algorithm for f that is correct on a fraction 1-epsilon of the\ninputs, weighed according to the hardest distribution mu over the inputs. In\nthis paper we investigate to what extent such a principle holds for quantum\nalgorithms. We propose two natural candidate quantum Yao principles, a ``weak\u0027\u0027\nand a ``strong\u0027\u0027 one. For both principles, we prove that the quantum\nbounded-error complexity is a lower bound on the quantum analogues of max mu\nD_epsilon^mu(f). We then prove that equality cannot be obtained for the\n``strong\u0027\u0027 version, by exhibiting an exponential gap. On the other hand, as a\npositive result we prove that the ``weak\u0027\u0027 version holds up to a constant\nfactor for the query complexity of all symmetric Boolean functions",
"arxiv_id": "quant-ph/0109070",
"authors": [
"Mart de Graaf",
"Ronald de Wolf"
],
"categories": [
"quant-ph",
"cs.CC"
],
"title": "On Quantum Versions of the Yao Principle",
"url": "https://arxiv.org/abs/quant-ph/0109070"
},
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