dc.contributor.author | Aaronson, Scott | |
dc.contributor.author | Drucker, Andrew Donald | |
dc.date.accessioned | 2012-06-27T18:40:42Z | |
dc.date.available | 2012-06-27T18:40:42Z | |
dc.date.issued | 2011-06 | |
dc.identifier.isbn | 978-3-642-22005-0 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/71224 | |
dc.description.abstract | We study the power of classical and quantum algorithms equipped with nonuniform advice, in the form of a coin whose bias encodes useful information. This question takes on particular importance in the quantum case, due to a surprising result that we prove: a quantum finite automaton with just two states can be sensitive to arbitrarily small changes in a coin’s bias. This contrasts with classical probabilistic finite automata, whose sensitivity to changes in a coin’s bias is bounded by a classic 1970 result of Hellman and Cover.
Despite this finding, we are able to bound the power of advice coins for space-bounded classical and quantum computation. We define the classes BPPSPACE/coin and BQPSPACE/coin, of languages decidable by classical and quantum polynomial-space machines with advice coins. Our main theorem is that both classes coincide with PSPACE/poly. Proving this result turns out to require substantial machinery. We use an algorithm due to Neff for finding roots of polynomials in NC; a result from algebraic geometry that lower-bounds the separation of a polynomial’s roots; and a result on fixed-points of superoperators due to Aaronson and Watrous, originally proved in the context of quantum computing with closed timelike curves. | en_US |
dc.language.iso | en_US | |
dc.publisher | Springer Berlin / Heidelberg | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/978-3-642-22006-7_6 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike 3.0 | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/ | en_US |
dc.source | MIT web domain | en_US |
dc.title | Advice coins for classical and quantum computation | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Aaronson, Scott, and Andrew Drucker. “Advice Coins for Classical and Quantum Computation.” Automata, Languages and Programming. Ed. Luca Aceto, Monika Henzinger, & Jiří Sgall. Vol. 6755. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. 61–72. Web. 27 June 2012. © Springer Berlin / Heidelberg | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | en_US |
dc.contributor.approver | Aaronson, Scott | |
dc.contributor.mitauthor | Aaronson, Scott | |
dc.contributor.mitauthor | Drucker, Andrew Donald | |
dc.relation.journal | Automata, Languages and Programming | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Aaronson, Scott; Drucker, Andrew | en |
dc.identifier.orcid | https://orcid.org/0000-0003-1333-4045 | |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |