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Author Ambainis, Andris ♦ Nayak, Ashwin ♦ Ta-Shma, Amnon ♦ Vazirani, Umesh
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2002
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Automaton size ♦ Communication complexity ♦ Encoding ♦ Finite automata ♦ Quantum communication ♦ Quantum computation
Abstract We consider the possibility of encoding $\textit{m}$ classical bits into many fewer $\textit{n}$ quantum bits (qubits) so that an arbitrary bit from the original $\textit{m}$ bits can be recovered with good probability. We show that nontrivial quantum codes exist that have no classical counterparts. On the other hand, we show that quantum encoding cannot save more than a logarithmic additive factor over the best classical encoding. The proof is based on an entropy coalescence principle that is obtained by viewing Holevo's theorem from a new perspective.In the existing implementations of quantum computing, qubits are a very expensive resource. Moreover, it is difficult to reinitialize existing bits during the computation. In particular, reinitialization is impossible in NMR quantum computing, which is perhaps the most advanced implementation of quantum computing at the moment. This motivates the study of quantum computation with restricted memory and no reinitialization, that is, of quantum finite automata. It was known that there are languages that are recognized by quantum finite automata with sizes exponentially smaller than those of corresponding classical automata. Here, we apply our technique to show the surprising result that there are languages for which quantum finite automata take exponentially more states than those of corresponding classical automata.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2002-07-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 49
Issue Number 4
Page Count 16
Starting Page 496
Ending Page 511

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Source: ACM Digital Library