IEICE TRANSACTIONS on Fundamentals
Exploiting the Difference in Probability Calculation between Quantum and Probabilistic Computations
Summary :
The main purpose of this paper is to show that we can exploit the difference (l1-norm and l2-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It is shown that there is a finite language L which contains sentences of length up to O(nc+1) such that: (i) There is a one-way quantum finite automaton (qfa) of O(nc+4) states which recognizes L. (ii) However, if we try to simulate this qfa by a probabilistic finite automaton (pfa) using the same algorithm, then it needs Ω(n2c+4) states. It should be noted that we do not prove real lower bounds for pfa's but show that if pfa's and qfa's use exactly the same algorithm, then qfa's need much less states.
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- IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.5 pp.1004-1011
- Publication Date
- 2004/05/01
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- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
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Masami AMANO, Kazuo IWAMA, Raymond H. PUTRA, "Exploiting the Difference in Probability Calculation between Quantum and Probabilistic Computations" in IEICE TRANSACTIONS on Fundamentals,
vol. E87-A, no. 5, pp. 1004-1011, May 2004, doi: .
Abstract: The main purpose of this paper is to show that we can exploit the difference (l1-norm and l2-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It is shown that there is a finite language L which contains sentences of length up to O(nc+1) such that: (i) There is a one-way quantum finite automaton (qfa) of O(nc+4) states which recognizes L. (ii) However, if we try to simulate this qfa by a probabilistic finite automaton (pfa) using the same algorithm, then it needs Ω(n2c+4) states. It should be noted that we do not prove real lower bounds for pfa's but show that if pfa's and qfa's use exactly the same algorithm, then qfa's need much less states.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e87-a_5_1004/_p
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@ARTICLE{e87-a_5_1004,
author={Masami AMANO, Kazuo IWAMA, Raymond H. PUTRA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Exploiting the Difference in Probability Calculation between Quantum and Probabilistic Computations},
year={2004},
volume={E87-A},
number={5},
pages={1004-1011},
abstract={The main purpose of this paper is to show that we can exploit the difference (l1-norm and l2-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It is shown that there is a finite language L which contains sentences of length up to O(nc+1) such that: (i) There is a one-way quantum finite automaton (qfa) of O(nc+4) states which recognizes L. (ii) However, if we try to simulate this qfa by a probabilistic finite automaton (pfa) using the same algorithm, then it needs Ω(n2c+4) states. It should be noted that we do not prove real lower bounds for pfa's but show that if pfa's and qfa's use exactly the same algorithm, then qfa's need much less states.},
keywords={},
doi={},
ISSN={},
month={May},}
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TY - JOUR
TI - Exploiting the Difference in Probability Calculation between Quantum and Probabilistic Computations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1004
EP - 1011
AU - Masami AMANO
AU - Kazuo IWAMA
AU - Raymond H. PUTRA
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2004
AB - The main purpose of this paper is to show that we can exploit the difference (l1-norm and l2-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It is shown that there is a finite language L which contains sentences of length up to O(nc+1) such that: (i) There is a one-way quantum finite automaton (qfa) of O(nc+4) states which recognizes L. (ii) However, if we try to simulate this qfa by a probabilistic finite automaton (pfa) using the same algorithm, then it needs Ω(n2c+4) states. It should be noted that we do not prove real lower bounds for pfa's but show that if pfa's and qfa's use exactly the same algorithm, then qfa's need much less states.
ER -
English
