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Bibliography.bib
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Bibliography.bib
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@article{SGQC,
author = {Stan Gudder},
title = {Quantum Computation},
journal = {The American Mathematical Monthly},
volume = {110},
number = {3},
pages = {181-201},
year = {2003},
publisher = {Taylor & Francis},
doi = {10.1080/00029890.2003.11919955},
URL = {
https://doi.org/10.1080/00029890.2003.11919955
},
eprint = {
https://doi.org/10.1080/00029890.2003.11919955
},
}
@book{Book:QCQI,
title = {Quantum Computation and Quantum Information: 10th Anniversary Edition},
author = {Nielsen, Michael A. and Chuang, Isaac L.},
publisher = {Cambridge University Press},
isbn = {9780511985249},
year = {2011},
series = {Cambridge Series on Information and the Natural Sciences},
edition = {1},
url = {http://michaelnielsen.org/qcqi/},
}
@article{Article:Shor:1997,
author = {Shor, Peter W.},
title = {Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer},
journal = {SIAM Journal on Computing},
issue_date = {Oct. 1997},
volume = {26},
number = {5},
month = oct,
year = {1997},
issn = {0097-5397},
pages = {1484--1509},
numpages = {26},
url = {http://dx.doi.org/10.1137/S0097539795293172},
doi = {10.1137/S0097539795293172},
acmid = {264406},
publisher = {Society for Industrial and Applied Mathematics},
address = {Philadelphia, PA, USA},
keywords = {Church's thesis, Fourier transforms, algorithmic number theory, discrete logarithms, foundations of quantum mechanics, prime factorization, quantum computers, spin systems},
}
@Article{Article:FTCL,
author = "Fredkin, Edward and Toffoli, Tommaso",
title = "Conservative logic",
journal = "International Journal of Theoretical Physics",
year = "1982",
month = "Apr",
day = "01",
volume = "21",
number = "3",
pages = "219--253",
abstract = "Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and the conservation of certainadditive quantities (among which energy plays a distinguished role). Because it more closely mirrors physics than traditional models of computation, conservative logic is in a better position to provide indications concerning the realization of high-performance computing systems, i.e., of systems that make very efficient use of the ``computing resources'' actually offered by nature. In particular, conservative logic shows that it is ideally possible to build sequential circuits with zero internal power dissipation. After establishing a general framework, we discuss two specific models of computation. The first uses binary variables and is the conservative-logic counterpart of switching theory; this model proves that universal computing capabilities are compatible with the reversibility and conservation constraints. The second model, which is a refinement of the first, constitutes a substantial breakthrough in establishing a correspondence between computation and physics. In fact, this model is based on elastic collisions of identical ``balls,'' and thus is formally identical with the atomic model that underlies the (classical) kinetic theory of perfect gases. Quite literally, the functional behavior of a general-purpose digital computer can be reproduced by a perfect gas placed in a suitably shaped container and given appropriate initial conditions.",
issn = "1572-9575",
doi = "10.1007/BF01857727",
url = "https://doi.org/10.1007/BF01857727",
}
@InProceedings{Article:TRC,
author = "Toffoli, Tommaso",
editor = "de Bakker, Jaco and van Leeuwen, Jan",
title = "Reversible computing",
booktitle = "Automata, Languages and Programming",
year = "1980",
publisher = "Springer Berlin Heidelberg",
address = "Berlin, Heidelberg",
pages = "632--644",
abstract = "The theory of reversible computing is based on invertible primitives and composition rules that preserve invertibility. With these constraints, one can still satisfactorily deal with both functional and structural aspects of computing processes; at the same time, one attains a closer correspondence between the behavior of abstract computing systems and the microscopic physical laws (which are presumed to be strictly reversible) that underly any concrete implementation of such systems.",
isbn = "978-3-540-39346-7",
}
@book{Book:Jacobson,
title = {Basic Algebra I: Second Edition},
author = {Jacobson, Nathan},
isbn = {9780486135229},
series = {Dover Books on Mathematics},
url = {https://books.google.co.jp/books?id=JHFpv0tKiBAC},
year = {2012},
publisher = {Dover Publications},
}
@book{Book:Knuth_2,
title = {Art of Computer Programming, Volume 2: Seminumerical Algorithms},
author = {Knuth, Donald E},
publisher = {Addison-Wesley Professional},
isbn = {0-201-89684-2,978-0-201-89684-8,9780321635761},
year = {1997},
series = {Addison-Wesley series in computer science and information processing},
edition = {3ed.},
volume = {2},
}
@book{Book:CCModern,
title = {Computational complexity: A modern approach},
author = {Sanjeev Arora, Boaz Barak},
publisher = {Cambridge University Press},
isbn = {9780521424264,0521424267},
year = {2009},
series = {},
edition = {1},
volume = {},
}
@article{Article:PRIMESinP,
ISSN = {0003486X},
URL = {http://www.jstor.org/stable/3597229},
abstract = {We present an unconditional deterministic polynomial-time algorithm that determines whether an input number is prime or composite.},
author = {Manindra Agrawal and Neeraj Kayal and Nitin Saxena},
journal = {Annals of Mathematics},
number = {2},
pages = {781--793},
publisher = {Annals of Mathematics},
title = {PRIMES Is in P},
volume = {160},
year = {2004}
}
@book{Book:PapadimitriouCC,
title = {Computational Complexity},
author = {Christos H. Papadimitriou},
publisher = {Addison-Wesley},
isbn = {0201530821,9780201530827},
year = {1994},
}
@ARTICLE{Article:PerfectPowers,
author = {Daniel J. Bernstein},
title = {Detecting Perfect Powers In Essentially Linear Time},
journal = {Mathematics of computation},
year = {1998},
volume = {67},
pages = {1253--1283}
}