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Cited by 491Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyComplexity and Algorithms in Graphs

On the power of quantum computation

Simon, D.R.·2002·Proceedings 35th Annual Symposium on Foundations of Computer Science
DOI 10.1109/sfcs.1994.365701
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Abstract

The quantum model of computation is a probabilistic model, similar to the probabilistic Turing Machine, in which the laws of chance are those obeyed by particles on a quantum mechanical scale, rather than the rules familiar to us from the macroscopic world. We present here a problem of distinguishing between two fairly natural classes of function, which can provably be solved exponentially faster in the quantum model than in the classical probabilistic one, when the function is given as an oracle drawn equiprobably from the uniform distribution on either class. We thus offer compelling evidence that the quantum model may have significantly more complexity theoretic power than the probabilistic Turing Machine. In fact, drawing on this work, Shor (1994) has recently developed remarkable new quantum polynomial-time algorithms for the discrete logarithm and integer factoring problems.>

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Crossref · 10.1109/sfcs.1994.365701

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  • A quantum computer can in principle exploit coherent quantum interference and entanglement to perform computations such as factoring large numbers or searching an unsorted database more rapidly than classical computers.

    “In principle, it can exploit coherent quantum interference and entanglement to perform computations, such as factoring large numbers or searching an unsorted database, more rapidly than classical computers 1,2,6-8 .”

    From Experimental realization of a quantum algorithm (1998) · cites this paper as [7]

  • The version of the D-J algorithm realized is the simplest possible case, where f is a function from one bit to one bit, which is also the simplest instance of Simon's algorithm.

    “The D-J algorithm is well illustrated by its simplest possible case, when f is a function from one bit to one bit; this is the version that we have realized (it is also the simplest instance of Simon's algorithm 7 ).”

    From Experimental realization of a quantum algorithm (1998) · cites this paper as [7]

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Authors
Simon, D. R.
Affiliations
Microsoft (United States) (US)
Corresponding author
Simon, D.R.
Venue
Proceedings 35th Annual Symposium on Foundations of Computer Science
Publisher
IEEE Comput. Soc. Press
Published
2002-12-17
Pages
116-123
ISSN
0272-5428 (ISSN-L)
DOI
10.1109/sfcs.1994.365701
OpenAlex
W2137005141
Semantic Scholar
d34a810719d6c132d9fb697df1b5a38e2fd0dc05
Cited by
491
References
7
Citations by year
2026: 15 · 2025: 27 · 2024: 20 · 2023: 13 · 2022: 16 · 2021: 26 · 2020: 17 · 2019: 10 · 2018: 16 · 2017: 20 · 2016: 12 · 2015: 15 · 2014: 23 · 2013: 20 · 2012: 15
FWCI
14.10
Type
conference paper
Language
en
Open access
closed
Locations
Annual Symposium on Foundations of Computer Science (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
Keywords
quantum computing, oracle separation, exponential speedup, probabilistic Turing machines, discrete logarithm problem, integer factorization

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