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Quantum search algorithms
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Volume 35 ,  Issue 2  (June 2004) table of contents
COLUMN: Complexity theory table of contents
Pages: 22 - 35  
Year of Publication: 2004
ISSN:0163-5700
Author
A. Ambainis  Institute for Advanced Study, Princeton, NJ
Publisher
ACM  New York, NY, USA
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ABSTRACT

We review some of quantum algorithms for search problems: Grover's search algorithm, its generalization to amplitude amplification, the applications of amplitude amplification to various problems and the recent quantum algorithms based on quantum walks.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

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D. Aldous. Minimization algorithm and random walk on the d-cube. Annals of Probability, 11(2):403--413, 1983.
 
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A. Ambainis. Quantum walk algorithm for element distinctness. quant-ph/03110001.
 
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A. Ambainis. Quantum walks and their algorithmic applications. quant-ph/0403120.
 
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A. Ambainis, J. Kempe, A. Rivosh. Coins make quantum walks faster. quant-ph/0402107.
 
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P. Benioff. Space searches with a quantum robot. In Quantum computation and information (Washington, DC, 2000), volume 305 of AMS Series on Contemporary Mathematics, pp. 1--12. Also quant-ph/0003006.
 
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G. Brassard. P. Høyer, M. Mosca, A. Tapp. Quantum amplitude amplification and estimation. Quantum Computation and Quantum Information Science, AMS Contemporary Math Series, vol. 305, pp. 53--74. Also quant-ph/0005055.
 
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H. Buhrman, R. Spalek. manuscript, 2003.
 
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A. M. Childs and J. M. Eisenberg. Quantum algorithms for subset finding. quant-ph/0311038.
 
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C. Dürr, P. Høyer. A quantum algorithm for finding the minimum. quant-ph/9607014.
 
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C. Dürr, M. Heiligman, P. Høyer, M. Mhalla. Quantum query complexity of some graph problems. quant-ph/0401091.
 
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E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren and D. Preda, A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem, Science 292, 472 (2001), quant-ph/0104129.
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P. Høyer, J. Neerbek, Y. Shi. Quantum complexities of ordered searching, sorting, and element distinctness. Algorithmica, 34(4): 429--448, 2002. Also quant-ph/0102078.
 
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J. Kempe. Quantum random walks - an introductory overview, Contemporary Physics, 44 (4):307--327, 2003. Also quant-ph/0303081.
 
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F. Magniez, M. Santha, and M. Szegedy. Quantum algorithms for the triangle problem. quant-ph/0310134.
 
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G. Midrijānis. Exact quantum query complexity for total Boolean functions. quant-ph/0403168.
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D. Rolf. 3 -- SAT ε RT IM E(1.32971n). Diploma thesis, Humboldt-Universität zu Berlin, 2003.
 
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T. Rudolph, L. Grover. How significant are the known collision and element distinctness quantum algorithms? quant-ph/0309123.
 
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M. Szegedy. Spectra of quantized walks and a √Δε rule, quant-ph/0401053.
 
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C. Zalka. Grover's quantum searching algorithm is optimal. Physical Review A, 60:27462751, 1999. Also quant-ph/9711070.