D. Li, X. Li, H. Huang, “Phase Condition for the Grover Algorithm”, TMF, 144:3 (2005), 472–483; Theoret. and Math. Phys., 144:3 (2005), 1279

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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 144, Number 3, Pages 472–483
DOI: https://doi.org/10.4213/tmf1871 (Mi tmf1871)

This article is cited in 8 scientific papers (total in 8 papers)

Phase Condition for the Grover Algorithm

D.-F. Li^a, X.-X. Li^b, H.-T. Huang^c

^a Tsinghua University
^b Wayne State University
^c Michigan State University

Full-text PDF (242 kB) Citations (8)

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DOI: https://doi.org/10.4213/tmf1871

Abstract: For the Grover algorithm, we derive the exact formula of the norm of the amplitude in the marked state in a sine-function form and use this formula to derive the necessary and sufficient phase condition условие

sin Δ \leq | β |

$\sin\Delta\leq|\beta|$ for this algorithm with arbitrary phase rotations. We show that the condition of identical rotation angles

θ = ϕ

$\theta=\phi$ , which is a special case of our condition, is a sufficient but not necessary phase condition.

Keywords: Grover algorithm, quantum search algorithm, phase condition.

Received: 26.10.2003
Revised: 04.03.2005

English version:
Theoretical and Mathematical Physics, 2005, Volume 144, Issue 3, Pages 1279–1287
DOI: https://doi.org/10.1007/s11232-005-0159-x

Bibliographic databases:

Language: Russian

Citation: D. Li, X. Li, H. Huang, “Phase Condition for the Grover Algorithm”, TMF, 144:3 (2005), 472–483; Theoret. and Math. Phys., 144:3 (2005), 1279–1287

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf1871

https://doi.org/10.4213/tmf1871

https://www.mathnet.ru/eng/tmf/v144/i3/p472

This publication is cited in the following 8 articles:

Panchi Li, Ziyang Li, “A flexible fixed-phase quantum search algorithm for searching unordered databases with any size”, J Comput Electron, 23:1 (2024), 176
Xin Li, Panchi Li, “A Fixed-Phase Quantum Search Algorithm with More Flexible Behavior”, JQIS, 02:02 (2012), 28
Panchi Li, Kaoping Song, “Adaptive Phase Matching in Grover's Algorithm”, JQIS, 01:02 (2011), 43
Li X., Li D., Huang H., Li X., “Fixed-Point Search With Two Arbitrary Equal Phase Shifts for Any Number of Iterations”, International Journal of Quantum Information, 8:7 (2010), 1075–1087
Dafa Li, “Quantum fixed-point search algorithm with general phase shifts”, Front. Comput. Sci. China, 2:2 (2008), 138
Li D, Chen JP, Li X, et al, “Performance of equal phase-shift search for one iteration”, European Physical Journal D, 45:2 (2007), 335–340
Li PC, Li SY, “Phase matching in Grover's algorithm”, Physics Letters A, 366:1–2 (2007), 42–46
Li DF, Li XR, Huang HT, et al, “Fixed-point quantum search for different phase shifts”, Physics Letters A, 362:4 (2007), 260–264

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	212
References:	57
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