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Conserved Quantities in Linear and Nonlinear Quantum Search Cover

Conserved Quantities in Linear and Nonlinear Quantum Search

Quantum Information & Computation
Volume 25 (2025): Issue 4 (August 2025)
By: David A. Meyer and  Thomas G. Wong  
Open Access
|Aug 2025

Figures & Tables

Figure 1.

A complete graph of N = 6 vertices. A vertex is marked, as indicated by a double circle. In the search algorithm, vertices that evolve identically have the same label and color.
A complete graph of N = 6 vertices. A vertex is marked, as indicated by a double circle. In the search algorithm, vertices that evolve identically have the same label and color.

Figure 2.

Success probability versus time for (linear) quantum search on the complete graph with N = 100 vertices and various jumping rates. In (a), the solid black curve is γ = 0.001, the dashed red curve is γ = 0.005, the dotted green curve is γ = 0.008, the dot-dashed blue curve is γ = 0.009, and the dot-dot-dashed orange curve is γ = 0.01. In (b), the solid black curve is γ = 0.011, the dashed red curve is γ = 0.012, the dotted green curve is γ = 0.015, the dot-dashed blue curve is γ = 0.02, and the dot-dot-dashed orange curve is γ = 0.03.
Success probability versus time for (linear) quantum search on the complete graph with N = 100 vertices and various jumping rates. In (a), the solid black curve is γ = 0.001, the dashed red curve is γ = 0.005, the dotted green curve is γ = 0.008, the dot-dashed blue curve is γ = 0.009, and the dot-dot-dashed orange curve is γ = 0.01. In (b), the solid black curve is γ = 0.011, the dashed red curve is γ = 0.012, the dotted green curve is γ = 0.015, the dot-dashed blue curve is γ = 0.02, and the dot-dot-dashed orange curve is γ = 0.03.

Figure 3.

Success probability versus time for nonlinear quantum search on the complete graph with N = 100 vertices, λ = (2 – λ)/2N, and various values of λ. The solid black curve is γ = 0.2, the dashed red curve is λ = 0.6, the dotted green curve is λ = 0.611, the dot-dashed blue curve is λ = 0.612, and the dot-dot-dashed orange curve is λ = 0.8.
Success probability versus time for nonlinear quantum search on the complete graph with N = 100 vertices, λ = (2 – λ)/2N, and various values of λ. The solid black curve is γ = 0.2, the dashed red curve is λ = 0.6, the dotted green curve is λ = 0.611, the dot-dashed blue curve is λ = 0.612, and the dot-dot-dashed orange curve is λ = 0.8.

Figure 4.

Success probability versus time for nonlinear quantum search on the complete graph with N = 100 vertices, γ = γc(t), and various values of λ. The solid black curve is λ = 0, the dashed red curve is λ = –1, the dotted green curve is λ = –2, and the dot-dashed blue curve is λ = –3.
Success probability versus time for nonlinear quantum search on the complete graph with N = 100 vertices, γ = γc(t), and various values of λ. The solid black curve is λ = 0, the dashed red curve is λ = –1, the dotted green curve is λ = –2, and the dot-dashed blue curve is λ = –3.
DOI: https://doi.org/10.2478/qic-2025-0017 | Journal eISSN: 3106-0544 | Journal ISSN: 1533-7146
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Language: English
Page range: 315 - 328
Submitted on: Mar 10, 2025
Accepted on: Jun 27, 2025
Published on: Aug 22, 2025
Published by: Cerebration Science Publishing Co., Limited
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
quantum walk,
spatial search,
complete graph,
conservation laws,
Gross-Pitaevskii equation,
Bose-Einstein condensate
Related subjects:
Physics,
Quantum physics,
Mathematics,
Applied mathematics,
Computer sciences,
Computer sciences in the humanities,
Computer sciences,
Computer sciences in natural sciences

© 2025 David A. Meyer, Thomas G. Wong, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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