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Quantum Computing Algorithms and Computational Complexity

Quantum Computing Algorithms and Computational Complexity

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This reprint is mainly concerned with quantum algorithms, their mathematics from behind and the complexity issues arising from them. It comprises seven papers: Two of them are focused on improving the performance by means of quantum algorithms over the best instances of classical ones: “A Fast Quantum Image Component Labeling Algorithm” [1] by Yan Li, Dapeng Hao, Yang Xu and Kinkeung Lai. “Quantum Algorithms for Some Strings Problems Based on Quantum String Comparator” [2] by Kamil Khadiev, Artem Ilikaev and Jevgenijs Vihrovs. Another four papers deal with enhanced quantum algorithms: “Progress towards Analytically Optimal Angles in Quantum Approximate Optimisation”: [3] by Daniil Rabinovich, Richik Sengupta, Ernesto Campos, Vishwanathan Akshay and Jacob Biamonte. “Quantum Weighted Fractional Fourier Transform” [4] by Tieyu Zhao, Tianyu Yang and Yingying Chi. “On the Amplitude Amplification of Quantum States Corresponding to the Solutions of the Partition Problem” [5] by Mauro Mezzini, Jose J. Paulet, Fernando Cuartero, Hernan I. Cruz and Fernando L. Pelayo. “On the Complexity of Finding the Maximum Entropy Compatible Quantum State” [6] by Serena Di Giorgio and Paulo Mateus. Last, but not least, one paper researched a classical operational research problem by means of quantum annealing: “GPS: A New TSP Formulation for Its Generalizations Type QUBO” [7] by Saul Gonzalez-Bermejo, Guillermo Alonso-Linaje and Parfait Atchade-Adelomou. As Guest Editors, we would like to thank the authors and reviewers who made this possible by promoting, spreading research on and supporting quantum computing.

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Keywords

  • amplitude amplification
  • Combinatorial optimization
  • computational efficiency
  • image component labeling
  • Levialdi shrinking operator
  • local operator
  • Mathematics & science
  • maximum von Neumann entropy
  • n/a
  • QAOA
  • QSZK-completeness
  • quantum algorithm
  • quantum algorithms
  • quantum annealing
  • quantum circuit optimization
  • quantum computation
  • quantum computing
  • quantum Fourier transform
  • quantum image processing
  • quantum Markov chains
  • quantum weighted fractional Fourier transform
  • QUBO
  • Reference, information & interdisciplinary subjects
  • Research & information: general
  • sorting
  • string processing
  • subset sum problem
  • TSP
  • variatonal algorithms
  • VRP

Links

DOI: 10.3390/books978-3-0365-7747-0

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