Amplitude Amplification for Optimization via Subdivided Phase Oracle

Naphan Benchasattabuse, Takahiko Satoh, Michal Hajdusek, Rodney Van Meter

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We propose an algorithm using a modified variant of amplitude amplification to solve combinatorial optimization problems via the use of a subdivided phase oracle. Instead of dividing input states into two groups and shifting the phase equally for all states within the same group, the subdivided phase oracle changes the phase of each input state uniquely in proportion to their objective value. We provide visualization of how amplitudes change after each iteration of applying the subdivided phase oracle followed by conventional Grover diffusion in the complex plane. We then show via numerical simulation that for normal, skew normal, and exponential distribution of objective values, the algorithm can be used to amplify the probability of measuring the optimal solution to a significant degree independent of the search space size. In the case of skew normal and exponential distributions, this probability can be amplified to be close to unity, making our algorithm near deterministic. We then modify our algorithm in order to demonstrate how it can be extended to a broader set of objective value distributions. Finally, we discuss the speedup compared to classical schemes using the query complexity model, and show that our algorithm offers a significant advantage over these classical approaches.

Original languageEnglish
Title of host publicationProceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages22-30
Number of pages9
ISBN (Electronic)9781665491136
DOIs
Publication statusPublished - 2022
Event3rd IEEE International Conference on Quantum Computing and Engineering, QCE 2022 - Broomfield, United States
Duration: 2022 Sep 182022 Sep 23

Publication series

NameProceedings - 2022 IEEE International Conference on Quantum Computing and Engineering, QCE 2022

Conference

Conference3rd IEEE International Conference on Quantum Computing and Engineering, QCE 2022
Country/TerritoryUnited States
CityBroomfield
Period22/9/1822/9/23

Keywords

  • amplitude amplification
  • Grover's search algorithm
  • optimization
  • Quantum computing

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Science Applications
  • Control and Optimization
  • Atomic and Molecular Physics, and Optics

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