Gaussian Amplitude Amplification For Quantum Pathfinding

Abstract

We study an oracle operation, along with its circuit design, which combined with the Grover diffusion operator boosts the probability of finding the minimum or maximum solutions on a weighted directed graph. We focus on the geometry of sequentially connected bipartite graphs, which naturally gives rise to solution spaces describable by Gaussian distributions. We then demonstrate how an oracle that encodes these distributions can be used to solve for the optimal path via amplitude amplification. And finally, we explore the degree to which this algorithm is capable of solving cases that are generated using randomized weights, as well as a theoretical application for solving the Traveling Salesman problem.

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Document Details

Document Type
Technical Report
Publication Date
Jul 11, 2022
Accession Number
AD1196528

Entities

People

  • Daniel P. Koch
  • Laura Wessing
  • Massimiliano Cutugno
  • Paul M. Alsing
  • Saahil Patel
  • Samuel Karlson

Organizations

  • Air Force Research Laboratory
  • United States Air Force Academy

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Algorithms
  • Computers
  • Data Science
  • Databases
  • Gaussian Distributions
  • Geometry
  • Hilbert Space
  • Logic Gates
  • Quantum Algorithms
  • Quantum Bits
  • Quantum Circuits
  • Quantum Computers
  • Quantum Computing
  • Quantum Information
  • Quantum Information Science
  • Quantum States
  • Simulations
  • Simulators
  • Standards

Readers

  • Calculus or Mathematical Analysis
  • Neural Network Machine Learning.
  • Operations Research

Technology Areas

  • Quantum Computing
  • Space
  • Space - Spacecraft Maneuvers