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Generalized Grover's Algorithm for Multiple Phase Inversion States.

Tim Byrnes1,2,3,4,5, Gary Forster4,6, Louis Tessler2,7

  • 1State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China.

Physical Review Letters
|February 27, 2018
PubMed
Summary

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This summary is machine-generated.

This study generalizes Grover's search algorithm to invert signs on multiple states. Researchers bypass Grover's algorithm entirely, achieving a near-optimal time complexity for quantum search.

Area of Science:

  • Quantum Computing
  • Quantum Algorithms
  • Information Science

Background:

  • Grover's algorithm is a quantum search algorithm.
  • The standard algorithm inverts the sign on only one state.
  • Generalizing this to multiple states presents a challenge.

Purpose of the Study:

  • To provide an exact solution for Grover's search when the Grover operator inverts the sign on N states.
  • To explore the underlying structure of this generalized problem.
  • To derive an appropriate initial state for Grover evolution in this scenario.

Main Methods:

  • Analyzing the eigenspectrum of the generalized Hamiltonian.
  • Deriving a suitable initial state for the quantum evolution.
  • Utilizing the quantum phase estimation algorithm to solve the generalized search problem.

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Main Results:

  • An exact solution for Grover's search with N-state sign inversion is presented.
  • The quantum phase estimation algorithm is shown to solve this generalized search problem, bypassing Grover's algorithm.
  • A time complexity of sqrt[D/M^α] was obtained, where D is search space dimension and M is the number of target states (α≈1).

Conclusions:

  • The generalized Grover's search problem can be solved efficiently using quantum phase estimation.
  • This approach offers a significant advancement over the standard Grover's algorithm for specific search tasks.
  • The derived time complexity approaches optimal scaling, highlighting the potential of this generalized quantum search method.