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Fixed-point quantum search.

Lov K Grover1

  • 1Bell Laboratories, Lucent Technologies, 600-700 Mountain Avenue, Murray Hill, New Jersey 07974, USA.

Physical Review Letters
|October 26, 2005
PubMed
Summary
This summary is machine-generated.

Quantum search algorithms find target states in databases using iterative operations. Modifying these operations with selective phase shifts enhances convergence and robustness, improving quantum control and error correction.

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Area of Science:

  • Quantum Computing
  • Quantum Information Science

Background:

  • The quantum search algorithm efficiently finds a target state in an unsorted database of size N using approximately sqrt[N] queries.
  • The standard algorithm relies on iterative selective inversions and diffusion operations, achieving results through state vector rotations in a Hilbert space.

Purpose of the Study:

  • To investigate the effect of replacing selective inversions with selective phase shifts in the quantum search algorithm.
  • To determine if this modification enhances convergence and robustness of the search process.

Main Methods:

  • The study theoretically analyzes the quantum search algorithm by substituting selective inversion operations with selective phase shifts of pi/3.
  • The convergence properties of the modified algorithm are examined concerning step size and the number of iterations.

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Main Results:

  • Replacing selective inversions with selective phase shifts of pi/3 leads to preferential convergence to the target state.
  • This convergence is robust, irrespective of the specific step size or the total number of iterations performed.

Conclusions:

  • The modified quantum search algorithm demonstrates enhanced robustness and preferential convergence.
  • This approach offers potential for developing improved quantum control techniques and error correction schemes.