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Quantifying computational advantage of Grover's algorithm with the trace speed.

Valentin Gebhart1,2, Luca Pezzè3, Augusto Smerzi3

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Researchers discovered a link between trace speed and quantum speed-up in Grover's algorithm. This finding quantifies quantum speed-up using measurable resources like entanglement and coherence.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing Algorithms
  • Quantum Thermodynamics

Background:

  • The physical origin of quantum algorithm speed-up, like Grover's search, is not fully understood.
  • No single physical resource, such as entanglement, has been identified as universally responsible for quantum speed-up.

Purpose of the Study:

  • To investigate the relationship between trace speed and quantum speed-up in Grover's algorithm.
  • To identify a measurable physical resource that quantifies quantum speed-up.

Main Methods:

  • Analysis of Grover's search algorithm using pure and pseudo-pure states.
  • Investigation of the impact of partial depolarization and interrupted searches on speed-up.
  • Correlation of quantum speed-up with state polarization and trace speed.

Main Results:

  • A one-to-one correspondence was found between quantum speed-up and pseudo-pure state polarization in noiseless Grover's algorithm.
  • Quantum speed-up is bounded by the maximal trace speed during noisy or interrupted operations.
  • Trace speed is linked to quantum statistical speeds, multipartite entanglement, and quantum coherence.

Conclusions:

  • Trace speed is a key physical resource quantifying quantum speed-up in Grover's algorithm.
  • The findings provide an experimentally measurable link between quantum speed-up and resources like entanglement and coherence.
  • This work advances the understanding of the physical underpinnings of quantum computational advantage.