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Multiseed Krylov Complexity.

Ben Craps1, Oleg Evnin1,2, Gabriele Pascuzzi1

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Summary

This study introduces a new method using multiple quantum operator seeds to reliably distinguish between integrable and chaotic quantum dynamics. This approach overcomes limitations of traditional Krylov complexity, offering a robust tool for analyzing complex quantum systems.

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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Quantum Computing

Background:

  • Krylov complexity measures operator spreading in quantum systems.
  • Traditional Krylov complexity's effectiveness is limited by the choice of initial operator seed.
  • Distinguishing integrable from chaotic quantum dynamics is a key challenge.

Purpose of the Study:

  • To develop a robust method for distinguishing integrable and chaotic quantum dynamics.
  • To overcome the seed-dependence limitations of conventional Krylov complexity.
  • To propose a novel application of operator complexity in quantum system analysis.

Main Methods:

  • Applying Krylov complexity considerations to a collection of initial operator seeds simultaneously.
  • Utilizing the block-Lanczos algorithm framework for simultaneous seed analysis.
  • Considering all simple (few-body) operators as the collection of initial seeds.

Main Results:

  • The proposed method reliably distinguishes between integrable and chaotic Hamiltonians.
  • The new construction does not require fine-tuning of initial seeds.
  • This approach offers a more robust measure of quantum dynamics than conventional Krylov complexity.

Conclusions:

  • A novel, seed-independent method for analyzing quantum dynamics has been developed.
  • This approach provides a reliable way to differentiate integrable and chaotic systems.
  • The findings have implications for quantum chaos research and quantum information processing.