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Extending echo state property for quantum reservoir computing.

Shumpei Kobayashi1, Quoc Hoan Tran2, Kohei Nakajima1,2,3

  • 1Department of Creative Informatics, <a href="https://ror.org/057zh3y96">The University of Tokyo</a>, Bunkyo-ku, Tokyo 113-8656, Japan.

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Summary
This summary is machine-generated.

We introduce new echo state properties (ESP) for nonstationary systems in reservoir computing (RC). This extends RC theory for quantum reservoir computers (QRC) and other complex systems.

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Area of Science:

  • Quantum Computing
  • Machine Learning
  • Complex Systems

Background:

  • The echo state property (ESP) is crucial for reservoir computing (RC), enabling output-only training by ignoring initial states and past inputs.
  • Traditional ESP definitions are insufficient for nonstationary systems where statistical properties change over time.

Purpose of the Study:

  • To extend the concept of ESP to nonstationary systems.
  • To introduce nonstationary ESP and subspace/subset ESP for systems with evolving statistical properties.
  • To validate these new ESP definitions within the quantum reservoir computer (QRC) framework.

Main Methods:

  • Developed definitions for nonstationary ESP and subspace/subset ESP.
  • Numerically demonstrated nonstationary ESP in QRC using Hamiltonian dynamics and input encoding.
  • Employed nonlinear autoregressive moving-average tasks for validation.
  • Calculated linear and nonlinear memory capacities to quantify reservoir state properties.

Main Results:

  • Successfully demonstrated the correspondence between nonstationary ESP and QRC dynamics.
  • Validated the effectiveness of the new ESP definitions in practical QRC scenarios.
  • Quantified input-dependent components within reservoir states using memory capacities.

Conclusions:

  • The study provides a theoretical and numerical foundation for understanding and designing nonstationary RC systems, particularly QRCs.
  • The introduced ESP categories are essential for exploiting nonstationary dynamics and subsystems in advanced RC applications.
  • This work advances the practical design and application of quantum and other nonstationary reservoir computing systems.