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Optimal protocols for slowly driven quantum systems.

Patrick R Zulkowski1, Michael R DeWeese2

  • 1Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA Department of Mathematics, Berkeley City College, Berkeley, California 94704, USA and Redwood Center for Theoretical Neuroscience, University of California, Berkeley, Berkeley, California 94720, USA.

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Summary
This summary is machine-generated.

This study introduces a geometric framework to optimize quantum information processing by minimizing entropy production in driven quantum systems. This framework is applied to a two-state quantum system, aiding in quantum annealing applications.

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Area of Science:

  • Quantum physics
  • Information theory
  • Thermodynamics

Background:

  • Efficient quantum information processing requires optimal control of driven quantum systems.
  • A geometric framework for classical systems offers a foundation for quantum system optimization.
  • Nonequilibrium transitions are crucial for quantum computation and information transfer.

Purpose of the Study:

  • To develop a general geometric framework for optimizing average information entropy in driven quantum systems.
  • To minimize entropy production during finite-time transitions in quantum systems.
  • To provide a method for designing efficient quantum information processing protocols.

Main Methods:

  • Extension of a geometric framework from classical to quantum systems.
  • Utilizing geodesics on a parameter manifold with a positive semidefinite metric.
  • Explicit computation of optimal entropy production for a specific quantum system.

Main Results:

  • A general framework for optimizing average information entropy in driven quantum systems was established.
  • Protocols minimizing average information entropy production correspond to geodesics on the parameter manifold.
  • Optimal entropy production was explicitly calculated for a two-state quantum system coupled to a bosonic heat bath.

Conclusions:

  • The developed framework enables the design of efficient quantum information processing protocols.
  • The findings have direct applications in optimizing quantum annealing processes.
  • This work provides a theoretical basis for controlling quantum dynamics to minimize thermodynamic costs.