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Completely positive approximate solutions of driven open quantum systems.

Farhang Haddadfarshi1, Jian Cui1, Florian Mintert1

  • 1Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universität, Albertstraße 19, 79104 Freiburg, Germany, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom.

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We developed a new approximation for quantum systems that ensures accuracy in simulations and control. This method guarantees complete positivity, a crucial property for reliable quantum computing applications.

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Area of Science:

  • Quantum Mechanics
  • Quantum Information Science
  • Computational Physics

Background:

  • Lindblad master equations describe open quantum systems.
  • Time-dependent generators pose challenges for accurate quantum simulations.
  • Complete positivity is a fundamental requirement for physical quantum evolutions.

Purpose of the Study:

  • To introduce a novel perturbative approximation for Lindblad master equations with time-dependent generators.
  • To ensure the proposed approximation satisfies complete positivity.
  • To demonstrate the accuracy improvements gained by enforcing complete positivity.

Main Methods:

  • Definition of a perturbative approximation tailored for time-dependent generators.
  • Mathematical formulation ensuring the preservation of complete positivity.
  • Application to explicit examples to validate the approximation's performance.

Main Results:

  • A new perturbative approximation for Lindblad master equations was successfully defined.
  • The approximation inherently satisfies the property of complete positivity.
  • Significant improvements in accuracy were observed compared to standard perturbative methods when complete positivity is ensured.

Conclusions:

  • The developed perturbative approximation offers a reliable approach for quantum simulations and optimal control.
  • Enforcing complete positivity is critical for enhancing the accuracy of perturbative solutions.
  • This work provides a valuable tool for advancing quantum technologies.