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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Dynamics

Background:

  • Characterizing open quantum systems is crucial for quantum technologies.
  • Determining steady states of quantum dynamics presents significant computational challenges.
  • Existing variational quantum approaches face limitations in solving for steady states.

Purpose of the Study:

  • To develop a quantum-assisted algorithm for efficiently determining steady states of open quantum systems.
  • To address limitations associated with variational quantum methods in solving Lindblad dynamics.
  • To enable the estimation of steady states for higher-dimensional quantum systems.

Main Methods:

  • Reformulation of finding fixed points in Lindblad dynamics as a feasibility semidefinite program.
  • Development of a hybrid quantum-classical algorithm.
  • Demonstration on higher-dimensional open quantum systems.

Main Results:

  • The proposed algorithm successfully estimates steady states of open quantum systems.
  • The method bypasses known issues encountered with variational quantum approaches.
  • The algorithm demonstrates capability in handling higher-dimensional systems.
  • The approach can identify multiple steady states in systems exhibiting symmetries.

Conclusions:

  • The quantum-assisted semidefinite programming approach offers a robust method for finding steady states in open quantum systems.
  • This hybrid algorithm enhances the scalability and applicability of quantum methods in studying complex quantum dynamics.
  • The ability to find multiple steady states opens new avenues for exploring quantum system symmetries.