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Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems.

Lucas T Brady1,2, Christopher L Baldwin1,2, Aniruddha Bapat1,2

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Quantum annealing (QA) and quantum approximate optimization algorithm (QAOA) effectiveness is clarified. Optimal quantum control reveals that "bang-anneal-bang" protocols, combining pulsed and smooth structures, are generally more effective for quantum optimization.

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Area of Science:

  • Quantum computing
  • Quantum optimization algorithms
  • Theoretical physics

Background:

  • Quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA) are key quantum optimization strategies.
  • The relative effectiveness of QA and QAOA remains an open question in quantum control.
  • Both QA and QAOA are special cases of a broader quantum control problem.

Purpose of the Study:

  • To analytically determine the optimal control strategy for minimizing quantum state energy.
  • To compare the effectiveness of different quantum control protocols, including QA and QAOA.
  • To provide theoretical guidance for experimental quantum optimization implementations.

Main Methods:

  • Application of optimal control theory to a general quantum control problem.
  • Analytical derivation of optimal control structures.
  • Numerical simulations of transverse field Ising models to validate theoretical predictions.

Main Results:

  • Generically, optimal quantum control protocols exhibit a "bang-anneal-bang" structure.
  • This structure combines the pulsed (bang-bang) nature of QAOA at the start and end with a smooth annealing phase in between.
  • Simulations confirm that bang-anneal-bang protocols are frequently optimal for transverse field Ising models.

Conclusions:

  • The study reveals that a hybrid "bang-anneal-bang" approach is often superior to purely pulsed (QAOA) or purely smooth (QA) protocols.
  • Theoretical insights offer practical guidance for designing and implementing more effective quantum optimization algorithms.
  • This work advances the understanding of quantum control for practical quantum computation and optimization.