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Quantum annealing can prepare ground states faster than previously thought. This study derives lower bounds for quantum annealing time, proving optimal scaling for fast schedules and highlighting quantum coherence as a key resource.

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Area of Science:

  • Quantum Computing
  • Quantum Annealing
  • Theoretical Physics

Background:

  • The adiabatic theorem offers guidelines for preparing ground states in quantum systems.
  • Faster quantum annealing protocols exist but lack rigorous theoretical bounds outside the adiabatic regime.

Purpose of the Study:

  • To derive rigorous lower bounds on the time required for successful quantum annealing.
  • To demonstrate the optimality of known fast annealing schedules.
  • To identify the role of quantum coherence in rapid annealing.

Main Methods:

  • Derivation of analytical lower bounds for quantum annealing time.
  • Analysis of specific models including the Roland and Cerf unstructured search, Hamming spike, and p-spin models.
  • Asymptotic analysis of annealing schedules.

Main Results:

  • Established rigorous lower bounds on quantum annealing time.
  • Demonstrated that the derived bounds are asymptotically saturated by known fast annealing schedules, proving their optimal scaling.
  • Showcased that rapid annealing necessitates coherent superpositions of energy eigenstates.

Conclusions:

  • The derived bounds provide a theoretical foundation for understanding the limits of quantum annealing speed.
  • Fast quantum annealing schedules for specific problems exhibit optimal time scaling.
  • Quantum coherence is identified as an essential computational resource for achieving rapid quantum annealing.