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Floquet adiabatic evolution offers a more efficient quantum computing approach for optimization problems. This method significantly reduces gate counts, enabling optimal solutions for problems like Max-Cut on quantum computers.

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Area of Science:

  • Quantum Mechanics
  • Computational Science
  • Optimization Algorithms

Background:

  • The adiabatic theorem of quantum mechanics states that a system in its ground state remains in the ground state under slow Hamiltonian changes.
  • Adiabatic quantum computation principles can solve complex problems but often require large gate counts on digital quantum computers due to Trotter step scaling.

Purpose of the Study:

  • To investigate a novel approach, Floquet adiabatic evolution, for efficiently implementing adiabatic dynamics on digital quantum computers.
  • To demonstrate the effectiveness of Floquet adiabatic evolution for solving classical optimization problems, specifically the Max-Cut problem.

Main Methods:

  • Proposed Floquet adiabatic evolution, utilizing a fixed, finite Trotter step for adiabatic dynamics.
  • Employed matrix-product-state simulations to provide numerical evidence for the method's efficacy.
  • Tested the approach on the Max-Cut problem for 3-regular graphs.

Main Results:

  • Floquet adiabatic evolution significantly reduces gate counts by several orders of magnitude compared to continuous-time adiabatic evolution.
  • Numerical simulations show optimal solutions for the Max-Cut problem on 3-regular graphs with low runtime and bond dimensions.
  • Resource estimation suggests potential for quantum computers to outperform classical solvers for this problem.

Conclusions:

  • Floquet adiabatic evolution presents a computationally efficient alternative for adiabatic quantum computation.
  • This method shows promise for solving hard optimization problems like Max-Cut on near-term quantum devices.