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Perturbative framework for engineering arbitrary Floquet Hamiltonian.

Yingdan Xu1, Lingzhen Guo1,2

  • 1Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300072, People's Republic of China.

Reports on Progress in Physics. Physical Society (Great Britain)
|January 30, 2025
PubMed
Summary
This summary is machine-generated.

We present a new perturbative framework to engineer target Hamiltonians in periodically driven quantum systems. This method corrects errors and creates specific quantum states for advanced quantum computation.

Keywords:
Floquet engineeringMagnus expansionbosonic codesquantum control

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Area of Science:

  • Quantum Physics
  • Quantum Computing
  • Theoretical Physics

Background:

  • Periodically driven quantum systems offer unique control over Hamiltonians.
  • Engineering precise Hamiltonians is crucial for quantum computation.
  • Floquet engineering allows manipulation of system properties through driving.

Purpose of the Study:

  • To develop a systematic perturbative framework for engineering arbitrary target Hamiltonians in Floquet phase space.
  • To mitigate high-order errors in engineered Floquet Hamiltonians.
  • To enable the creation of specific quantum states for fault-tolerant quantum computation.

Main Methods:

  • Utilizing Floquet-Magnus expansion for theoretical analysis.
  • Employing a perturbative approach to add high-order driving potentials.
  • Introducing a transformation method for analytical expressions of correction drives.
  • Developing a numerically efficient procedure for calculating high-order correction drives.

Main Results:

  • A systematic framework for engineering target Hamiltonians in Floquet phase space.
  • Mitigation of high-order errors in the engineered Floquet Hamiltonian.
  • Analytical expression for the leading-order correction drive for Hamiltonians with discrete symmetries.
  • Numerical procedure to engineer target Hamiltonians with degenerate eigenstates, including multi-component cat states.

Conclusions:

  • The developed framework provides a robust method for precise Floquet engineering.
  • The approach is applicable to creating complex quantum states relevant for quantum computation.
  • This work advances the capabilities for designing quantum systems with desired properties.