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Classical mechanics provides a mathematical description of the motion of bodies under the influence of forces. A key principle within this field is the work-energy theorem, which establishes a bridge between the net work done on an object and its kinetic energy.The work-energy theorem states that the net work done on a particle by all the forces acting on it equals the change in its kinetic energy.In simple terms, the work-energy theorem is a method to analyze the effects of forces on an...
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Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.

Shengshi Pang1,2, Andrew N Jordan1,2,3

  • 1Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.

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This study explores quantum metrology for time-dependent Hamiltonians, revealing that optimal control is key. We demonstrate breaking the standard time scaling limits for enhanced precision in quantum measurements.

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Area of Science:

  • Quantum physics
  • Metrology
  • Quantum information science

Background:

  • Quantum metrology typically focuses on time-independent systems.
  • The dynamics of time-dependent Hamiltonians present challenges for quantum metrology.

Purpose of the Study:

  • Investigate quantum metrology for systems with time-dependent Hamiltonians.
  • Determine optimal strategies for enhancing measurement precision.

Main Methods:

  • Derive optimal quantum Fisher information for time-dependent Hamiltonians.
  • Develop optimal Hamiltonian control and measurement schemes.
  • Analyze a qubit in a rotating magnetic field as a model system.

Main Results:

  • Optimal Hamiltonian control is generally necessary for maximizing Fisher information.
  • An adaptive control strategy and measurement scheme are derived.
  • A qubit system demonstrated breaking the standard T^2 scaling limit, achieving T^4 scaling for frequency estimation.

Conclusions:

  • Time-dependent Hamiltonians offer new possibilities for quantum metrology beyond traditional limits.
  • Adaptive Hamiltonian control is crucial for optimizing quantum measurements.
  • Further control is needed to address level crossings in Hamiltonian derivatives.