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Invariant-Parameterized Exact Evolution Operator for SU(2) Systems with Time-Dependent Hamiltonian.

Hiromichi Nakazato1, Alessandro Sergi2,3, Agostino Migliore4

  • 1Department of Physics, Waseda University, Tokyo 169-8555, Japan.

Entropy (Basel, Switzerland)
|January 21, 2023
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Summary
This summary is machine-generated.

Researchers derived an exact formula for the qubit evolution operator under time-dependent magnetic fields. This method utilizes dynamical invariants and offers practical applications in quantum control and simulations.

Keywords:
control fieldgeometric methodsquantum dynamical invariantsqubittime-dependent SU(2) Hamiltonian models

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Area of Science:

  • Quantum mechanics
  • Quantum information science
  • Atomic, molecular, and optical physics

Background:

  • Understanding qubit dynamics is crucial for quantum computing.
  • Controlling qubit evolution in time-dependent fields is experimentally challenging.

Purpose of the Study:

  • To derive an exact, closed-form expression for the qubit evolution operator.
  • To develop a method applicable to arbitrary time-dependent fields, specifically magnetic fields.
  • To demonstrate the utility of the derived method through practical examples.

Main Methods:

  • Utilizing two independent dynamical invariants.
  • Introducing two time-dependent parameters related to SU(2) symmetry.
  • Constructing the explicit expression for the evolution operator U(t).

Main Results:

  • An exact, closed-form expression for the qubit evolution operator U(t) was obtained.
  • The method successfully solves the quantum dynamics of a qubit in a controllable time-dependent field.
  • The approach is validated for laboratory-realizable experimental conditions.

Conclusions:

  • The derived method provides a powerful tool for analyzing and controlling qubit dynamics.
  • The approach has broad applicability to SU(2) models and realistic physical systems.
  • This work facilitates advancements in quantum control and simulation.