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Nielsen complexity of coherent spin state operators.
Kunal Pal1, Kuntal Pal1, Tapobrata Sarkar1
1Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India.
Physical Review. E
|July 20, 2022
Summary
We calculated Nielsen
Area of Science:
- Quantum Information Theory
- Quantum Computing
- Quantum Physics
Background:
- Nielsen's circuit complexity quantifies the minimum number of elementary quantum gates required to implement a unitary operation.
- Understanding quantum complexity is crucial for developing efficient quantum algorithms and error correction codes.
- Coherent spin states and their dynamics are fundamental in various quantum systems.
Purpose of the Study:
- To calculate Nielsen's circuit complexity for coherent spin state operators.
- To explore the relationship between quantum complexity, entanglement, and system dynamics.
- To address challenges in complexity calculations for specific quantum models.
Main Methods:
- Utilized the small angle approximation of Euler angle parametrization for SO(3) rotations.
- Extended calculations to arbitrary times for systems with external field couplings and nonlinear interactions.
- Employed Tait-Bryan parametrization to resolve complexity calculation issues for the Lipkin-Meshkov-Glick model.
Main Results:
- Derived an expression for Nielsen's circuit complexity of coherent spin states.
- Demonstrated a connection between Nielsen complexity and squeezing parameters in one-axis twisted Hamiltonians, indicating a link to pairwise entanglement.
- Successfully computed complexity for the Lipkin-Meshkov-Glick model using Tait-Bryan parametrization.
Conclusions:
- Nielsen's circuit complexity provides insights into the structure and dynamics of quantum systems.
- The study establishes a link between circuit complexity and entanglement measures.
- The developed methods offer a pathway for calculating quantum complexity in diverse physical models.
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