Constructions of Optimal-Speed Quantum Evolutions: A Comparative Study ...
We present a comparative analysis of two different constructions of optimal-speed quantum Hamiltonian evolutions on the Bloch sphere. In the first approach (Mostafazadeh's approach), the evolution is specified by a traceless stationary Hermitian Hamiltonian and occurs between two arbitrary qubi...
| Main Authors: | , , |
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| Format: | Text |
| Language: | unknown |
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arXiv
2024
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| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.2405.08144 https://arxiv.org/abs/2405.08144 |
| Summary: | We present a comparative analysis of two different constructions of optimal-speed quantum Hamiltonian evolutions on the Bloch sphere. In the first approach (Mostafazadeh's approach), the evolution is specified by a traceless stationary Hermitian Hamiltonian and occurs between two arbitrary qubit states by maximizing the energy uncertainty. In the second approach (Bender's approach), instead, the evolution is characterized by a stationary Hermitian Hamiltonian which is not traceless and occurs between an initial qubit state on the north pole and an arbitrary final qubit state. In this second approach, the evolution occurs by minimizing the evolution time subject to the constraint that the difference between the largest and the smallest eigenvalues of the Hamiltonian is kept fixed. For both approaches we calculate explicitly the optimal Hamiltonian, the optimal unitary evolution operator and, finally, the optimal magnetic field configuration. Furthermore, we show in a clear way that Mostafazadeh's and Bender's ... : 18 pages, 2 figures, 1 table ... |
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