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It is known that the Frenet-Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves.
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R. A. Bertlmann and P. Krammer, Bloch vectors for qudits , J. Phys. A: Math. Theor. 41
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D. C. Brody and Eva-Marie Graefe, Information geometry of complex Hamiltonians and exceptional points , Entropy 15
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F. Campaioli, W. Sloan, K. Modi, and F. A. Pollock, Algorithm for solving unconstrained unitary quantum brachistochrone problems , Phys. Rev. A100
2019
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C. Cafaro, S. Ray, and P. M. Alsing, Geometric aspects of analog quantum search evolutions , Phys. Rev. A102
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E. R. Loubenets and C. Kading, Specifying the unitary evolution of a qudit for a general nonstationary Hamiltonian via the generalized Gell-Mann representation , Entropy 22
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2021
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Kh. P. Gnatenko, H. P. Laba, and V. M. Tkachuk, Geometric properties of evolutionary graph states and their detection on a quantum computer , Phys. Lett. A452
2022
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C. Cafaro and P. M. Alsing, Complexity of pure and mixed qubit geodesic paths on curved manifolds , Phys. Rev. D106
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C. Cafaro, S. Ray, and P. M. Alsing, Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions , Phys. Rev. E105
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C. Cafaro and P. M. Alsing, Qubit geodesics on the Bloch sphere from optimal-speed Hamiltonian evolutions , Class. Quantum Grav. 40
2023
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P. M. Alsing, C. Cafaro, O. Luongo, C. Lupo, S. Mancini, and H. Quevedo, Comparing metrics for mixed quantum states: Sjöqvist and Bures , Phys. Rev. A107
2023
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P. M. Alsing and C. Cafaro, From the classical Frenet-Serret apparatus to the curvature and torsion of quantum-mechanical evolutions. Part II. Nonstationary Hamiltonians , arXiv:quant-ph/2311.18463 (2023)
2023
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A. S. Magalhaes de Castro, R. Grimaudo, D. Valenti, A. Migliore, H. Nakazato, and A. Messina, Analytically solvable Hamiltonian in invariant subspaces , Eur. Phys. J. Plus 138
2023
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