In this paper [J. Sun, S. Lu and F. Liu, Open Syst. Info. Dyn.23(3) (2016) 1650016], we have studied a general class of adiabatic evolutions in quantum adiabatic search type problem, and found another limitation on it, besides those reported in our early work. In this paper, we extend this study by considering adding an extra driving scheme to the system Hamiltonian of this type of quantum adiabatic evolution. It will be shown that, like the previous study in [J. Sun, S. Lu and F. Liu, Open Syst. Info. Dyn.23(3) (2016) 1650016], the limitation above can also possibly penetrate into the search type quantum-adiabatic computation even by this more general family of system Hamiltonian, which may shed light on what we should have in mind when solving practical problems by means of quantum adiabatic evolution.In this paper [J. Sun, S. Lu and F. Liu, Open Syst. Info. Dyn.23(3) (2016) 1650016], we have studied a general class of adiabatic evolutions in quantum adiabatic search type problem, and found another limitation on it, besides those reported in our early work. In this paper, we extend this study by considering adding an extra driving scheme to the system Hamiltonian of this type of quantum adiabatic evolution. It will be shown that, like the previous study in [J. Sun, S. Lu and F. Liu, Open Syst. Info. Dyn.23(3) (2016) 1650016], the limitation above can also possibly penetrate into the search type quantum-adiabatic computation even by this more general family of system Hamiltonian, which may shed light on what we should have in mind when solving practical problems by means of quantum adiabatic evolution.

International Journal of Quantum InformationMar 1, 20190 citations

Nonlinear Adiabatic Evolution of Quantum Systems

Jie Liu, Sheng-Chang Li, Libin Fu +1 more

Springer eBooksJan 1, 201811 citations

General conditions for quantum adiabatic evolution

D. Comparat

Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the Hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution $[H(ϵt),ϵ\ensuremath{\rightarrow}0]$, are insufficient to describe an evolution driven by the Hamiltonian $H(t)$ itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian $H(t)$ . As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions).Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the Hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution $[H(ϵt),ϵ\ensuremath{\rightarrow}0]$, are insufficient to describe an evolution driven by the Hamiltonian $H(t)$ itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian $H(t)$. As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions).

arXiv:quant-ph/0607118Physical Review AJul 15, 200993 citations

Nonlinear Adiabatic Evolution of Quantum Systems

Jie Liu, Sheng-Chang Li, Libin Fu +1 more

Springer eBooksJan 1, 20181 citation

General conditions for a quantum adiabatic evolution

D. Comparat

Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution (H(epsilon t), epsilon ? 0), are insufficient to describe an evolution driven by the hamiltonian H(t) itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any hamiltonian H(t). As a corollary we demonstrate that the commonly used condition of a slow hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the hamiltonian is real and non oscillating (for instance containing exponential or polynomial but no sinusoidal functions).Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution (H(epsilon t), epsilon ? 0), are insufficient to describe an evolution driven by the hamiltonian H(t) itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any hamiltonian H(t). As a corollary we demonstrate that the commonly used condition of a slow hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the hamiltonian is real and non oscillating (for instance containing exponential or polynomial but no sinusoidal functions).

arXiv:0906.4453Jun 24, 20092 citations

H(t)

itself. Here we derive general criteria and exact bounds, for the state and its phase, ensuring an adiabatic evolution for any Hamiltonian

H(t)

. As a corollary, we demonstrate that the commonly used condition of a slow Hamiltonian variation rate, compared to the spectral gap, is indeed sufficient to ensure adiabaticity but only when the Hamiltonian is real and nonoscillating (for instance, containing exponential or polynomial but no sinusoidal functions).