For ergodic adiabatic quantum systems, we study the evolution of energy distribution as the system evolves in time. Starting from the von Neumann equation for the density operator, we obtain the quantum analogue of the Smoluchowski equation on coarse-graining over the energy spectrum. This result brings out the precise notion of quantum diffusion. 1 There are many physical situations where a separation of time scales occurs, the adiabatic approximation to an evolution is one of the expressions of such a separation [1]. Classically, an important problem in this context is to describe the evolution in phase space of an ensemble of systems under an ergodic adiabatic Hamiltonian [2]. An ergodic adiabatic Hamiltonian can be defined as one which describes ergodic (usually specialized to chaotic) dynamics under a slowly time-dependent Hamiltonian. In this paper, we study the quantal version of this treatment and obtain results which, in anFor ergodic adiabatic quantum systems, we study the evolution of energy distribution as the system evolves in time. Starting from the von Neumann equation for the density operator, we obtain the quantum analogue of the Smoluchowski equation on coarse-graining over the energy spectrum. This result brings out the precise notion of quantum diffusion. 1 There are many physical situations where a separation of time scales occurs, the adiabatic approximation to an evolution is one of the expressions of such a separation [1]. Classically, an important problem in this context is to describe the evolution in phase space of an ensemble of systems under an ergodic adiabatic Hamiltonian [2]. An ergodic adiabatic Hamiltonian can be defined as one which describes ergodic (usually specialized to chaotic) dynamics under a slowly time-dependent Hamiltonian. In this paper, we study the quantal version of this treatment and obtain results which, in an

Jan 1, 19984 citations

Accelerated adiabatic quantum search algorithm via pulse control in a non-Markovian environment

Feng-Hua Ren, Zhao-Ming Wang, Lian-Ao Wu

Adiabatic quantum computation requires that the system remains in its ground state. However, an adiabatic process often loses partly or entirely its quantumness, such as entanglement in its long runtime, due to the system-environment interactions. Here we put forward an effective quantum control technique to realize the adiabatic quantum search algorithm in a nonadiabatic regime and in the presence of environment. Using the non-Markovian quantum state diffusion equation approach, we numerically study the system dynamics characterized by the success probability. The results show that the probability increases with decreasing coupling strength and temperature. In particular, non-Markovianity from the environment can help to enhance the success probability. By choosing a suitable pulse intensity and period, a high success probability can be obtained in a short runtime for weak system-bath coupling, low temperature, and strong non-Markovian heat baths.Adiabatic quantum computation requires that the system remains in its ground state. However, an adiabatic process often loses partly or entirely its quantumness, such as entanglement in its long runtime, due to the system-environment interactions. Here we put forward an effective quantum control technique to realize the adiabatic quantum search algorithm in a nonadiabatic regime and in the presence of environment. Using the non-Markovian quantum state diffusion equation approach, we numerically study the system dynamics characterized by the success probability. The results show that the probability increases with decreasing coupling strength and temperature. In particular, non-Markovianity from the environment can help to enhance the success probability. By choosing a suitable pulse intensity and period, a high success probability can be obtained in a short runtime for weak system-bath coupling, low temperature, and strong non-Markovian heat baths.

Physical Review ADec 4, 202018 citations

Nonlinear Adiabatic Evolution of Quantum Systems

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

Springer eBooksJan 1, 201811 citations

Non-Markovian response of complex quantum systems

S. V. Radionov

We study the perturbative response of a complex quantum system on time changes of an external parameter $X$ . The driven dynamics is treated in adiabatic basis of the system's Hamiltonian $\hat{H}[X]$ . Within a random matrix approach we obtained non--Markovian Fokker--Planck equation for the occupancy of given adiabatic state. We observed normal diffusion regime of the driven quantum dynamics at quite small values of the memory time defined by the time scales of the $X$ --correlations and energy--distribution of the coupling matrix elements $(\partial \hat{H}/\partial X)_{nm}$ . Here the normal energy diffusion was found to drop out with the width of the matrix elements' energy--distribution and the diffusion may be significantly suppressed with the decrease of the correlations between the matrix elements. In the opposite limit of relatively large memory times we obtained ballistic regime of the dynamics.We study the perturbative response of a complex quantum system on time changes of an external parameter $X$. The driven dynamics is treated in adiabatic basis of the system's Hamiltonian $\hat{H}[X]$. Within a random matrix approach we obtained non--Markovian Fokker--Planck equation for the occupancy of given adiabatic state. We observed normal diffusion regime of the driven quantum dynamics at quite small values of the memory time defined by the time scales of the $X$--correlations and energy--distribution of the coupling matrix elements $(\partial \hat{H}/\partial X)_{nm}$. Here the normal energy diffusion was found to drop out with the width of the matrix elements' energy--distribution and the diffusion may be significantly suppressed with the decrease of the correlations between the matrix elements. In the opposite limit of relatively large memory times we obtained ballistic regime of the dynamics.

arXiv:1911.01820Nov 4, 20190 citations

We study the perturbative response of a complex quantum system on time changes of an external parameter

X

. The driven dynamics is treated in adiabatic basis of the system's Hamiltonian

\hat{H}[X]

. Within a random matrix approach we obtained non--Markovian Fokker--Planck equation for the occupancy of given adiabatic state. We observed normal diffusion regime of the driven quantum dynamics at quite small values of the memory time defined by the time scales of the

X

--correlations and energy--distribution of the coupling matrix elements

(\partial \hat{H}/\partial X)_{nm}

. Here the normal energy diffusion was found to drop out with the width of the matrix elements' energy--distribution and the diffusion may be significantly suppressed with the decrease of the correlations between the matrix elements. In the opposite limit of relatively large memory times we obtained ballistic regime of the dynamics.