A density matrix evolution(DME) method to simulate the dynamics of quantum systems embedded in a classical environment is presented. The method is applicable when the quantum dynamical degrees of freedom can be described in a Hilbert space of limited dimensionality. The method is applied to the case of proton-transfer reactions in a fluctuating double-well potential [details are given in the following paper in this issue] and compared to other analytical and numerical solutions. The embedding of the quantum system within the classical system by using consistent equations of motion for the classical system with-proper conservation properties is discussed and applied to the one-dimensional collision of a classical particle with a quantum oscillator.
The simulation of non-equil. electron dynamics in real systems provides a challenge for theor. methods due to the need to treat both large system sizes and electron correlation. Towards this goal, we present an extension of the d. matrix embedding theory (DMET) for the simulation of real-time electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. The dynamics of the coupled impurity and bath embedding problem are obtained through use of the time-dependent variational principle. The methodol. allows for the efficient and accurate simulation of non-equil. electron dynamics in the presence of strong correlation, reaching total system sizes unobtainable by conventional methodol.
In the study of open quantum systems, one typically obtains the decoherence dynamics by solving a master equation. The master equation is derived using knowledge of some basic properties of the system, the environment, and their interaction: One basically needs to know the operators through which the system couples to the environment and the spectral density of the environment. For a large system, it could become prohibitively difficult to even write down the appropriate master equation, let alone solve it on a classical computer. In this paper, we present a quantum algorithm for simulating the dynamics of an open quantum system. On a quantum computer, the environment can be simulated using ancilla qubits with properly chosen single-qubit frequencies and with properly designed coupling to the system qubits. The parameters used in the simulation are easily derived from the parameters of the system
+ environment Hamiltonian. The algorithm is designed to simulate Markovian dynamics, but it can also be used to simulate non-Markovian dynamics provided that this dynamics can be obtained by embedding the system of interest into a larger system that obeys Markovian dynamics. We estimate the resource requirements for the algorithm. In particular, we show that for sufficiently slow decoherence a single ancilla qubit could be sufficient to represent the entire environment, in principle.