Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Abstract

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

Quantum trajectory theory of few-photon cavity-QED systems with a time-delayed coherent feedback

“…When limited to the linear regime, results can be computed analytically but this significantly restricts the phenomena that can be investigated [1,3,59,60]. A popular method for modelling coherent feedback is matrix product states (MPSs) [21,26,34,52,[61][62][63][64], a powerful technique where tensor networks are used to limit the entanglement within the Hilbert space. Quantum trajectory (QT) theory is a less popular technique which has also recently been used to investigate the effects of a time-delayed coherent feedback [28,31,34].…”

Modelling quantum light-matter interactions in waveguide-QED with retardation and a time-delayed feedback: matrix product states versus a space-discretized waveguide model

“…Although we find that the approximation to two photons is highly accurate for the results presented in this paper, the presence of more photons can become important in other cases, giving the opportunity to describe more complex systems in future work, e.g. three quantum emitters (TLSs) in a waveguide [100] (where the side atoms can behave like mirrors in cavity QED [101]), a higher number of qubits [102,103], and 1D atomic arrays [104,105].…”

Sampling asymmetric open quantum systems for artificial neural networks

“…In this Letter, we demonstrate that commonly applied sampling techniques are highly unfavorable for the training of RBMs representing asymmetric open quantum systems, i.e., systems without symmetries of translational [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. First, we provide converging results for a symmetric scenario and further improve computational efficiency by proposing an adjustment to the default Metropolis sampling approach.…”

“…An isotropic Heisenberg chain featuring N sites, next-neighbor coupling and open boundary conditions is subject to both incoherent dissipation and driving on all sites. The corresponding Hamiltonian is given by [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]…”