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We consider the dynamics $tmapstotau_t$ of an infinite quantum lattice system that is generated by a local interaction. If the interaction decomposes into a finite number of terms that are themselves local interactions, we show that $tau_t$ can be efficiently approximated by a product of $n$ automorphisms, each of them being an alternating product generated by the individual terms. For any integer $m$, we construct a product formula (in the spirit of Trotter) such that the approximation error scales as $n^{-m}$. We do so in the strong topology of the operator algebra, namely by approximating $tau_t(O)$ for sufficiently localized observables $O$.
An approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by Hudson- Parthasarathy quantum stochastic differential equations, aiming to reduce the computational burden associated with on
In this paper a general definition of quantum conditional entropy for infinite-dimensional systems is given based on recent work of Holevo and Shirokov arXiv:1004.2495 devoted to quantum mutual and coherent informations in the infinite-dimensional ca
The Trotter-Suzuki decomposition is an important tool for the simulation and control of physical systems. We provide evidence for the stability of the Trotter-Suzuki decomposition. We model the error in the decomposition and determine sufficiency con
Generically, spectral statistics of spinless systems with time reversal invariance (TRI) and chaotic dynamics are well described by the Gaussian Orthogonal ensemble (GOE). However, if an additional symmetry is present, the spectrum can be split into
We present a general construction of matrix product states for stationary density matrices of one-dimensional quantum spin systems kept out of equilibrium through boundary Lindblad dynamics. As an application we review the isotropic Heisenberg quantu