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We devise a numerical scheme for the time evolution of matrix product operators by adapting the time-dependent variational principle for matrix product states [J. Haegeman et al, Phys. Rev. B 94, 165116 (2016)]. A simple augmentation of the initial operator $mathcal{O}$ by the Hamiltonian $H$ helps to conserve the average energy $mathrm{tr}[H mathcal{O}(t)]$ in the numerical scheme and increases the overall precision. As demonstration, we apply the improved method to a random operator on a small one-dimensional lattice, using the spin-1 Heisenberg XXZ model Hamiltonian; we observe that the augmentation reduces the trace-distance to the numerically exact time-evolved operator by a factor of 10, at the same computational cost.
Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. I
Matrix Product States form the basis of powerful simulation methods for ground state problems in one dimension. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the area law. In this work, we
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced by F. Verstraete et al. in 2005 and characterize the tensors corresponding to the fixe
Any quantum process is represented by a sequence of quantum channels. We consider ergodic processes, obtained by sampling channel valued random variables along the trajectories of an ergodic dynamical system. Examples of such processes include the ef
Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial dimension. U