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Although the Schr{\"o}dinger and Heisenberg pictures are equivalent formulations of quantum mechanics, simulations performed choosing one over the other can greatly impact the computational resources required to solve a problem. Here we demonstrate that in Gaussian boson sampling, a central problem in quantum computing, a good choice of representation can shift the boundary between feasible and infeasible numerical simulability. To achieve this, we introduce a novel method for computing the probability distribution of boson sampling based on the time evolution of tensor networks in the Heisenberg picture. In addition, we overcome limitations of existing methods enabling simulations of realistic setups affected by non-uniform photon losses. Our results demonstrate the effectiveness of the method and its potential to advance quantum computing research., Comment: 6 pages, 2 figures

Conducting precise electronic-vibrational dynamics simulations of molecular systems poses significant challenges when dealing with realistic environments composed of numerous vibrational modes. Here, we introduce a technique for the construction of effective phonon spectral densities that capture accurately open system dynamics over a finite time interval of interest. When combined with existing non-perturbative simulation tools, our approach can reduce significantly the computational costs associated with many-body open system dynamics.

Electron-hole pairs in organic photovoltaics dissociate efficiently despite their Coulomb-binding energy exceeding thermal energy at room temperature. The electronic states involved in charge separation couple to structured vibrational environments containing multiple underdamped modes. The non-perturbative simulations of such large, spatially extended electronic-vibrational (vibronic) systems remains an outstanding challenge. Current methods bypass this difficulty by considering effective one-dimensional Coulomb potentials or unstructured environments. Here we extend and apply a recently developed method for the non-perturbative simulation of open quantum systems to the dynamics of charge separation in one, two and three-dimensional donor-acceptor networks. This allows us to identify the precise conditions in which underdamped vibrational motion induces efficient long-range charge separation. Our analysis provides a comprehensive picture of ultrafast charge separation by showing how different mechanisms driven either by electronic or vibronic couplings are well differentiated for a wide range of driving forces and how entropic effects become apparent in large vibronic systems. These results allow us to quantify the relative importance of electronic and vibronic contributions in organic photovoltaics and provide a toolbox for the design of efficient charge separation pathways in artificial nanostructures.