Our paper “Proposal for Quantum Simulation via All-Optically-Generated Tensor Network States” is now published in PRL. (Phys. Rev. Lett. 120, 130501 | arXiv:1710.06103). This paper combines ideas from my two main research interests: quantum optics and tensor networks. Here is an accessible (to a quantum optics audience) summary of the paper:
General quantum states possess a complex entanglement structure that makes their description on a classical computer inefficient. That is, the computational effort for simulating their properties can grow exponentially with the number of subsystems. This is typically because of large entanglement in the system. However, in a wide variety of important states, including the ground and thermal states of local Hamiltonians, the entanglement and correlations are typically more limited as they satisfy area laws. Such states can be approximated well in terms of tensor network (TN) states parametrisation, in which only a polynomial, in the number of subsystems, number of parameters is required to describe the state. Although TNs in one dimension can be efficiently manipulated on a classical computer, the treatment of TN states in higher spatial dimensions remains challenging because the computational effort grows rapidly in the number of subsystems and bond dimension. Therefore, the experimental generation of TN states and their use for quantum simulation is of considerable interest. Furthermore, the generation of TNs is important as they include important resource states for quantum communication, teleportation and metrology. In our work, we propose an all-optical scheme for the generation of TN states in one and higher dimensions. Our scheme exploits well established parametric down-conversion methods to build entanglement in the generated state. The scheme also promises robustness against loss and mode mismatch and can be realised with current and near-future optical technology.