Abstract: Matrix Product States (MPS) and Matrix Product Operators (MPO) are tensor network frameworks for efficiently representing and manipulating quantum many-body systems, particularly in one-dimensional settings. Originally developed in condensed matter physics, MPS provide a compact description of quantum states with limited entanglement, while MPO enable efficient representation of operators such as Hamiltonians and density matrices. These techniques are widely used in numerical methods like the Density Matrix Renormalization Group (DMRG) and are increasingly applied in quantum computing and quantum information science to study entanglement properties, simulate open quantum systems, and optimize variational algorithms.
One key application in quantum optics is the simulation of noisy Gaussian Boson Sampling (GBS). GBS is a variant of boson sampling which uses squeezed light to encode input states. It shows a great capacity to demonstrate quantum advantage in optical systems which has motivated the search for real-world applications of this non-universal model of quantum computing, e.g. dense graph searching, molecular vibronic spectra calculations and molecular docking. However, it is currently being plagued by experimental imperfections such as photon loss, partial distinguishability of photons, phase instability and many more. So far, these imperfections have inspired a number of classical algorithms which use these to simulate the results of noisy Gaussian boson sampling efficiently, some of the most popular ones based on MPO.
First, this talk will introduce the general framework of computing with tensor networks, more specifically with MPS and MPO. After that it will continue by introducing GBS and presenting some results of studying the phase noisy GBS system using MPO algorithm.