Recent Theoretical and Experimental Progress on Boson Sampling

Boson sampling is a restricted model of quantum computation, designed to achieve quantum advantage using nonuniversal quantum systems. By harnessing the quantum interference of indistinguishable bosons (typically photons), it becomes possible to sample from a probability distribution, which is intractable for classical computers. This paper reviews the theoretical foundations of boson sampling and its variations, including Fock-state, scattershot, and Gaussian boson sampling, along with significant experimental progress, from early small-scale demonstrations to large-scale quantum supremacy claims. We further explore classical algorithms for simulating boson sampling, which are crucial for bench- marking the performance of experimental results. Finally we examine potential applications of boson sampling in various fields, including simulation of molecular vibronic spectra in quantum chemistry, and solution of graph-based problems in optimization. These applications demonstrate the wide-ranging impact that boson sampling could have on industries that rely on complex computational models, making it a promising quantum technology for near-term applications.