Hierarchy in Sampling Gaussian-correlated Bosons
Joonsuk Huh, Man‐Hong Yung · arXiv (Cornell University) · 2016
Boson Sampling represents a class of physical processes potentially intractable for classical devices to simulate. The Gaussian extension of Boson Sampling remains a computationally hard problem, where the input state is a product of uncorrelated Gaussian modes. Besides, motivated by molecular spectroscopy, Vibronic Boson Sampling involves operations that can generate Gaussian correlation among different Boson modes. Therefore, Gaussian Boson Sampling is a special case of Vibronic Boson Sampling. However, this does not necessarily mean that Vibronic Boson Sampling is more complex than Gaussian Boson Sampling. Here we develop a hierarchical structure to show how the initial correlation in Vibronic Boson Sampling can be absorbed in Gaussian Boson Sampling with ancillary modes and in a scattershot fashion. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes.