A classical sampling algorithm for Gaussian boson sampling decomposes Hafnians into smaller Hafnians and permanents, enabling simulation of 18-30 photons and lowering the estimated quantum-supremacy threshold.
A detailed study of Gaussian Boson Sampling
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abstract
Since the development of Boson sampling, there has been a quest to construct more efficient and experimentally feasible protocols to test the computational complexity of sampling from photonic states. In this paper we interpret and extend the results presented in [Phys. Rev. Lett. 119, 170501 (2017)]. We derive an expression that relates the probability to measure a specific photon output pattern from a Gaussian state to the \textit{hafnian} matrix function and us it to design a Gaussian Boson sampling protocol. Then, we discuss the advantages that this protocol has relative to other photonic protocols and the experimental requirements for Gaussian Boson Sampling. Finally, we relate it to the previously most general protocol, Scattershot Boson Sampling [Phys. Rev. Lett. 113, 100502 (2014)]
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Speedup in Classical Simulation of Gaussian Boson Sampling
A classical sampling algorithm for Gaussian boson sampling decomposes Hafnians into smaller Hafnians and permanents, enabling simulation of 18-30 photons and lowering the estimated quantum-supremacy threshold.