Polynomial-time solution for the #P problem based on classical electronic circuits

Abstract

The #P problem is believed to be intractable using classical computers due to difficulties presented by exponential time. It is generally assumed that the best way to solve this problem is to use an algorithm based on quantum mechanics. Here, we propose and demonstrate experimentally an alternative way to solve the #P problem by implementing classical electronic circuits. The typical #P problem to calculate the permanent of a matrix and the related boson sampling problem are solved in polynomial time with exponential frequency bandwidth which limits the scalability of the scheme. The running time of our scheme to solve these problems is equivalent to those based on quantum mechanics. It is also important that our method has good stability of classical circuits. Thus, our findings are advantageous for information processing in the era of big data.