The Multiphoton Boson Sampling Machine Doesn't Beat Early Classical Computers for Five-boson Sampling

TL;DR

The paper demonstrates that a classical algorithm outperforms a five-boson quantum sampling machine, indicating that current multiphoton boson sampling devices do not surpass early classical computers in this task.

Contribution

It introduces the Store-zechin algorithm, which efficiently computes matrix permanents and shows classical methods outperform quantum boson sampling for small cases.

Findings

Store-zechin algorithm has fewer operations than Ryser's algorithm.

Classical computation of five-boson sampling is faster than quantum sampling on early devices.

Quantum boson sampling does not outperform early classical computers for five bosons.

Abstract

A new algorithm which is called Store-zechin, and utilizes stored data repetitively for calculating the permanent of an n * n matrix is proposed. The analysis manifests that the numbers of multiplications and additions taken by the new algorithm are respectively far smaller than those taken by the famous Ryser algorithm. Especially, for a 5-boson sampling task, the running time of the Store-zechin algorithm computing the correspondent permanent on ENIAC as well as TRADIC is lower than that of the sampling operation on a multiphoton boson sampling machine (shortly MPBSM), and thus MPBSM does not beat the early classical computers (despite of this, it is possible that when n gets large enough, a quantum boson sampling machine will beat a classical computer). On a computer, people can design an algorithm that exchanges space for time while on MPBSM, people can not do so, which is the greatest difference between a universal computer and MPBSM. This difference is right the reason why MPBSM may not be called a (photonic) quantum computer.